Tamilnadu Board Maths Question papers for 12th Standard EM (English Medium) Question paper & Study Materials

12th Standard Maths English Medium Model 5 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Solve: \(\frac { 2 }{ x } +\frac { 3 }{ y } +\frac { 10 }{ z } =4,\frac { 4 }{ x } -\frac { 6 }{ y } +\frac { 5 }{ z } =1,\frac { 6 }{ x } +\frac { 9 }{ y } -\frac { 20 }{ z } \)=2

  • 2)

    Verify that arg(1+i) + arg(1-i) = arg[(1+i) (1-i)]

  • 3)

    If a, b, c, d and p are distinct non-zero real numbers such that (a2+b2+c2) p2-2 (ab+bc+cd) p+(b2+c2+d2)≤ 0 the n. Prove that a,b,c,d are in G.P and ad=bc

  • 4)

    If \({ tan }^{ -1 }\left( \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right) =a\) than prove that x2=sin2a

  • 5)

    A kho-kho player In a practice Ion while running realises that the sum of tne distances from the two kho-kho poles from him is always 8m. Find the equation of the path traced by him of the distance between the poles is 6m.

12th Standard Maths English Medium Model 5 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 4 & 3 \\ 2 & 5 \end{matrix} \right] \), find x and y such that A2 + xA + yI2 = O2. Hence, find A-1.

  • 2)

    The prices of three commodities A, B and C are Rs.x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C . Person Q purchases 2 units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C . In the process, P, Q and R earn Rs.15,000, Rs.1,000 and Rs.4,000 respectively. Find the prices per unit of A, B and C . (Use matrix inversion method to solve the problem.)

  • 3)

    If ax2 + bx + c is divided by x + 3, x − 5, and x − 1, the remainders are 21,61 and 9 respectively. Find a,b and c. (Use Gaussian elimination method.)

  • 4)

    Investigate for what values of λ and μ the system of linear equations
    x + 2y + z = 7, x + y + λz = μ, x + 3y − 5z = 5 has
    (i) no solution
    (ii) a unique solution
    (iii) an infinite number of solutions

  • 5)

    If the system of equations px + by + cz = 0, ax + qy + cz = 0, ax + by + rz = 0 has a non-trivial solution and p ≠ a,q ≠ b,r ≠ c, prove that \(\frac { p }{ p-a } +\frac { q }{ q-b } +\frac { r }{ r-c } =2\).

12th Standard Maths English Medium Sample 5 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    For what value of λ, the system of equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ2 is consistent.

  • 2)

    Verify that arg(1+i) + arg(1-i) = arg[(1+i) (1-i)]

  • 3)

    If c ≠ 0 and \(\frac { p }{ 2x } =\frac { a }{ x+x } +\frac { b }{ x-c } \) has two equal roots, then find p. 

  • 4)

    Simplify \({ sin }^{ -1 }\left( \cfrac { sinx+cosx }{ \sqrt { 2 } } \right) ,\cfrac { \pi }{ 4 } <x<\cfrac { \pi }{ 4 } \)
     

  • 5)

    A kho-kho player In a practice Ion while running realises that the sum of tne distances from the two kho-kho poles from him is always 8m. Find the equation of the path traced by him of the distance between the poles is 6m.

12th Standard Maths English Medium Sample 5 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\frac { 1 }{ 7 } \left[ \begin{matrix} 6 & -3 & a \\ b & -2 & 6 \\ 2 & c & 3 \end{matrix} \right] \) is orthogonal, find a, b and c , and hence A−1.

  • 2)

    In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 ball left to go in the last over. The last ball was bowled and the batsman at the crease hit it high up. The ball traversed along a path in a vertical plane and the equation of the path is y = ax2 + bx + c with respect to a xy-coordinate system in the vertical plane and the ball traversed through the points (10, 8), (20, 16) (30, 18) can you conclude that Chennai Super Kings won the match?
    Justify your answer. (All distances are measured in metres and the meeting point of the plane of the path with the farthest boundary line is (70, 0).)

  • 3)

    Test for consistency of the following system of linear equations and if possible solve:
    4x − 2y + 6z = 8, x + y − 3z = −1, 15x − 3y + 9z = 21.

  • 4)

    Investigate the values of λ and μ the system of linear equations 2x + 3y + 5z = 9, 7x + 3y - 5z = 8, 2x + 3y + λz = μ, have
    (i) no solution
    (ii) a unique solution
    (iii) an infinite number of solutions.

  • 5)

    Find the inverse of each of the following by Gauss-Jordan method:
    \(\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 5 & 3 \\ 1 & 0 & 8 \end{matrix} \right] \)

12th Standard Maths English Medium Important 5 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    For what value of λ, the system of equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ2 is consistent.

  • 2)

    Find all the roots \((2-2i)^{ \frac { 1 }{ 3 } }\) and also find the product of its roots.

  • 3)

    If c ≠ 0 and \(\frac { p }{ 2x } =\frac { a }{ x+x } +\frac { b }{ x-c } \) has two equal roots, then find p. 

  • 4)

    Simplify \({ sin }^{ -1 }\left( \cfrac { sinx+cosx }{ \sqrt { 2 } } \right) ,\cfrac { \pi }{ 4 } <x<\cfrac { \pi }{ 4 } \)
     

  • 5)

    The foci of a hyperbola coincides with the foci of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\). Find the equation of the hyperbola if its eccentricity is 2.

12th Standard Maths English Medium Important 5 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A2 - 3A - 7I2 = O2. Hence find A−1.

  • 2)

    The prices of three commodities A, B and C are Rs.x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C . Person Q purchases 2 units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C . In the process, P, Q and R earn Rs.15,000, Rs.1,000 and Rs.4,000 respectively. Find the prices per unit of A, B and C . (Use matrix inversion method to solve the problem.)

  • 3)

    A boy is walking along the path y = ax2 + bx + c through the points (−6, 8),(−2, −12) , and (3, 8) . He wants to meet his friend at P(7,60) . Will he meet his friend? (Use Gaussian elimination method.)

  • 4)

    Find the value of k for which the equations kx - 2y + z = 1, x - 2ky + z = -2, x - 2y + kz = 1 have
    (i) no solution
    (ii) unique solution
    (iii) infinitely many solution

  • 5)

    Solve the following system of homogenous equations.
    3x + 2y + 7z = 0, 4x − 3y − 2z = 0,5x + 9y + 23z = 0

12th Standard Maths English Medium Model 3 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Verify that (A-1)T = (AT)-1 for A=\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

  • 2)

    Find the locus of Z if |3z - 5| = 3 |z + 1| where z=x+iy.

  • 3)

    Solve:(x-1)4+(x-5)4=82

  • 4)

    Evaluate \(cos\left[ { cos }^{ -1 }\left( \cfrac { -\sqrt { 3 } }{ 2 } +\cfrac { \pi }{ 6 } \right) \right] \)

  • 5)

    For the hyperbola 3x2 - 6y2 = -18, find the length of transverse and conjugate axes and eccentricity.

12th Standard Maths English Medium Model 3 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)-1 = B-1A-1

  • 2)

    Find the inverse of the non-singular matrix A =  \(\left[ \begin{matrix} 0 & 5 \\ -1 & 6 \end{matrix} \right] \), by Gauss-Jordan method.

  • 3)

    Find the adjoint of the following:
    \(\left[ \begin{matrix} 2 & 3 & 1 \\ 3 & 4 & 1 \\ 3 & 7 & 2 \end{matrix} \right] \)

  • 4)

    Find the values of the real numbers x and y, if the complex numbers (3−i)x−(2−i)y+2i +5 and 2x+(−1+2i)y+3+ 2i are equal.

  • 5)

    If |z| =1, show that \(2\le \left| { z }^{ 2 }-3 \right| \le 4\)

12th Standard Maths English Medium Sample 3 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Verify that (A-1)T = (AT)-1 for A=\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

  • 2)

    Show that \(\left| \frac { z-3 }{ z+3 } \right| \) = 2 represent a circle.

  • 3)

    Solve:(x-1)4+(x-5)4=82

  • 4)

    Evaluate \(cos\left[ { cos }^{ -1 }\left( \cfrac { -\sqrt { 3 } }{ 2 } +\cfrac { \pi }{ 6 } \right) \right] \)

  • 5)

    Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x2 +y2 - 64 = 0.

12th Standard Maths English Medium Sample 3 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Verify (AB)-1 = B-1A-1 with A = \(\left[ \begin{matrix} 0 & -3 \\ 1 & 4 \end{matrix} \right] \), B = \(\left[ \begin{matrix} -2 & -3 \\ 0 & -1 \end{matrix} \right] \).

  • 2)

    Find the inverse of the non-singular matrix A =  \(\left[ \begin{matrix} 0 & 5 \\ -1 & 6 \end{matrix} \right] \), by Gauss-Jordan method.

  • 3)

    Test for consistency of the following system of linear equations and if possible solve:
    x - y + z = -9, 2x - 2y + 2z = -18, 3x - 3y + 3z + 27 = 0.

  • 4)

    Solve the following system of linear equations by matrix inversion method:
    2x − y = 8, 3x + 2y = −2

  • 5)

    The complex numbers u,v, and w are related by \(\cfrac { 1 }{ u } =\cfrac { 1 }{ v } +\cfrac { 1 }{ w } \) If v=3−4i and w=4+3i, find u in rectangular form.

12th Standard Maths English Medium Important 3 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Verify that (A-1)T = (AT)-1 for A=\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

  • 2)

    Find the locus of Z if |3z - 5| = 3 |z + 1| where z=x+iy.

  • 3)

    Solve: 2x+2x-1+2x-2=7x+7x-1+7x-2

  • 4)

    Evaluate \(cos\left[ { cos }^{ -1 }\left( \cfrac { -\sqrt { 3 } }{ 2 } +\cfrac { \pi }{ 6 } \right) \right] \)

  • 5)

    Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

12th Standard Maths English Medium Important 3 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 8 & -4 \\ -5 & 3 \end{matrix} \right] \), verify that A(adj A) = |A|I2.

  • 2)

    Find the rank of the matrix \(\left[ \begin{matrix} 2 \\ \begin{matrix} -3 \\ 6 \end{matrix} \end{matrix}\begin{matrix} -2 \\ \begin{matrix} 4 \\ 2 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} -2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} -1 \\ 7 \end{matrix} \end{matrix} \right] \) by reducing it to an echelon form.

  • 3)

    Solve the system of linear equations, by Gaussian elimination method 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1.

  • 4)

    Find the values of the real numbers x and y, if the complex numbers (3−i)x−(2−i)y+2i +5 and 2x+(−1+2i)y+3+ 2i are equal.

  • 5)

    If \(\cfrac { 1+z }{ 1-z } =cos2\theta +isin2\theta \), show that z=itan\(\theta\)

12th Standard Mathematics English Medium Model 2 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  • 2)

    If 1, ω, ω2 are the cube roots of unity show that (1+ω2)3 - (1+ω)3 =0

  • 3)

    Find value of a for which the sum of the squares of the equation x2 - (a- 2) x - a-1=0 assumes the least value.

  • 4)

    Find the principal value of sin-1(-l).

  • 5)

    Prove that \(2{ tan }^{ -1 }\left( \cfrac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \cfrac { 12 }{ 5 } \right) \)
     

12th Standard Mathematics English Medium Model 2 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Prove that \(\left[ \begin{matrix} \cos { \theta } & -\sin { \theta } \\ \sin { \theta } & \cos { \theta } \end{matrix} \right] \) is orthogonal

  • 2)

    Find the rank of the matrix \(\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{matrix} \right] \) by reducing it to a row-echelon form.

  • 3)

    Solve the following system of homogenous equations.
    2x + 3y − z = 0, x − y − 2z = 0, 3x + y + 3z = 0

  • 4)

    Evaluate the following if z=5−2i and w= −1+3i
    z+w

  • 5)

    If the area of the triangle formed by the vertices z,iz and z+iz is 50 square units, find the value of |z|

12th Standard Mathematics English Medium Sample 2 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the rank of the matrix A =\(\left[ \begin{matrix} 4 \\ 7 \end{matrix}\begin{matrix} 5 \\ -3 \end{matrix}\begin{matrix} -6 \\ 0 \end{matrix}\begin{matrix} 1 \\ 8 \end{matrix} \right] \).

  • 2)

    If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

  • 3)

    Find value of a for which the sum of the squares of the equation x2 - (a- 2) x - a-1=0 assumes the least value.

  • 4)

    Ecalute \(sin\left( { cos }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) \right) \)
     

  • 5)

    Find the length of the tangent from (2, -3) to the circle x2 + y2 - 8x - 9y + 12 = 0.

12th Standard Mathematics English Medium Sample 2 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find a matrix A if adj(A) = \(\left[ \begin{matrix} 7 & 7 & -7 \\ -1 & 11 & 7 \\ 11 & 5 & 7 \end{matrix} \right] \).

  • 2)

    Find the rank of the following matrices which are in row-echelon form :
    \(\left[ \begin{matrix} 2 & 0 & -7 \\ 0 & 3 & 1 \\ 0 & 0 & 1 \end{matrix} \right] \)

  • 3)

    Find the rank of each of the following matrices:
    \(\left[ \begin{matrix} 4 & 3 \\ -3 & -1 \\ 6 & 7 \end{matrix}\begin{matrix} 1 & -2 \\ -2 & 4 \\ -1 & 2 \end{matrix} \right] \)

  • 4)

    If z1=3-2i and z2=6+4i, find \(\cfrac { { z }_{ 1 } }{ z_{ 2 } } \)

  • 5)

    Obtain the Cartesian equation for the locus of z=x+iy in
    |z-4|=16

12th Standard Mathematics English Medium Important 2 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  • 2)

    If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

  • 3)

    Find the modules of (1+ 3i)3

  • 4)

    Find x If \(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+....+upto\infty } } } \)

  • 5)

    Find the principal value of \({ cos }^{ -1 }\left( \cfrac { -1 }{ 2 } \right) \)

12th Standard Mathematics English Medium Important 2 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A is a non-singular matrix of odd order, prove that |adj A| is positive

  • 2)

    Find the rank of the matrix \(\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{matrix} \right] \) by reducing it to a row-echelon form.

  • 3)

    Find the rank of the following matrices which are in row-echelon form :
    \(\left[ \begin{matrix} -2 & 2 & -1 \\ 0 & 5 & 1 \\ 0 & 0 & 0 \end{matrix} \right] \)

  • 4)

    Find the following \(\left| \cfrac { 2+i }{ -1+2i } \right| \)
     

  • 5)

    Write in polar form of the following complex numbers
    \(2+i2\sqrt { 3 } \)

12th Standard Mathematics English Medium Model 1 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is

  • 2)

    If \(\rho\)(A) = \(\rho\)([A/B]) = number of unknowns, then the system is

  • 3)

    If \(\rho\)(A) ≠ \(\rho\)([AIB]), then the system is

  • 4)

    If, i2 = -1, then i1 + i2 + i3 + ....+ up to 1000 terms is equal to

  • 5)

    The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) =1 lies on

12th Standard Mathematics English Medium Model 1 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If (AB)-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B-1 = 

  • 2)

    If 0 ≤ θ  ≤ π and the system of equations x + (sinθ)y - (cosθ)z = 0, (cosθ)x - y +z = 0, (sinθ)x + y - z = 0 has a non-trivial solution then θ is

  • 3)

    If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 
     

  • 4)

    The principal argument of \(\cfrac { 3 }{ -1+i } \)

  • 5)

    If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

12th Standard Mathematics English Medium Sample 1 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\rho\)(A) = r then which of the following is correct?

  • 2)

    In the non - homogeneous system of equations with 3 unknowns if \(\rho\)(A) = \(\rho\)([AIB]) = 2, then the system has _______

  • 3)

    If z=\(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) =

  • 4)

    The modular of \(\frac { (-1+i)(1-i) }{ 1+i\sqrt { 3 } } \) is ______

  • 5)

    If (2+√3)x2-2x+1+(2-√3)x2-2x-1=\(\frac { 2 }{ 2-\sqrt { 3 } } \) then x=

12th Standard Mathematics English Medium Sample 1 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 2)

    If (AB)-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B-1 = 

  • 3)

    If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

  • 4)

    Which of the following is/are correct?
    (i) Adjoint of a symmetric matrix is also a symmetric matrix.
    (ii) Adjoint of a diagonal matrix is also a diagonal matrix.
    (iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).
    (iv) A(adjA) = (adjA)A = |A| I

  • 5)

    If z is a complex number such that \(z\varepsilon C/R\quad \)and \(z+\cfrac { 1 }{ z } \epsilon R\) then|z| is

12th Standard Mathematics English Medium Important 1 Mark Creative Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Which of the following is not an elementary transformation?

  • 2)

    If, i2 = -1, then i1 + i2 + i3 + ....+ up to 1000 terms is equal to

  • 3)

    If z = a + ib lies in quadrant then \(\frac { \bar { z } }{ z } \) also lies in the III quadrant if

  • 4)

    If x=cosθ + i sinθ, then xn+\(\frac { 1 }{ { x }^{ n } } \) is ______

  • 5)

    If ∝, β,૪ are the roots of 9x3-7x+6=0, then ∝ β ૪ is __________

12th Standard Mathematics English Medium Important 1 Mark Book Back Questions (New Syllabus) 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 2)

    If ρ(A) = ρ([A | B]), then the system AX = B of linear equations is

  • 3)

    If \(\left| z-\cfrac { 3 }{ z } \right| =2\) then the least value |z| is

  • 4)

    If \(\omega \neq 1\) is a cubic root of unity and \(\left( 1+\omega \right) ^{ 7 }=A+B\omega \) ,then (A,B) equals

  • 5)

    A polynomial equation in x of degree n always has

12th Standard Mathematics English Medium All Chapter One Marks Book Back and Creative Questions 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If 0 ≤ θ  ≤ π and the system of equations x + (sinθ)y - (cosθ)z = 0, (cosθ)x - y +z = 0, (sinθ)x + y - z = 0 has a non-trivial solution then θ is

  • 2)

    If A = \(\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] \), then adj(adj A) is

  • 3)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

  • 4)

    In the system of equations with 3 unknowns, if Δ = 0, and one of Δx, Δy of Δz is non zero then the system is ______

  • 5)

    in+in+1+in+2+in+3 is

12th Standard Mathematics English Medium All Chapter Two Marks Book Back and Creative Questions 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the inverse (if it exists) of the following:
    \(\left[ \begin{matrix} -2 & 4 \\ 1 & -3 \end{matrix} \right] \)
     

  • 2)

    Reduce the matrix \(\left[ \begin{matrix} 3 & -1 & 2 \\ -6 & 2 & 4 \\ -3 & 1 & 2 \end{matrix} \right] \) to a row-echelon form.

  • 3)

    Show that the equations 3x + y + 9z = 0, 3x + 2y + 12z = 0 and 2x + y + 7z = 0 have nontrivial solutions also.

  • 4)

    Solve 6x - 7y = 16, 9x - 5y = 35 using (Cramer's rule).

  • 5)

    Find z−1, if z=(2+3i)(1− i).

12th Standard Mathematics English Medium All Chapter Three Marks Book Back and Creative Questions 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the inverse of the non-singular matrix A =  \(\left[ \begin{matrix} 0 & 5 \\ -1 & 6 \end{matrix} \right] \), by Gauss-Jordan method.

  • 2)

    Solve the following system of linear equations by matrix inversion method:
    2x + 5y = −2, x + 2y = −3

  • 3)

    Solve: 2x + 3y = 10, x + 6y = 4 using Cramer's rule.

  • 4)

    Verify that (A-1)T = (AT)-1 for A=\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

  • 5)

    If z1=3,z2=-7i, and z3=5+4i, show that z1(z2+z3)=z1z2+z1z3

12th Standard Mathematics English Medium All Chapter Five Marks Book Back and Creative Questions 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Determine the values of λ for which the following system of equations (3λ − 8)x + 3y + 3z = 0, 3x + (3λ − 8)y + 3z = 0, 3x + 3y + (3λ − 8)z = 0. has a non-trivial solution.

  • 2)

    Solve the following system of linear equations by matrix inversion method:
    2x + 3y − z = 9, x + y + z = 9, 3x − y − z  = −1

  • 3)

    Show that the equations -2x + y + z = a, x - 2y + z = b, x + y -2z = c are consistent only if a + b + c =0.

  • 4)

    Using Gaussian Jordan method, find the values of λ and μ so that the system of equations 2x - 3y + 5z = 12, 3x + y + λz =μ, x - 7y + 8z = 17 has (i) unique solution (ii) infinite solutions and (iii) no solution.

  • 5)

    Let z1,z2, and z3 be complex numbers such that \(\left| { z }_{ 1 } \right\| =\left| { z }_{ 2 } \right| =\left| { z }_{ 3 } \right| =r>0\) and z1+z2+z3 \(\neq \) 0 prove that \(\left| \cfrac { { z }_{ 1 }{ z }_{ 2 }+{ z }_{ 2 }{ z }_{ 3 }+{ z }_{ 3 }{ z }_{ 1 } }{ { z }_{ 1 }+{ z }_{ 2 }+{ z }_{ 3 } } \right| \) =r

12th Standard Mathematics Public Exam Model Question Paper III 2019 - 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If 0 ≤ θ  ≤ π and the system of equations x + (sinθ)y - (cosθ)z = 0, (cosθ)x - y +z = 0, (sinθ)x + y - z = 0 has a non-trivial solution then θ is

  • 2)

    If A = [2 0 1] then the rank of AAT is ______

  • 3)

    If a=cosθ + i sinθ, then \(\frac { 1+a }{ 1-a } \) =

  • 4)

    If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

  • 5)

    If ax2 + bx + c = 0, a, b, c E R has no real zeros, and if a + b + c < 0, then __________

12th Standard Mathematics Public Exam Model Question Paper II 2019 - 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

  • 2)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 3)

    \(\frac { (cos\theta +isin\theta )^{ 6 } }{ (cos\theta -isin\theta )^{ 5 } } \) = ________

  • 4)

    If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

  • 5)

    If x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

12th Maths - Discrete Mathematics - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
    a*b = a + 3ab − 5b2;∀a,b∈Z

  • 2)

    Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
    \(a*b=\left( \frac { a-1 }{ b-1 } \right) ,\forall a,b\in Q\)

  • 3)

    How many rows are needed for following statement formulae?
    p ∨ ¬ t ( p ∨ ¬s)

  • 4)

    Determine whether ∗ is a binary operation on the sets given below.
    (A*v)=a√b is binary on R

  • 5)

    Let A={a+\(\sqrt5\)b:a,b∈Z}. Check whether the usual multiplication is a binary operation on A.

12th Maths - Probability Distributions - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values ofthe random variable X and number of points in its inverse images.

  • 2)

    An urn contains 5 mangoes and 4 apples Three fruits are taken at randaom If the number of apples taken is a random variable, then find the values of the random variable and number of points in its inverse images.

  • 3)

    A six sided die is marked '1' on one face, '3' on two of its faces, and '5' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find
    (i) the probability mass function
    (ii) the cumulative distribution function
    (iii) P(4 ≤ X < 10)
    (iv) P(X ≥ 6)

  • 4)

    The cumulative distribution function of a discrete random variable is given by

    Find
    (i) the probability mass function
    (ii) P(X < 1 ) and
    (iii) P(X ~ 2

  • 5)

    A random variable X has the following probability mass function.

    x 1 2 3 4 5
    f(x) k2 2k2 3k2 2k 3k

12th Maths - Ordinary Differential Equations - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    A differential equation, determine its order, degree (if exists)
    \(\frac { dy }{ dx } +xy=cotx\)

  • 2)

    A differential equation, determine its order, degree (if exists)
    \({ \left( \frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } \right) }^{ \frac { 2 }{ 3 } }-3\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +5\frac { dy }{ dx } +4=0\)

  • 3)

    A differential equation, determine its order, degree (if exists)
    \({ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0\)

  • 4)

    A differential equation, determine its order, degree (if exists)
    \({ \left( \frac { dy }{ dx } \right) }^{ 3 }=\sqrt { 1+\left( \frac { dy }{ dx } \right) } \)

  • 5)

    Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be-8x, where A and B are arbitrary constants.

12th Maths - Applications of Integration - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Evaluate \(\int _{ 0 }^{ x }{ { x }^{ 2 } } \)cos nxdx, where n is a positive integer.

  • 2)

    Evaluate the following:
    \(\int _{ 0 }^{ 1 }{ { x }^{ 3 }{ e }^{ -2x }dx } \)

  • 3)

    Evaluate \(\int ^\frac {\pi}{2}_{0} \)( sin2 x + cos4 x ) dx

  • 4)

    Evaluate the following
    \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x{ cos }^{ 4 }xdx } \)

  • 5)

    Evaluate the following
    \(\int _{ 0 }^{ 1 }{ { x }^{ 2 }{ (1-x) }^{ 3 }dx } \)

12th Maths - Differentials and Partial Derivatives - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Use the linear approximation to find approximate values of
    \({ (123) }^{ \frac { 2 }{ 3 } }\)

  • 2)

    Find a linear approximation for the following functions at the indicated points.
    \({ h }({ x })=\frac { x }{ 1+x } =\frac { 1 }{ 2 } \)

  • 3)

    A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9-8 cm. Find approximations for the following:
    change in the volume

  • 4)

    Find ∆f and df for the function f for the indicated values of x, ∆x and compare
    f(x) = x2 + 2x + 3; x = -0.5, ∆x = dx = 0.1 

  • 5)

    Let g(x, y) = \(\frac { { x }^{ 2 }y }{ { x }^{ 4 }+{ y }^{ 2 } } \) for (x, y) ≠ (0, 0) and f(0, 0) = 0
    Show that \(\begin{matrix} lim \\ (x,y)\rightarrow (1,2) \end{matrix}\) g(x, y) = 0 along every line y = mx, m ∈ R

12th Maths - Application of Differential Calculus - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    A person learnt 100 words for an English test. The number of words the person remembers in t days after learning is given by W(t) =100×(1− 0.1t)2, 0 ≤ t ≤ 10. What is the rate at which the person forgets the words 2 days after learning?

  • 2)

    A point moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres
    Find the instantaneous velocities at t = 3 and t = 6 seconds.

  • 3)

    A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s =16t2 in t seconds
    What is the instantaneous velocity of the camera when it hits the ground?

  • 4)

    Compute the value of 'c' satisfied by the Rolle’s theorem for the function f (x) = x2 (1 - x)2, x ∈ [0.1]

  • 5)

    Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals.
    \(f(x)=|\frac{1}{x}|, x\in [-1,1]\)

12th Maths - Applications of Vector Algebra - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Show that the vectors \(\hat { i } +\hat { 2j } -\hat { 3k } \),\(\hat { i } +\hat { 2j } -\hat { 3k } \) and \(\hat { 3i } +\hat { j } -\hat { k } \)

  • 2)

    Determine whether the three vectors \(2\hat { i } +3\hat { j } +\hat { k } \)\(\hat { i } -2\hat { j } +2\hat { k } \) and \(\hat { 3i } +\hat { j } +2\hat { k } \) are coplanar.

  • 3)

    Find the non-parametric form of vector equation and Cartesian equations of the straight line passing through the point with position vector  \(4\hat { i } +3\hat { j } -7\hat { k } \) and parallel to the vector \(2\hat { i } -6\hat { j } +7\hat { k } \).

  • 4)

    Find the angle between the line \(\vec { r } =(2\hat { i } -\hat { j } +\hat { k } )+t(\hat { i } +2\hat { j } -2\hat { k } )\) and the plane \(\vec { r } =(6\hat { i } +3\hat { j } +2\hat { k } )=8\)

  • 5)

    Find the angle between the following lines.
    2x = 3y =  −z and 6x = − y = −4z.

12th Maths - Two Dimensional Analytical Geometry II - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

  • 2)

    Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

  • 3)

    11x2−25y2−44x+50y−256 = 0

  • 4)

    Find centre and radius of the following circles.
     x2+y2+6x−4y+4=0

  • 5)

    Find centre and radius of the following circles.
    2x2+2y2−6x+4y+2=0

12th Maths - Inverse Trigonometric Functions - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Find the principal value of sin-1(2), if it exists.

  • 2)

    Find the period and amplitude of
    y=sin 7x

  • 3)

    Find the value of
    \(2{ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right) \)

  • 4)

    Find the value of sec−1\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

  • 5)

    Prove that \(\frac{\pi}{2}\le sin^{-1}x+2 cos^{-1} x\le\frac{3\pi}{2}\).

12th Maths - Theory of Equations - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Construct a cubic equation with roots 1,2, and 3

  • 2)

    If α, β, γ  and \(\delta\) are the roots of the polynomial equation 2x4+5x3−7x2+8=0 , find a quadratic equation with integer coefficients whose roots are α + β + γ + \(\delta\) and αβ૪\(\delta\).

  • 3)

    Show that the equation 2x2−6x+7=0 cannot be satisfied by any real values of x.

  • 4)

    Show that, if p,q,r are rational, the roots of the equation x2−2px+p2−q2+2qr−r2=0 are rational.

  • 5)

    Obtain the condition that the roots of x3+px2+qx+r=0 are in A.P.

12th Maths - Complex Numbers - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    Simplify \(\left( \cfrac { 1+i }{ 1-i } \right) ^{ 3 }-\left( \cfrac { 1-i }{ 1+i } \right) ^{ 3 }\)

  • 2)

    If z1=3-2i and z2=6+4i, find \(\cfrac { { z }_{ 1 } }{ z_{ 2 } } \)

  • 3)

    Find the modulus of the following complex numbers
    \(\cfrac { 2i }{ 3+4i } \)

  • 4)

    Find the square roots of 4+3i

  • 5)

    Show that the following equations represent a circle, and, find its centre and radius|
    \(\left| z-2-i \right| =3\)

12th Maths - Application of Matrices and Determinants - Two Marks Study Materials - by 8682895000 View & Read

  • 1)

    If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \) is non-singular, find A−1.

  • 2)

    If A is a non-singular matrix of odd order, prove that |adj A| is positive

  • 3)

    If A is symmetric, prove that then adj Ais also symmetric.

  • 4)

    If adj(A) = \(\left[ \begin{matrix} 0 & -2 & 0 \\ 6 & 2 & -6 \\ -3 & 0 & 6 \end{matrix} \right] \), find A−1.

  • 5)

    Find the rank of each of the following matrices:
    \(\left[ \begin{matrix} 3 & 2 & 5 \\ 1 & 1 & 1 \\ 3 & 3 & 6 \end{matrix} \right] \)
     

12th Maths - Full Portion Five Marks Question Paper - by 8682895000 View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 4 & 3 \\ 2 & 5 \end{matrix} \right] \), find x and y such that A2 + xA + yI2 = O2. Hence, find A-1.

  • 2)

    In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 ball left to go in the last over. The last ball was bowled and the batsman at the crease hit it high up. The ball traversed along a path in a vertical plane and the equation of the path is y = ax2 + bx + c with respect to a xy-coordinate system in the vertical plane and the ball traversed through the points (10, 8), (20, 16) (30, 18) can you conclude that Chennai Super Kings won the match?
    Justify your answer. (All distances are measured in metres and the meeting point of the plane of the path with the farthest boundary line is (70, 0).)

  • 3)

    Determine the values of λ for which the following system of equations (3λ − 8)x + 3y + 3z = 0, 3x + (3λ − 8)y + 3z = 0, 3x + 3y + (3λ − 8)z = 0. has a non-trivial solution.

  • 4)

    Solve the following systems of linear equations by Cramer’s rule:
     3x + 3y − z = 11, 2x − y + 2z = 9, 4x + 3y + 2z = 25.

  • 5)

    For what value of λ, the system of equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ2 is consistent.

12th Maths - Full Portion Three Marks Questions - by 8682895000 View & Read

  • 1)

    If adj(A) = \(\left[ \begin{matrix} 2 & -4 & 2 \\ -3 & 12 & -7 \\ -2 & 0 & 2 \end{matrix} \right] \), find A.

  • 2)

    4 men and 4 women can finish a piece of work jointly in 3 days while 2 men and 5 women can finish the same work jointly in 4 days. Find the time taken by one man alone and that of one woman alone to finish the same work by using matrix inversion method.

  • 3)

    Find,the rank of the matrix math \(\left[ \begin{matrix} 4 \\ -2 \\ 1 \end{matrix}\begin{matrix} 4 \\ 3 \\ 4 \end{matrix}\begin{matrix} 0 \\ -1 \\ 8 \end{matrix}\begin{matrix} 3 \\ 5 \\ 7 \end{matrix} \right] \).

  • 4)

    The complex numbers u,v, and w are related by \(\cfrac { 1 }{ u } =\cfrac { 1 }{ v } +\cfrac { 1 }{ w } \) If v=3−4i and w=4+3i, find u in rectangular form.

  • 5)

    If (x1+iy1)(x2+iy2)(x3+iy3)...(xn+iyn) =a+ib, show that
    i) (x12+y12)(x22+y22)(x32+y32)...(xn2+yn2)=a2+b2
    ii) \(\sum _{ r=1 }^{ n }{ tan^{ -1 } } \left( \cfrac { { y }_{ r } }{ { x }_{ r } } \right) ={ tan }^{ -1 }\left( \cfrac { b }{ a } \right) +2k\pi ,k\epsilon Z\)

12th Maths - Full Portion Two Marks Question Paper - by 8682895000 View & Read

  • 1)

    If A is a non-singular matrix of odd order, prove that |adj A| is positive

  • 2)

    Find the rank of the matrix \(\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{matrix} \right] \) by reducing it to a row-echelon form.

  • 3)

    Solve the following system of homogenous equations.
    2x + 3y − z = 0, x − y − 2z = 0, 3x + y + 3z = 0

  • 4)

    Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  • 5)

    Find z−1, if z=(2+3i)(1− i).

REVISION TEST - by 9894814613 View & Read

  • 1)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 2)

    If A is a non-singular matrix such that A-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (AT)−1 =

  • 3)

    If A is a square matrix that IAI = 2, than for any positive integer n, |An| =

  • 4)

    The conjugate of a complex number is \(\cfrac { 1 }{ i-2 } \)/Then the complex number is

  • 5)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

12th Maths -Public Exam Model Question Paper 2019 - 2020 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 2)

    If A = [2 0 1] then the rank of AAT is ______

  • 3)

    If x=cosθ + i sinθ, then xn+\(\frac { 1 }{ { x }^{ n } } \) is ______

  • 4)

    A polynomial equation in x of degree n always has

  • 5)

    If the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

12th Maths - Applications of Integration Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    If \(f(x)=\int _{ 0 }^{ x }{ t\ cos\ t\ dt,\ then\ \frac { dx }{ dx } } \)

  • 2)

    The value of \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

  • 3)

    The value of  \(\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx } \) is

  • 4)

    The value of \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } } \) dx is

  • 5)

    The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is

12th Maths - Differentials and Partial Derivatives Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

  • 2)

    If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

  • 3)

    If u = log \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \), then \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } } \) is

  • 4)

    If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

  • 5)

    If f(x,y) = 2x2 - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is

12th Standard Maths - Applications of Vector Algebra Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    If a vector \(\vec { \alpha } \) lies in the plane of \(\vec { \beta } \) and \(\vec { \gamma } \) , then

  • 2)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are non-coplanar, non-zero vectors such that \([\vec { a } ,\vec { b } ,\vec { c } ]\) = 3, then \({ \{ [\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a } }]\} ^{ 2 }\) is equal to

  • 3)

    The coordinates of the point where the line \(\vec { r } =(6\hat { i } -\hat { j } -3\hat { k } )+t(\hat { i } +4\hat { j } )\) meets the plane \(\vec { r } =(\hat { i } +\hat { j } -\hat { k } )\) = 3 are

  • 4)

    The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is

  • 5)

    If \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \), then

Plus 2 Maths - Two Dimensional Analytical Geometry-II Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

  • 2)

    The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
    2x+4y=3 is

  • 3)

    If x+y=k is a normal to the parabola y2 =12x, then the value of k is

  • 4)

    y2 - 2x - 2y + 5 = 0 is a

  • 5)

    If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

12th Stateboard Maths - Probability Distributions Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    Let X be random variable with probability density function
    \(f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x\ge l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}\)
    Which of the following statement is correct 

  • 2)

    A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

  • 3)

    Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

  • 4)

    If the function  \(f(x)=\cfrac { 1 }{ 12 } \) for. a < x < b, represents a probability density function of a continuous random variable X, then which of the followingcannot be the value of a and b?

  • 5)

    If P{X = 0} = 1- P{X = I}. IfE[X) = 3Var(X), then P{X = 0}.

12th Maths Chapter 12 Discrete Mathematics Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    Subtraction is not a binary operation in

  • 2)

    Which one of the following statements has truth value F?

  • 3)

    Which one is the contrapositive of the statement (pVq)⟶r?

  • 4)

    The Identity element of \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\} \) |x\(\in \)R, x≠0} under matrix multiplication is

  • 5)

    Which of the following is a contradiction?

12th Maths - Ordinary Differential Equations Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

  • 2)

    The solution of the differential equation 2x\(\frac{dy}{dx}-y=3\)represents

  • 3)

    If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\)When

  • 4)

    The solution of sec2x tan y dx+sec2y tan x dy=0 is

  • 5)

    The solution of (x2-ay)dx=(ax-y2)dy is

12th Maths - Application of Differential Calculus Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t -16t2. The stone reaches the maximum height in time t seconds is given by

  • 2)

    The tangent to the curve y2 - xy + 9 = 0 is vertical when 

  • 3)

    The number given by the Mean value theorem for the function \(\cfrac { 1 }{ x } \),x∈[1,9] is

  • 4)

    The point on the curve y=x2 is the tangent parallel to X-axis is

  • 5)

    The value of \(\underset { x\rightarrow \infty }{ lim } { e }^{ -x }\) is

12th Maths - Inverse Trigonometric Functions Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    sin−1(cos x)\(=\frac{\pi}{2}-x \) is valid for

  • 2)

    If cot−1x=\(\frac{2\pi}{5}\) for some x\(\in\)R, the value of tan-1 x is

  • 3)

    The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

  • 4)

    \({ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right) \) =

  • 5)

    If \({ cos }^{ -1 }x>x>{ sin }^{ -1 }x\) then

12th Maths - Theory of Equations Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

  • 2)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

  • 3)

    If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

  • 4)

    Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

  • 5)

    If ∝, β, ૪ are the roots of the equation x3-3x+11=0, then ∝+β+૪ is __________.

12th Maths - Complex Numbers Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 2)

    If |z-2+i|≤2, then the greatest value of |z| is

  • 3)

    If |z1|=1,|z2|=2|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is 

  • 4)

    If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

  • 5)

    If z=\(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) =

12th Maths - Application of Matrices and Determinants Model Question Paper 1 - by 8682895000 View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) then the value of a23 is

  • 4)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

  • 5)

    If A is a square matrix that IAI = 2, than for any positive integer n, |An| =

12th Maths - Discrete Mathematics Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Which one of the following statements has the truth value T?

  • 2)

    Which one of the following is not true?

  • 3)

    The number of binary operations that can be defined on a set of 3 elements is

  • 4)

    The identity element in the group {R - {1},x} where a * b = a + b - ab is

  • 5)

    If p is true and q is false, then which of the following is not true?
    (1) p ⟶ q is F
    (2) p v q is T
    (3) p ∧ q is F
    (4) p ⇔ q is F

12th Maths - Probability Distributions Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

  • 2)

    If P{X = 0} = 1- P{X = I}. IfE[X) = 3Var(X), then P{X = 0}.

  • 3)

    A six sided die is marked '1' on one face, '3' on two of its faces, and '5' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find
    (i) the probability mass function
    (ii) the cumulative distribution function
    (iii) P(4 ≤ X < 10)
    (iv) P(X ≥ 6)

  • 4)

    A random variable X has the following probability mass function.

    x 1 2 3 4 5
    f(x) k2 2k2 3k2 2k 3k
  • 5)

    Find the binomial distribution function for each of the following.
    (i) Five fair coins are tossed once and X denotes the number of heads.
    (ii) A fair die is rolled 10 times and X denotes the number of times 4 appeared.

12th Maths - Ordinary Differential Equations Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The general solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } \) is

  • 2)

    If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\)When

  • 3)

    The slope at any point of a curve y = f (x) is given by \(\frac{dy}{dx}=3x^2\) and it passes through (-1,1). Then the equation of the curve is

  • 4)

    The I.F. of cosec x\(\frac{dy}{dx}+y\)sec2x=0 is

  • 5)

    The differential equation associated with the family of concentric circles having their centres at the origin is _________.

12th Maths - Applications of Integration Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3xdx } \)

  • 2)

    If f(x)\(f(x)=\int _{ 1 }^{ x }{ \frac { { e }^{ { sin }^{ u } } }{ u } } du,x>1\quad and\quad \int _{ 1 }^{ 3 }{ \frac { { e }^{ { sinx }^{ 2 } } }{ x } } dx=\frac { 1 }{ 2 } [f(a)-f(1)]\), then one of the possible value of a is

  • 3)

    The value of \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }xcosxdx } \) is

  • 4)

    The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is

  • 5)

    The area enclosed by the curve y2 = 4x, the x-axis and its latus rectum is ............ sq.units.

12th Maths - Differentials and Partial Derivatives Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If g(x, y) = 3x2 - 5y + 2y, x(t) = et and y(t) = cos t, then \(\frac{dg}{dt}\) is equal to

  • 2)

    If u(x, y) = x2+ 3xy + y - 2019, then \(\frac { \partial u }{ \partial x } \)(4, -5) is equal to

  • 3)

    If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

  • 4)

    If y = sin x and x changes from \(\frac{\pi}{2}\) to ㅠ the approximate change in y is ..............

  • 5)

    If u = log \(\left( \frac { { x }^{ 2 }+{ y }^{ 2 } }{ xy } \right) \) then
    (1) u is a homogeneous function
    (2) \(x\frac { { \partial }u }{ \partial { x } } +y\frac { { \partial }u }{ { \partial y } } \) = 0
    (3) \(\frac { { x }^{ 2 }+{ y }^{ 2 } }{ xy } \) is a homogeneous function
    (4) \(\frac { { x }^{ 2 }+{ y }^{ 2 } }{ xy } \) is a homogeneous function of  degree 0.

12th Maths - Application of Differential Calculus Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

  • 2)

    The function sin4 x + cos4X is increasing in the interval

  • 3)

    One of the closest points on the curve x2 - y2.= 4 to the point (6, 0) is

  • 4)

    The critical points of the function f(x) = \((x-2)^{ \frac { 2 }{ 3 } }(2x+1)\) are

  • 5)

    The statement " If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

Applications of Vector Algebra Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \([\vec { a } ,\vec { b } ,\vec { c } ]=1\)\(\frac { \vec { a } .(\vec { b } \times \vec { c } ) }{ (\vec { c } \times \vec { a } ).\vec { b } ) } +\frac { \vec { b } .(\vec { c } \times \vec { a } ) }{ (\vec { a } \times \vec { b } ).\vec { c } } +\frac { \vec { c } .(\vec { a } \times \vec { b } ) }{ (\vec { c } \times \vec { b } ).\vec { a } } \) is

  • 2)

    If \(\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c } \) where \(\vec { a } ,\vec { b } ,\vec { c } \) are any three vectors such that \(\vec { a } ,\vec { b } \) \(\neq \) 0 and  \(\vec { a } .\vec { b } \) \(\neq \) 0 then \(\vec { a } \) and \(\vec { c } \) are

  • 3)

    The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is

  • 4)

    The angle between the vector \(3\overset { \wedge }{ i } +4\overset { \wedge }{ j } +\overset { \wedge }{ 5k } \) and the z-axis is

  • 5)

    The distance from the origin to the plane \(\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +5\overset { \wedge }{ k } \right) =7\) is ______________ 

12th Maths - Two Dimensional Analytical Geometry-II Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
    and x+2y=4 is

  • 2)

    The area of quadrilateral formed with foci of the hyperbolas \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\\ \) and \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =-1\)

  • 3)

    Equation of tangent at (-4, -4) on x2 = -4y is

  • 4)

    y2 - 2x - 2y + 5 = 0 is a

  • 5)

    The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

12th Maths - Inverse Trigonometric Functions Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\\ \\ \\ { cot }^{ -1 }\left( \sqrt { sin\alpha } \right) +{ tan }^{ -1 }\left( \sqrt { sin\alpha } \right) =u\), then cos2u is equal to

  • 2)

    If |x|\(\le\)1, then 2tan-1 x-sin-1 \(\frac{2x}{1+x^2}\) is equal to

  • 3)

    If sin-1 \(\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}\), then the value of x is

  • 4)

    sin(tan-1x), |x|<1 ia equal to

  • 5)

    The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

12th Maths - Theory of Equations Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

  • 2)

    The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

  • 3)

    Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

  • 4)

    The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has

  • 5)

    If the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

12th Maths - Complex Numbers Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    in+in+1+in+2+in+3 is

  • 2)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 3)

    If |z|=1, then the value of \(\cfrac { 1+z }{ 1+\overline { z } }\) is

  • 4)

    If \(\cfrac { z-1 }{ z+1 } \) is purely imaginary, then |z| is

  • 5)

    The value of (1+i) (1+i2) (1+i3) (1+i4) is

12th Maths - Application of Matrices and Determinants Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 4)

    If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

  • 5)

    The rank of any 3 x 4 matrix is
    (1) May be 1
    (2) May be 2
    (3) May be 3
    (4) Maybe 4

12th Maths - Discrete Mathematics Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A binary operation on a set S is a function from

  • 2)

    In the set Q define a⊙b= a+b+ab. For what value of y, 3⊙(y⊙5)=7?

  • 3)

    Which one is the contrapositive of the statement (pVq)⟶r?

  • 4)

    Which of the following is a tautology?

  • 5)

    The identity element in the group {R - {1},x} where a * b = a + b - ab is

12th Maths - Probability Distributions Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Consider a game where the player tosses a sixsided fair die. H the face that comes up is 6, the player wins Rs.36, otherwise he loses Rs. k2 , where k is the face that comes up k = {I, 2,3,4, 5}.
    The expected amount to win at this game in Rs is

  • 2)

    A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is roUed and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

  • 3)

    Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E[X] and E[Y] respectively are

  • 4)

    If P{X = 0} = 1- P{X = I}. IfE[X) = 3Var(X), then P{X = 0}.

  • 5)

    Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, P(X = I) = k P(X = i-I) i = 1, 2 and P(X = 0) =\(\cfrac { 1 }{ 7 } \) then the value of k is

12th Maths - Ordinary Differential Equations Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

  • 2)

    The solution of the differential equation 2x\(\frac{dy}{dx}-y=3\)represents

  • 3)

    The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

  • 4)

    The solution of (x2-ay)dx=(ax-y2)dy is

  • 5)

    The transformation y=vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \)

12th Maths - Applications of Integration Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx } \) is

  • 2)

    The value of \(\int _{ 0 }^{ \infty }{ { e }^{ -3x }{ x }^{ 2 }dx } \\ \) is

  • 3)

    The value of \(\int _{ 0 }^{ \frac { 2 }{ 3 } }{ \frac { dx }{ \sqrt { 4-9{ x }^{ 2 } } } } \) is 

  • 4)

    If \(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ a }{ f(x) } \) then

  • 5)

    The ratio of the volumes generated by revolving the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 about major and minor axes is

12th Maths - Differentials and Partial Derivatives Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If w (x, y) = xy, x > 0, then \(\frac { \partial w }{ \partial x } \) is equal to

  • 2)

    If f (x, y) = exy then \(\frac { { \partial }^{ 2 }f }{ \partial x\partial y } \) is equal to

  • 3)

    The change in the surface area S = 6x2 of a cube when the edge length varies from xo to xo+ dx is

  • 4)

    If u = log \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \), then \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } } \) is

  • 5)

    If u = xy + yx then ux + uy at x = y = 1 is

12th Maths - Application of Differential Calculus Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

  • 2)

    The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?

  • 3)

    The slope of the line normal to the curve f(x) = 2cos 4x at \(x=\cfrac { \pi }{ 12 } \)

  • 4)

    The point on the curve y=x2 is the tangent parallel to X-axis is

  • 5)

    The equation of the tangent to the curve y=x2-4x+2 at (4,2) is

12th Maths - Applications of Vector Algebra Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If a vector \(\vec { \alpha } \) lies in the plane of \(\vec { \beta } \) and \(\vec { \gamma } \) , then

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between

  • 4)

    The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is

  • 5)

    If \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \), then

12th Maths - Two Dimensional Analytical Geometry II Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

  • 2)

    The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

  • 3)

    If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
    is

  • 4)

    If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

  • 5)

    If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

12th Maths - Inverse Trigonometric Functions Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If sin-1 x+sin-1 y=\(\frac{2\pi}{3};\)then cos-1x+cos-1 y is equal to

  • 2)

    If cot−1x=\(\frac{2\pi}{5}\) for some x\(\in\)R, the value of tan-1 x is

  • 3)

    If the function f(x)sin-1(x2-3), then x belongs to

  • 4)

    The value of \({ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right) \) is 

  • 5)

    If \({ tan }^{ -1 }\left( \cfrac { x+1 }{ x-1 } \right) +{ tan }^{ -1 }\left( \cfrac { x-1 }{ x } \right) ={ tan }^{ -1 }\left( -7 \right) \) then x Is

12th Maths - Theory of Equations Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

  • 2)

    A polynomial equation in x of degree n always has

  • 3)

    Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

  • 4)

    The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has

  • 5)

    If (2+√3)x2-2x+1+(2-√3)x2-2x-1=\(\frac { 2 }{ 2-\sqrt { 3 } } \) then x=

12th Maths - Complex Numbers Important Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |z-2+i|≤2, then the greatest value of |z| is

  • 2)

    If \(\left| z-\cfrac { 3 }{ z } \right| =2\) then the least value |z| is

  • 3)

    The principal argument of the complex number \(\cfrac { \left( 1+i\sqrt { 3 } \right) ^{ 2 } }{ 4i\left( 1-i\sqrt { 3 } \right) } \) is

  • 4)

    If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

  • 5)

    If x+iy =\(\frac { 3+5i }{ 7-6i } \), they y =

12th Maths - Application of Matrices and Determinants Important Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 2)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

  • 3)

    If A is a non-singular matrix such that A-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (AT)−1 =

  • 4)

    The augmented matrix of a system of linear equations is \(\left[ \begin{matrix} 1 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 1 \\ 0 \end{matrix} \end{matrix}\begin{matrix} 7 \\ \begin{matrix} 4 \\ \lambda -7 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ \mu +5 \end{matrix} \end{matrix} \right] \). The system has infinitely many solutions if

  • 5)

    If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

12th Maths Half Yearly Model Question Paper 2019 - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

  • 3)

    The principal argument of \(\cfrac { 3 }{ -1+i } \)

  • 4)

    If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

  • 5)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

12th Maths - Applications of Vector Algebra One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    If a vector \(\vec { \alpha } \) lies in the plane of \(\vec { \beta } \) and \(\vec { \gamma } \) , then

  • 3)

    \(\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0\) , then the value of \([\vec { a } ,\vec { b } ,\vec { c } ]\) is

  • 4)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are three unit vectors such that \(\vec { a } \) is perpendicular to \(\vec { b } \) and is parallel to \(\vec { c } \) then \(\vec { a } \times (\vec { b } \times \vec { c } )\) is equal to

  • 5)

    If \([\vec { a } ,\vec { b } ,\vec { c } ]=1\)\(\frac { \vec { a } .(\vec { b } \times \vec { c } ) }{ (\vec { c } \times \vec { a } ).\vec { b } ) } +\frac { \vec { b } .(\vec { c } \times \vec { a } ) }{ (\vec { a } \times \vec { b } ).\vec { c } } +\frac { \vec { c } .(\vec { a } \times \vec { b } ) }{ (\vec { c } \times \vec { b } ).\vec { a } } \) is

12th Maths - Two Dimensional Analytical Geometry II One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

  • 2)

    Equation of tangent at (-4, -4) on x2 = -4y is

  • 3)

    If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

  • 4)

    The eccentricity of the ellipse 9x2+ 5y2 - 30y= 0 is

  • 5)

    The length of the latus rectum of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 } \) = 1 is

12th Maths - Inverse Trigonometric Functions One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \({ tan }^{ -1 }\left\{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right\} =\alpha \) then x2 =

  • 2)

    If \({ sin }^{ -1 }x-cos^{ -1 }x=\cfrac { \pi }{ 6 } \) then

  • 3)

    The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

  • 4)

    If \(\alpha ={ tan }^{ -1 }\left( tan\cfrac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\cfrac { 2\pi }{ 3 } \right) \) then

  • 5)

    The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi \) is

12th Maths - Theory of Equations One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

  • 3)

    A polynomial equation in x of degree n always has

  • 4)

    If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

  • 5)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

12th Maths - Complex Numbers One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of (1+i) (1+i2) (1+i3) (1+i4) is

  • 2)

    If \(\sqrt { a+ib } \) =x+iy, then possible value of \(\sqrt { a-ib }\) is

  • 3)

    If, i2 = -1, then i1 + i2 + i3 + ....+ up to 1000 terms is equal to

  • 4)

    If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

  • 5)

    If a=cosθ + i sinθ, then \(\frac { 1+a }{ 1-a } \) =

12th Maths - Application of Matrices and Determinants One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 2)

    If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

  • 3)

    Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

  • 4)

    If AT is the transpose of a square matrix A, then

  • 5)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

12th Maths - Discrete Mathematics Five Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Write the statements in words corresponding to ¬p, p ∧ q , p ∨ q and q ∨ ¬p, where p is ‘It is cold’ and q is ‘It is raining.’

  • 2)

    How many rows are needed for following statement formulae?
    p ∨ ¬ t ( p ∨ ¬s)

  • 3)

    How many rows are needed for following statement formulae?
    (( p ∧ q) ∨ (¬r ∨¬s)) ∧ (¬ t ∧ v))

  • 4)

    Construct the truth table for \((p\overset { \_ \_ }{ \vee } q)\wedge (p\overset { \_ \_ }{ \vee } \neg q)\)

  • 5)

    Verify
    (i) closure property,
    (ii) commutative property,
    (iii) associative property,
    (iv) existence of identity, and
    (v) existence of inverse for the operation +5 on Z5 using table corresponding to addition modulo 5.

12th Maths - Probability Distributions Five Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Two fair coins are tossed simultaneously (equivalent to a fair coin is tossed twice). Find the probability mass function for number of heads occurred.
     

  • 2)

    A pair of fair dice is rolled once. Find the probability mass function to get the number of fours.

  • 3)

    If the probability mass function f (x) of a random variable X isx

    x 1 2 3 4
    f (x) \(\cfrac { 1 }{ 12 } \) \(\cfrac { 5 }{ 12 } \) \(\cfrac { 5 }{ 12 } \) \(\cfrac { 1 }{ 12 } \)

    find (i) its cumulative distribution function, hence find
    (ii) P(X ≤ 3) and,
    (iii) P(X ≥ 2)

  • 4)

    A six sided die is marked ‘1’ on one face, ‘2’ on two of its faces, and ‘3’ on remaining three faces. The die is rolled twice. If X denotes the total score in two throws.
    (i) Find the probability mass function.
    (ii) Find the cumulative distribution function.
    (iii) Find P(3 ≤ X< 6) (iv) Find P(X ≥ 4) .

  • 5)

    Find the probability mass function f (x) of the discrete random variable X whose cumulative distribution function F(x) is given by

    Also find (i) P(X < 0) and (ii)\(P(X\ge -1\) 

12th Maths - Ordinary Differential Equations Five Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Form the differential equation by eliminating the arbitrary constants A and B from y = Acos x + B sin x.

  • 2)

    Find the differential equation of the family of circles passing through the points (a,0) and (−a,0).

  • 3)

    Find the differential equation of the family of all ellipses having foci on the x -axis and centre at the origin.

  • 4)

    Find the particular solution of (1+ x3 )dy − x2 ydx = satisfying the condition y(1) = 2.

  • 5)

    Solve y ' = sin2 (x − y + )1.

12th Maths - Applications of Integration Five Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Evaluate\(\int _{ 0 }^{ 1 }{ x^3dx } \), as the limit of a sum.

  • 2)

    Evaluate\(\int _{ 1 }^{ 4 }{ ({ 2x }^{ 2 }-3) } \) dx, as the limit of a sum

  • 3)

    Evaluate \(\int _{ 0 }^{ x }{ { x }^{ 2 } } \)cos nxdx, where n is a positive integer.

  • 4)

    Evaluate: \(\\ \\ \int _{ -1 }^{ 1 }{ { e }^{ -\lambda x }(1-{ x }^{ 2 }) } dx\)

  • 5)

    Evaluate \(\int ^\frac {\pi}{2}_{0} \)( sin2 x + cos4 x ) dx

12th Maths - Application of Differential Calculus Five Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    For what value of x the tangent of the curve y = x3 − x2 + x − 2 is parallel to the line y = x.

  • 2)

    Find the equation of the tangent and normal to the Lissajous curve given by x = 2cos3t and y = 3sin 2t, t ∈ R

  • 3)

    Expand log(1+ x) as a Maclaurin’s series upto 4 non-zero terms for –1 < x ≤ 1.

  • 4)

    Expand tan x in ascending powers of x upto 5th power for \( (-\frac{\pi}{2} <x<\frac{\pi}{2} )\)

  • 5)

    Find the intervals of monotonicity and hence find the local extrema for the function f (x) = x2 − 4x + 4

12th Maths - Differentials and Partial Derivatives Five Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Let f , g : (a,b)→R be differentiable functions. Show that d(fg) = fdg + gdf

  • 2)

    Let g(x) = x2 + sin x. Calculate the differential dg.

  • 3)

    If the radius of a sphere, with radius 10 cm, has to decrease by 0 1. cm, approximately how much will its volume decrease?

  • 4)

    Let f (x, y) = 0 if xy ≠ 0 and f (x, y) =1 if xy = 0.
    (i) Calculate: \(\frac { \partial f }{ \partial x } (0,0),\frac { \partial f }{ \partial y } (0,0).\)
    (ii) Show that f is not continuous at (0,0)

  • 5)

    Let F(x, y) = x3 y + y2x + 7 for all (x, y)∈ R2. Calculate \(\frac { \partial F }{ \partial x } \)(-1,3) and \(\frac { \partial F }{ \partial y } \)(-2,1).

12th Maths - Discrete Mathematics Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation - on Z.

  • 2)

    Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation + on
    Ze = the set of all even integers

  • 3)

    Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation + on
    Zo = the set of all even integers

  • 4)

    Verify
    (i) closure property
    (ii) commutative property, and
    (iii) associative property of the following operation on the given set.
    (a*b) = ab;∀a,b∈N (exponentiation property)

  • 5)

    Determine whether ∗ is a binary operation on the sets given below.
    a*b=b=a.|b| on R

12th Maths - Probability Distributions Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Suppose two coins are tossed once. If X denotes the number of tails,
    (i) write down the sample space
    (ii) find the inverse image of 1
    (iii) the values of the random variable and number of elements in its inverse images

  • 2)

    Suppose a pair of unbiased dice is rolled once. If X denotes the total score of two dice, write down
    (i) the sample space
    (ii) the values taken by the random variable X,
    (iii) the inverse image of 10, and
    (iv) the number of elements in inverse image of X.

  • 3)

    An urn contains 2 white balls and 3 red balls. A sample of 3 balls are chosen at random from the urn. If X denotes the number of red balls chosen, find the values taken by the random variable X and its number of inverse images

  • 4)

    Two balls are chosen randomly from an urn containing 6 white and 4 black balls. Suppose that we win Rs.30 for each black ball selected and we lose Rs.20 for each white ball selected. If X denotes the winning amount, then find the values of X and number of points in its inverse images.

  • 5)

    Find the constant C such that the function \(f(x)=\begin{cases} \begin{matrix} { Cx }^{ 2 } & 1 is a density function, and compute (i) P(1.5 < X < 3.5)
    (ii) P(X ≤2)
    (iii) P(3 < X ) .

12th Maths - Ordinary Differential Equations Three Marks Questions Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Determine the order and degree (if exists) of the following differential equations: 
    \(\frac { dy }{ dx } =x+y+5\)

  • 2)

    Determine the order and degree (if exists) of the following differential equations: 
    \({ \left( \frac { { d }^{ 4 }y }{ { dx }^{ 4 } } \right) }^{ 3 }+4{ \left( \frac { dy }{ dx } \right) }^{ 7 }+6y=5cos3x\)

  • 3)

    Determine the order and degree (if exists) of the following differential equations: 
    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +3{ \left( \frac { dy }{ dx } \right) }^{ 2 }={ x }^{ 2 }log\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) \)

  • 4)

    Determine the order and degree (if exists) of the following differential equations: 
    \(3\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ={ \left[ 4+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 3 }{ 2 } }\)

  • 5)

    Determine the order and degree (if exists) of the following differential equations: 
    dy + (xy − cos x)dx = 0

12th Maths - Applications of Integration Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Estimate the value of \(\int _{ 0 }^{ 0.5 }{ { x }^{ 2 } } dx\)using the Riemann sums corresponding to 5 subintervals of equal width and applying (i) left-end rule (ii) right-end rule (iii) the mid-point rule.

  • 2)

    Evaluate: \(\int _{ 0 }^{ 3 }{ (3{ x }^{ 2 }-4x+5) } dx\)

  • 3)

    Evaluate :\(\int _{ 0 }^{ 1 }{ \frac { 2x+7 }{ { 5x }^{ 2 }+9 } } dx\)

  • 4)

    Evaluate :\(\int _{ 0 }^{ 9 }{ \frac { 1 }{ x+\sqrt { x } } dx } \)

  • 5)

    Show that \(\int ^\frac{\pi}{2}_0\) \(\frac {dx}{4+5 sin x}\) = \(\frac {1}{3}\) log2

12th Maths - Differentials and Partial Derivatives Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the linear approximation for f(x) = \(\sqrt { 1+x } ,x\ge -1\) at x0 = 3. Use the linear approximation to estimate f(3.2) 

  • 2)

    Use linear approximation to find an approximate value of \(\sqrt { 9.2 } \) without using a calculator.

  • 3)

    Let us assume that the shape of a soap bubble is a sphere. Use linear approximation to approximate the increase in the surface area of a soap bubble as its radius increases from 5 cm to 5.2 cm. Also, calculate the percentage error.

  • 4)

    A right circular cylinder has radius r =10 cm. and height h = 20 cm. Suppose that the radius of the cylinder is increased from 10 cm to 10. 1 cm and the height does not change. Estimate the change in the volume of the cylinder. Also, calculate the relative error and percentage error.

  • 5)

    Let f (x,y) = \(\frac { 3x-5y+8 }{ { x }^{ 2 }+{ y }^{ 2 }+1 } \) for all (x, y) ∈RShow that f is continuous on R2 

12th Maths - Application of Differential Calculus Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    For the function f(x) = x2 ∈ [0, 2] compute the average rate of changes in the subintervals [0,0.5], [0.5,1], [1,1.5], [1.5,2] and the instantaneous rate of changes at the points x = 0.5,1,1.5, 2

  • 2)

    The temperature in celsius in a long rod of length 10 m, insulated at both ends, is a function of
    length x given by T = x(10 − x). Prove that the rate of change of temperature at the midpoint of the
    rod is zero.

  • 3)

    A particle moves along a horizontal line such that its position at any time t ≥ 0 is given by s(t) = t3 − t2 + t + 6 9 1, where s is measured in metres and t in seconds?
    (1) At what time the particle is at rest?
    (2) At what time the particle changes direction?
    (3) Find the total distance travelled by the particle in the first 2 seconds.

  • 4)

    The price of a product is related to the number of units available (supply) by the equation Px + 3P −16x = 234, where P is the price of the product per unit in Rupees(Rs) and x is the number of units. Find the rate at which the price is changing with respect to time when 90 units are available and the supply is increasing at a rate of 15 units/week.

  • 5)

    Compute the value of 'c' satisfied by the Rolle’s theorem for the function f (x) = x2 (1 - x)2, x ∈ [0.1]

12th Maths - Discrete Mathematics Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
    a*b = a + 3ab − 5b2;∀a,b∈Z

  • 2)

    Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
    \(a*b=\left( \frac { a-1 }{ b-1 } \right) ,\forall a,b\in Q\)

  • 3)

    Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation + on Z.

  • 4)

    Let A =\(\begin{bmatrix} 0 & 1 \\ 1 & 1 \end{bmatrix},B=\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}\)be any two boolean matrices of the same type. Find AvB and A^B.

  • 5)

    Let p: Jupiter is a planet and q: India is an island be any two simple statements. Give
    verbal sentence describing each of the following statements.
    (i) ¬p
    (ii) p ∧ ¬q
    (iii) ¬p ∨ q
    (iv) p➝ ¬q
    (v) p↔q

12th Maths - Probability Distributions Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values ofthe random variable X and number of points in its inverse images.

  • 2)

    Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred

  • 3)

    A six sided die is marked '1' on one face, '3' on two of its faces, and '5' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find
    (i) the probability mass function
    (ii) the cumulative distribution function
    (iii) P(4 ≤ X < 10)
    (iv) P(X ≥ 6)

  • 4)

    Find the probability mass function and cumulative distribution function of number of girl child in families with 4 children, assuming equal probabilities for boys and girls.

  • 5)

    The probability density function of X is given by \(f(x)=\begin{cases} \begin{matrix} kxe^{ -2x } & forx>0 \end{matrix} \\ \begin{matrix} 0 & for\quad x\le 0 \end{matrix} \end{cases}\) Find the value opf .

12th Maths - Ordinary Differential Equations Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A differential equation, determine its order, degree (if exists)
    \({ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0\)

  • 2)

    A differential equation, determine its order, degree (if exists)
    \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +5\frac { dy }{ dx } +\int { ydx } ={ x }^{ 3 }\)

  • 3)

    Find the differential equation of the family of all nonhorizontal lines in a plane.

  • 4)

    Form the differential equation of all straight lines touching the circle x2 + y2 = r2.

  • 5)

    Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin.

12th Maths - Applications of Integration Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Evaluate the following integrals as the limits of sums.
    \(\int _{ 0 }^{ 1 }{ (5x+4)dx } \)

  • 2)

    Evaluate the following integrals as the limits of sums.
    \(\int _{ 1 }^{ 2 }{ 4x^2-1)dx } \)

  • 3)

    Evaluate the following definite integrals:
    \(\int _{ 3 }^{ 4 }{ \frac { dx }{ { x }^{ 2 }-4 } } \)

  • 4)

    Evaluate the following definite integrals:
    \(\int _{ -1 }^{ 1 }{ \frac { dx }{ { x }^{ 2 }+2x+5 } } \)

  • 5)

    Evaluate the following integrals using properties of integration:
    \(\int _{ 0 }^{ 2\pi }{ xlog\left( \frac { 3+cos\quad x }{ 3-cos\quad x } \right) } dx\)

12th Maths - Differentials and Partial Derivatives Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find a linear approximation for the following functions at the indicated points.
    g(x) = \(g(x)=\sqrt { { x }^{ 2 }+9 } ,{ x }_{ 0 }=-4\)

  • 2)

    The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm.find the following in calculating the area of the circular plate:
    Absolute error

  • 3)

    The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm.find the following in calculating the area of the circular plate:
    Relative error

  • 4)

    Find differential dy for each of the following function
    \(y=\frac { { \left( 1-2x \right) }^{ 3 } }{ 3-4x } \)

  • 5)

    Find differential dy for each of the following function
    y = (3 + sin(2x)) 2/3 

12th Maths - Application of Differential Calculus Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A particle moves along a line according to the law s(t) = 2t3 − 9t2 +12t − 4, where t ≥ 0.
    Find the total distance travelled by the particle in the first 4 seconds.

  • 2)

    A particle moves along a line according to the law s(t) = 2t3 − 9t2 +12t − 4, where t ≥ 0.
    Find the particle’s acceleration each time the velocity is zero.

  • 3)

    A police jeep, approaching an orthogonal intersection from the northern direction, is chasing a speeding car that has turned and moving straight east. When the jeep is 0.6 km north of the intersection and the car is 0.8 km to the east. The police determine with a radar that the distance between them and the car is increasing at 20 km/hr. If the jeep is moving at 60 km/hr at the instant of measurement, what is the speed of the car?

  • 4)

    Find the slope of the tangent to the curves at the respective given points.
    y = x4 + 2x2 − x at x =1

  • 5)

    Find the equations of the tangents to the curve y =1+ x3 for which the tangent is orthogonal with the line x +12y =12

12th Maths - Discrete Mathematics One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A binary operation on a set S is a function from

  • 2)

    Subtraction is not a binary operation in

  • 3)

    Which one of the following is a binary operation on N?

  • 4)

    In the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R?

  • 5)

    The operation * defined by a*b =\(\frac{ab}{7}\) is not a binary operation on

12th Maths - Probability Distributions One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Let X be random variable with probability density function
    \(f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x\ge l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}\)
    Which of the following statement is correct 

  • 2)

    A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
    \(f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x>l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}\)

  • 3)

    Consider a game where the player tosses a sixsided fair die. H the face that comes up is 6, the player wins Rs.36, otherwise he loses Rs. k2 , where k is the face that comes up k = {I, 2,3,4, 5}.
    The expected amount to win at this game in Rs is

  • 4)

    A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is roUed and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

  • 5)

    A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

12th Maths - Ordinary Differential Equations One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The order and degree of the differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0\)are respectively

  • 2)

    The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

  • 3)

    The order and degree of the differential equation \(\sqrt { sin\quad x } (dx+dy)=\sqrt { cos\quad x } (dx-dy)\)

  • 4)

    The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

  • 5)

    The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

12th Maths - Applications of Integration One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx } \) is

  • 2)

    The value of \(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ \left( \frac { { 2x }^{ 7 }-{ 3x }^{ 5 }+{ 7x }^{ 3 }-x+1 }{ { cos }^{ 2 }x } \right) dx } \) is 

  • 3)

    If \(f(x)=\int _{ 0 }^{ x }{ t\ cos\ t\ dt,\ then\ \frac { dx }{ dx } } \)

  • 4)

    The area between y2 x = 4 and its latus rectum is

  • 5)

    The value of \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

12th Maths - Differentials and Partial Derivatives One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

  • 2)

    The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

  • 3)

    If u (x, y) = ex2+y2, then \(\frac { \partial u }{ \partial x } \) is equal to

  • 4)

    If v (x, y) = log (ex + ev), then \(\frac { { \partial }v }{ \partial x } +\frac { \partial v }{ \partial y } \) is equal to

  • 5)

    If w (x, y) = xy, x > 0, then \(\frac { \partial w }{ \partial x } \) is equal to

12th Maths - Application of Differential Calculus One Mark Questions with Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is \(\cfrac { 1 }{ 2 } \) cm

  • 2)

    A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. Find the rate of change of the balloon's angle of elevation in radian per second when the balloon is 30 metres above the ground.

  • 3)

    The position of a particle moving along a horizontal line of any time t is given by set) = 3t2 -2t- 8. The time at which the particle is at rest is

  • 4)

    A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t -16t2. The stone reaches the maximum height in time t seconds is given by

  • 5)

    Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

12th Standard Maths - Discrete Mathematics Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A binary operation on a set S is a function from

  • 2)

    Which one of the following statements has the truth value T?

  • 3)

    Which one of the following statements has truth value F?

  • 4)

    Which one is the contrapositive of the statement (pVq)⟶r?

  • 5)

    Which one of the following is incorrect? For any two propositions p and q, we have

12th Standard Maths - Probability Distributions Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Let X be random variable with probability density function
    \(f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x\ge l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}\)
    Which of the following statement is correct 

  • 2)

    Consider a game where the player tosses a sixsided fair die. H the face that comes up is 6, the player wins Rs.36, otherwise he loses Rs. k2 , where k is the face that comes up k = {I, 2,3,4, 5}.
    The expected amount to win at this game in Rs is

  • 3)

    A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is roUed and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

  • 4)

    A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

  • 5)

    Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E[X] and E[Y] respectively are

12th Standard Maths - Ordinary Differential Equations Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

  • 2)

    The general solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } \) is

  • 3)

    The solution of \(\frac{dy}{dx}+\)p(x)y=0 is

  • 4)

    The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

  • 5)

    If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\)When

12th Standard Maths - Applications of Integration Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx } \) is

  • 2)

    The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3xdx } \)

  • 3)

    The value of  \(\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx } \) is

  • 4)

    The value of \(\int _{ 0 }^{ a }{ { (\sqrt { { a }^{ 2 }-{ x }^{ 2 } } ) }^{ 2 } } dx\)

  • 5)

    The value of \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }xcosxdx } \) is

12th Standard Maths - Differentials and Partial Derivatives Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

  • 2)

    If f (x, y) = exy then \(\frac { { \partial }^{ 2 }f }{ \partial x\partial y } \) is equal to

  • 3)

    If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

  • 4)

    If g(x, y) = 3x2 - 5y + 2y, x(t) = et and y(t) = cos t, then \(\frac{dg}{dt}\) is equal to

  • 5)

    If f(x) = \(\frac{x}{x+1}\) then its differential is given by

12th Standard Maths - Application of Differential Calculus Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is \(\cfrac { 1 }{ 2 } \) cm

  • 2)

    Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

  • 3)

    The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?

  • 4)

    The tangent to the curve y2 - xy + 9 = 0 is vertical when 

  • 5)

    The value of the limit \(\\ \\ \\ \underset { x\rightarrow 0 }{ lim } \left( cotx-\cfrac { 1 }{ x } \right) \) 

12th Maths - Term II Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 3)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 4)

    The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

  • 5)

    The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

12th Standard Maths - Applications of Vector Algebra Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    \(\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0\) , then the value of \([\vec { a } ,\vec { b } ,\vec { c } ]\) is

  • 3)

    If \(\vec { a } =\hat { i } +\hat { j } +\hat { k } \)\(\vec { b } =\hat { i } +\hat { j } \)\(\vec { c } =\hat { i } \) and \((\vec { a } \times \vec { b } )\times\vec { c } \) = \(\lambda \vec { a } +\mu \vec { b } \) then the value of \(\lambda +\mu \) is

  • 4)

    Consider the vectors \(\vec { a } ,\vec { b } ,\vec { c } ,\vec { c } \) such that \((\vec { a } \times \vec { b } )\times (\vec { c } \times \vec { d } )\) = \(\vec { 0 } \) Let \({ P }_{ 1 }\) and \({ P }_{ 2 }\) be the planes determined by the pairs of vectors \(\vec { a } ,\vec { b } \) and \(\vec { c } ,\vec { d } \) respectively. Then the angle between \({ P }_{ 1 }\) and \({ P }_{ 2 }\) is

  • 5)

    If \(\vec { a } =2\hat { i } +3\hat { j } -\hat { k } ,\vec { b } =\hat { i } +2\hat { j } +5\hat { k } ,\vec { c } =3\hat { i } +5\hat { j } -\hat { k } \) then a vector perpendicular to \(\vec { a } \) and lies in the plane containing \(\vec { b } \) and \(\vec { c } \) is

12th Standard Maths - Two Dimensional Analytical Geometry-II Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The radius of the circle3x2+by2+4bx−6by+b2 =0 is

  • 3)

    The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
    2x+4y=3 is

  • 4)

    The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
    and x+2y=4 is

  • 5)

    If x+y=k is a normal to the parabola y2 =12x, then the value of k is

12th Standard Maths - Inverse Trigonometric Functions Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    sin−1(cos x)\(=\frac{\pi}{2}-x \) is valid for

  • 3)

    The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

  • 4)

    \({ sin }^{ -1 }\left( tan\frac { \pi }{ 4 } \right) -{ sin }^{ -1 }\left( \sqrt { \frac { 3 }{ x } } \right) =\frac { \pi }{ 6 } \).Then x is a root of the equation

  • 5)

    sin(tan-1x), |x|<1 ia equal to

12th Standard Maths - Theory of Equations Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 3)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

  • 4)

    For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has

  • 5)

    If x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

12th Maths - Applications of Vector Algebra Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Dot product of a vector with vector \(\overset { \wedge }{ 3i } -5\overset { \wedge }{ k } \)\(2\overset { \wedge }{ i } +7\overset { \wedge }{ j } \) and \(\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k } \) are respectively -1, 6 and 5. Find the vector.

  • 2)

    Find the Cartesian form of the equation of the plane \(\overset { \rightarrow }{ r } =\left( s-2t \right) \overset { \wedge }{ i } +\left( 3-t \right) \overset { \wedge }{ j } +\left( 2s+t \right) \overset { \wedge }{ k } \)

  • 3)

    Find the equation of the plane through the intersection of the planes lx-3y+ z-4 -0 and x - y + Z + 1 - 0 and perpendicular to the plane x + 2y - 3z + 6 = 0

  • 4)

    Find the angle between the line \(\frac { x-2 }{ 3 } =\frac { y-1 }{ -1 } =\frac { z-3 }{ 2 } \) and the plane 3x + 4y + z + 5 = 0

  • 5)

    If \(\overset { \rightarrow }{ a } =\overset { \wedge }{ i } -\overset { \wedge }{ j } ,\overset { \rightarrow }{ b } =\overset { \wedge }{ j } -\overset { \wedge }{ k } ,\overset { \rightarrow }{ c } =\overset { \wedge }{ k } -\overset { \wedge }{ i } \) then find \(\left[ \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ b } -\overset { \rightarrow }{ c } ,\overset { \rightarrow }{ c } -\overset { \rightarrow }{ a } \right] \)

12th Maths - Two Dimensional Analytical Geometry-II Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the circumference and area of the circle x2 +y2 - 2x + 5y + 7 = 0

  • 2)

    Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x2 +y2 - 64 = 0.

  • 3)

    Find the condition for the line lx + my + n = 0 is Rtangent to the circle x2 + y2 = a2

  • 4)

    Find the area of th triangle found by the Unel Joining the vertex of the parabola x2 = -36y to the ends of the latus rectum.

  • 5)

    Find the equatlon of the ellipse whose e = \(\frac34\), foci ony-axl ,centre at origin and passing through (6,4).

12th Maths - Inverse Trigonometric Functions Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Prove that \({ cos }^{ -1 }\left( \cfrac { 4 }{ 5 } \right) +{ tan }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) ={ tan }^{ -1 }\left( \cfrac { 27 }{ 11 } \right) \)

  • 2)

    Evaluate \(cos\left[ { sin }^{ -1 }\cfrac { 3 }{ 5 } +{ sin }^{ -1 }\cfrac { 5 }{ 13 } \right] \)

  • 3)

    Prove that \({ tan }^{ -1 }\left( \cfrac { m }{ n } \right) -{ tan }^{ -1 }\left( \cfrac { m-n }{ m+n } \right) =\cfrac { \pi }{ 4 } \)
     

  • 4)

    Solve: \({ tan }^{ -1 }\left( \cfrac { x-1 }{ x-2 } \right) +{ tan }^{ -1 }\left( \cfrac { x+1 }{ x+2 } \right) =\cfrac { \pi }{ 4 } \)

  • 5)

    Solve \({ tan }^{ -1 }\left( \cfrac { 2x }{ 1-{ x }^{ 2 } } \right) +{ cot }^{ -1 }\left( \cfrac { 1-{ x }^{ 2 } }{ 2x } \right) =\cfrac { \pi }{ 3 } ,x>0\)

12th Maths - Theory of Equations Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If α, β, and γ are the roots of the polynomial equation ax3+bx2+cx+d=0 , find the value of \(\Sigma \frac { \alpha }{ \beta \gamma } \) in terms of the coefficients.

  • 2)

    If p and q are the roots of the equation lx2+nx+n = 0, show that \(\sqrt { \frac { p }{ q } } +\sqrt { \frac { q }{ p } } +\sqrt { \frac { n }{ l } } \)=0.

  • 3)

    If the equations x2+px+q= 0 and x2+p'x+q'= 0 have a common root, show that it must  be equal to \(\frac { pq'-p'q }{ q-q' } \) or \(\frac { q-q' }{ p'-p } \).

  • 4)

    Solve the equation 9x-36x2+44x-16=0 if the roots form an arithmetic progression.

  • 5)

    Solve the equation 3x3-26x2+52x-24=0 if its roots form a geometric progression.

12th Maths - Complex Numbers Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Explain the falacy:

  • 2)

    Find the circle roots of -27.

  • 3)

    Find the principal value of -2i.

  • 4)

    Show that \(\left| \frac { z-3 }{ z+3 } \right| \) = 2 represent a circle.

  • 5)

    Show that the complex numbers 3 + 2i, 5i, -3 + 2i and -i form a square.

12th Maths - Application of Matrices and Determinants Three Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\frac { 1 }{ 9 } \left[ \begin{matrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{matrix} \right] \), prove that A−1 = AT.

  • 2)

    If A = \(\left[ \begin{matrix} 8 & -4 \\ -5 & 3 \end{matrix} \right] \), verify that A(adj A) = |A|I2.

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)-1 = B-1A-1

  • 4)

    Decrypt the received encoded message \(\left[ \begin{matrix} 2 & -3 \end{matrix} \right] \left[ \begin{matrix} 20 & 4 \end{matrix} \right] \) with the encryption matrix \(\left[ \begin{matrix} -1 & -1 \\ 2 & 1 \end{matrix} \right] \)
    and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 - 26 to the letters A - Z respectively, and the number 0 to a blank space.

  • 5)

    Find the rank of the following matrices by row reduction method:
    \(\left[ \begin{matrix} 1 \\ \begin{matrix} 3 \\ \begin{matrix} 1 \\ 1 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} -1 \\ \begin{matrix} -2 \\ -1 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} -1 \\ \begin{matrix} 2 \\ \begin{matrix} 3 \\ 1 \end{matrix} \end{matrix} \end{matrix} \right] \)

12th Standard Maths - Complex Numbers Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

  • 2)

    The solution of the equation |z|-z=1+2i is

  • 3)

    If \(\cfrac { z-1 }{ z+1 } \) is purely imaginary, then |z| is

  • 4)

    If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is

  • 5)

    If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| \)

12th Maths- Application of Matrices and Determinants Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 3)

    If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

  • 4)

    If ρ(A) = ρ([A | B]), then the system AX = B of linear equations is

  • 5)

    If A = \(\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] \), then adj(adj A) is

12th Maths Quarterly Exam Question Paper 2019 - by Satyadevi - Tiruchirappalli View & Read

12th Maths - Term 1 Model Question Paper - by Meera - Namakkal View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

  • 3)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 4)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

  • 5)

    If sin-1 x+sin-1 y+sin-1 z=\(\frac{3\pi}{2}\), the value of x2017+y2018+z2019\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

12th Maths - Term 1 Five Mark Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A2 - 3A - 7I2 = O2. Hence find A−1.

  • 2)

    If ax2 + bx + c is divided by x + 3, x − 5, and x − 1, the remainders are 21,61 and 9 respectively. Find a,b and c. (Use Gaussian elimination method.)

  • 3)

    Solve the system: x + y − 2z = 0, 2x − 3y + z = 0, 3x − 7y + 10z = 0, 6x − 9y + 10z = 0.

  • 4)

    Solve the following systems of linear equations by Cramer’s rule:
     3x + 3y − z = 11, 2x − y + 2z = 9, 4x + 3y + 2z = 25.

  • 5)

    Solve the equation z3+27=0 .

12th Maths - Applications of Vector Algebra Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the parametric form of vector equation and Cartesian equations of the straight line passing through the point (−2,3, 4) and parallel to the straight line \(\frac { x-1 }{ -4 } =\frac { y-3 }{ 5 } =\frac { z-8 }{ 6 } \)

  • 2)

    Find the vector and Cartesian equations of the plane passing through the point with position vector \(4\hat { i } +2\hat { j } -3\hat { k } \) and normal to vector \(2\hat { i } -\hat { j } +\hat { k } \)

  • 3)

    A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the coordinate axes is a constant. Show that the plane passes through a fixed point

  • 4)

    Find the vector and Cartesian equations of the plane passing through the point with position vector \(2\hat { i } +6\hat { j } +3\hat { k } \) and normal to the vector \(\hat { i } +3\hat { j } +5\hat { k } \)

  • 5)

    A plane passes through the point (−1,1, 2) and the normal to the plane of magnitude \(3\sqrt { 3 } \) makes equal acute angles with the coordinate axes. Find the equation of the plane.

12th Maths - Two Dimensional Analytical Geometry II Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    Find the general equation of a circle with centre(-3,-4) and radius 3 units.

  • 2)

    Find the general equation of the circle whose diameter is the line segment joining the points (−4,−2)and (1,1).

  • 3)

    Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

  • 4)

    Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

  • 5)

    Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

12th Maths - Inverse Trigonometric Functions Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    State the reason for cos-1\([cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.\)

  • 2)

    Is cos-1(-x)=\(\pi\)-cos−1(x) true? Justify your answer.

  • 3)

    Find the principal value of cos-1\((\frac{1}{2})\).

  • 4)

    Find the value of sec−1\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

  • 5)

    If cot-1\(\frac{1}{7}=\theta\), find the value of cos\(\theta\).
     

12th Maths - Theory of Equations Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

  • 2)

    Find the monic polynomial equation of minimum degree with real coefficients having 2-\(\sqrt{3}\)i as a root.

  • 3)

    Find a polynomial equation of minimum degree with rational coefficients, having 2+\(\sqrt{3}\)i as a root.

  • 4)

    Find a polynomial equation of minimum degree with rational coefficients, having 2i+3 as a root.

  • 5)

    Show that the polynomial 9x9+2x5-x4-7x2+2 has at least six imaginary roots.

12th Maths - Complex Numbers Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If z=x+iy, find the following in rectangular form.
    \(Re\left( \cfrac { 1 }{ z } \right) \)

  • 2)

    Represent the complex number −1−i

  • 3)

    Write the following in the rectangular form:
    \(\cfrac { 10-5i }{ 6+2i } \)

  • 4)

    Find the square roots of −6+8i

  • 5)

    Obtain the Cartesian form of the locus of z=x+iy in
    \(\overline { z } =2^{ -1 }\)

12th Maths Unit 1 Application of Matrices and Determinants Two Marks Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \) is non-singular, find A−1.

  • 2)

    If adj A = \(\left[ \begin{matrix} -1 & 2 & 2 \\ 1 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] \), find A−1.

  • 3)

    Find the rank of the following matrices which are in row-echelon form :
    \(\left[ \begin{matrix} 2 & 0 & -7 \\ 0 & 3 & 1 \\ 0 & 0 & 1 \end{matrix} \right] \)

  • 4)

    Find the rank of the following matrices by minor method:
    \(\left[ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 8 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 2 \\ 1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ 0 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 3 \\ 2 \end{matrix} \end{matrix} \right] \)

  • 5)

    Find the rank of the following matrices which are in row-echelon form :
    \(\left[ \begin{matrix} 6 \\ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} 0 \\ \begin{matrix} 2 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} -9 \\ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix} \right] \)

12th Maths Quarterly Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

  • 3)

    If xayb = em, xcyd = en, Δ1 = \(\left| \begin{matrix} m & b \\ n & d \end{matrix} \right| \), Δ2 = \(\left| \begin{matrix} a & m \\ c & n \end{matrix} \right| \), Δ3 = \(\left| \begin{matrix} a & b \\ c & d \end{matrix} \right| \), then the values of x and y are respectively,

  • 4)

    If AT is the transpose of a square matrix A, then

  • 5)

    If \(\rho\)(A) = \(\rho\)([A/B]) = number of unknowns, then the system is

TN 12th Standard Maths Official Model Question Paper 2019 - 2020 - by Satyadevi - Tiruchirappalli View & Read

unit test - by Maths TAMILMedium - New syllabus 2019 View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 5)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

12th Standard Maths Unit 6 Applications of Vector Algebra Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between

  • 4)

    If \(\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c } \) where \(\vec { a } ,\vec { b } ,\vec { c } \) are any three vectors such that \(\vec { a } ,\vec { b } \) \(\neq \) 0 and  \(\vec { a } .\vec { b } \) \(\neq \) 0 then \(\vec { a } \) and \(\vec { c } \) are

  • 5)

    The angle between the line \(\vec { r } =(\hat { i } +2\hat { j } -3\hat { k } )+t(2\hat { i } +\hat { j } -2\hat { k } )\) and the plane \(\vec { r } .(\hat { i } +\hat { j } )+4=0\) is

12th Maths - Two Dimensional Analytical Geometry-II Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The radius of the circle3x2+by2+4bx−6by+b2 =0 is

  • 3)

    If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
    is

  • 4)

    The ellipse E1\(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

  • 5)

    Tangents are drawn to the hyperbola  \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

12th Standard Maths - Theory of Equations Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

  • 2)

    According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

  • 3)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 4)

    The polynomial x3+2x+3 has

  • 5)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

12th Standard Maths - Inverse Trigonometric Functions Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    If cot−1x=\(\frac{2\pi}{5}\) for some x\(\in\)R, the value of tan-1 x is

  • 3)

    The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

  • 4)

    \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

  • 5)

    If the function f(x)sin-1(x2-3), then x belongs to

12th Standard Maths Unit 2 Complex Numbers Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 
     

  • 2)

    If |z-2+i|≤2, then the greatest value of |z| is

  • 3)

    If |z|=1, then the value of \(\cfrac { 1+z }{ 1+\overline { z } }\) is

  • 4)

    If |z1|=1,|z2|=2|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is 

  • 5)

    The principal argument of \(\cfrac { 3 }{ -1+i } \)

12th Standard Maths Unit 1 Application of Matrices and Determinants Book Back Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 5)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

12th Standard Maths Unit 3 Theory of Equations One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

  • 3)

    A polynomial equation in x of degree n always has

  • 4)

    If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

  • 5)

    The quadratic equation whose roots are ∝ and β is

12th Standard Maths Unit 2 Complex Numbers One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    in+in+1+in+2+in+3 is

  • 2)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 3)

    The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

  • 4)

    The principal value of the amplitude of (1+i) is

  • 5)

    The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\)  is a positive integer is

12th Standard Maths - Application of Matrices and Determinants One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 2)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) then the value of a23 is

  • 4)

    Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

  • 5)

    If AT is the transpose of a square matrix A, then

12th Standard Physics Unit 6 Applications of Vector Algebra One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } =\hat { i } +\hat { j } +\hat { k } \)\(\vec { b } =\hat { i } +\hat { j } \)\(\vec { c } =\hat { i } \) and \((\vec { a } \times \vec { b } )\times\vec { c } \) = \(\lambda \vec { a } +\mu \vec { b } \) then the value of \(\lambda +\mu \) is

  • 4)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are non-coplanar, non-zero vectors such that \([\vec { a } ,\vec { b } ,\vec { c } ]\) = 3, then \({ \{ [\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a } }]\} ^{ 2 }\) is equal to

  • 5)

    The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is

12th Physics Chapter 5 Two Dimensional Analytical Geometry-II One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The radius of the circle3x2+by2+4bx−6by+b2 =0 is

  • 3)

    The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

  • 4)

    Equation of tangent at (-4, -4) on x2 = -4y is

  • 5)

    y2 - 2x - 2y + 5 = 0 is a

12th Standard Physics Chapter 4 Inverse Trigonometric Functions One Mark Question and Answer - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    \({ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 } \)is equal to

  • 3)

    If sin-1 x+sin-1 y+sin-1 z=\(\frac{3\pi}{2}\), the value of x2017+y2018+z2019\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

  • 4)

    If \({ sin }^{ -1 }x-cos^{ -1 }x=\cfrac { \pi }{ 6 } \) then

  • 5)

    The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \) 

12th Physics Unit 2 Theory of Equations One Mark Question with Answer Key - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

  • 2)

    The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

  • 3)

    If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

  • 4)

    The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

  • 5)

    If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

12th Maths Chapter 2 Complex Numbers One Mark Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 2)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

  • 3)

    If |z-2+i|≤2, then the greatest value of |z| is

  • 4)

    If |z|=1, then the value of \(\cfrac { 1+z }{ 1+\overline { z } }\) is

  • 5)

    The solution of the equation |z|-z=1+2i is

Unit test 12th Standard Maths New syllabus - by Maths TAMILMedium - New syllabus 2019 View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 2)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

  • 3)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

  • 4)

    If (AB)-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B-1 = 

  • 5)

    If ATA−1 is symmetric, then A2 =

12th Maths Chapter 1 Application of Matrices and Determinants One Mark Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

  • 4)

    If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

  • 5)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

12th Maths Quarterly Exam Model Two Marks Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \) is non-singular, find A−1.

  • 2)

    Reduce the matrix \(\left[ \begin{matrix} 3 & -1 & 2 \\ -6 & 2 & 4 \\ -3 & 1 & 2 \end{matrix} \right] \) to a row-echelon form.

  • 3)

    Find the rank of the following matrices by minor method:
    \(\left[ \begin{matrix} 1 & -2 & 3 \\ 2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right] \)

  • 4)

    Simplify \(\left( \cfrac { 1+i }{ 1-i } \right) ^{ 3 }-\left( \cfrac { 1-i }{ 1+i } \right) ^{ 3 }\)

  • 5)

    Represent the complex number −1−i

12th Maths Unit 6 Applications of Vector Algebra Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If a vector \(\vec { \alpha } \) lies in the plane of \(\vec { \beta } \) and \(\vec { \gamma } \) , then

  • 2)

    If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

  • 3)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between

  • 4)

    The angle between the lines \(\frac { x-2 }{ 3 } =\frac { y+1 }{ -2 } \), z=2 and \(\frac { x-1 }{ 1 } =\frac { 2y+3 }{ 3 } =\frac { z+5 }{ 2 } \)

  • 5)

    Distance from the origin to the plane 3x - 6y + 2z 7 = 0 is

12th Standard Maths Quarterly Exam Model One Mark Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 3)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 4)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 5)

    If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

Plus 2 Maths Chapter 5 Two Dimensional Analytical Geometry - II Model Questions - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

  • 2)

    The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

  • 3)

    If x+y=k is a normal to the parabola y2 =12x, then the value of k is

  • 4)

    Equation of tangent at (-4, -4) on x2 = -4y is

  • 5)

    y2 - 2x - 2y + 5 = 0 is a

12th Standard Maths First Mid Term Model Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 2)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

  • 3)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 4)

    The value of (1+i)4 + (1-i)4 is

  • 5)

    The value of \(\frac { (cos{ 45 }^{ 0 }+isin{ 45 }^{ 0 })^{ 2 }(cos{ 30 }^{ 0 }-isin{ 30 }^{ 0 }) }{ cos{ 30 }^{ 0 }+isin{ 30 }^{ 0 } } \) is

11th Standard Mathematics Chapter 4 Inverse Trigonometric Functions Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of sin-1 (cos x),0\(\le x\le\pi\) is

  • 2)

    If sin-1 x+sin-1 y=\(\frac{2\pi}{3};\)then cos-1x+cos-1 y is equal to

  • 3)

    \({ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 } \)is equal to

  • 4)

    If \(\alpha ={ tan }^{ -1 }\left( tan\cfrac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\cfrac { 2\pi }{ 3 } \right) \) then

  • 5)

    The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi \) is

12th Standard Maths Chapter 3 Theory of Equations Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    A zero of x3 + 64 is

  • 2)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

  • 3)

    If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

  • 4)

    The polynomial x3+2x+3 has

  • 5)

    Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

Model MID-TERM - by MUTHU M View & Read

Model MID-TERM - by MUTHU M View & Read

12th Maths Unit 2 Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

  • 2)

    If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

  • 3)

    z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

  • 4)

    If z1, z2, z3 are the vertices of a parallelogram, then the fourth vertex z4 opposite to z2 is _____

  • 5)

    If xr=\(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x1, x2 ... x is

Slip Test Unit 3 (A2) - by MUTHU M View & Read

  • 1)

    Find the sum of squares of roots of the equation 2x4-8x+6x2-3=0.

  • 2)

    If α, β, γ  and \(\delta\) are the roots of the polynomial equation 2x4+5x3−7x2+8=0 , find a quadratic equation with integer coefficients whose roots are α + β + γ + \(\delta\) and αβ૪\(\delta\).

  • 3)

    Find a polynomial equation of minimum degree with rational coefficients, having \(\sqrt{5}\)\(\sqrt{3}\) as a root.

  • 4)

    Solve: (2x-1)(x+3)(x-2)(2x+3)+20=0

  • 5)

    Solve the equation 3x3-26x2+52x-24=0 if its roots form a geometric progression.

slip test - by MUTHU M View & Read

  • 1)

    Find the sum of squares of roots of the equation 2x4-8x+6x2-3=0.

  • 2)

    If the equations x2+px+q= 0 and x2+p'x+q'= 0 have a common root, show that it must  be equal to \(\frac { pq'-p'q }{ q-q' } \) or \(\frac { q-q' }{ p'-p } \).

  • 3)

    A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

  • 4)

    If α and β are the roots of the quadratic equation 17x2+43x−73 = 0 , construct a quadratic equation whose roots are α + 2 and β + 2.

  • 5)

    If α and β are the roots of the quadratic equation 2x2−7x+13 = 0 , construct a quadratic equation whose roots are α2 and β2.

Weekly test-1:JUNE2019 - by MUTHU M View & Read

  • 1)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 2)

    If A is a non-singular matrix such that A-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (AT)−1 =

  • 3)

    If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

  • 4)

    If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is

  • 5)

    In a square matrix the minor Mij and the' co-factor Aij of and element aij are related by _____

12th Maths - Unit 1 Full Important Question Paper - by Satyadevi - Tiruchirappalli View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 5)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

frequently asked two marks in twelfth standard maths english medium - by Mythily View & Read

  • 1)

    For any 2 x 2 matrix, if A (adj A) =\(\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix} \right] \) then find |A|.

  • 2)

    For the matrix A, if A3 = I, then find A-1.

  • 3)

    If A is a square matrix such that A3 = I, then prove that A is non-singular.

  • 4)

    Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  • 5)

    Flod the rank of the matrix \(\left[ \begin{matrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{matrix} \right] \).

+2 english medium creative multiple choice questions in maths chapter one - by Mythily View & Read

  • 1)

    The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

  • 2)

    If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

  • 3)

    Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

  • 4)

    If AT is the transpose of a square matrix A, then

  • 5)

    The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

Important one mark questions 12th maths english medium chapter one - by Mythily View & Read

  • 1)

    If |adj(adj A)| = |A|9, then the order of the square matrix A is

  • 2)

    If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

  • 3)

    If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

  • 4)

    If A\(\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right] \), then A = 

  • 5)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

UNIT TEST - 1 - by Palanivel View & Read

  • 1)

    If F(\(\alpha\)) = \(\left[ \begin{matrix} \cos { \alpha } & 0 & \sin { \alpha } \\ 0 & 1 & 0 \\ -\sin { \alpha } & 0 & \cos { \alpha } \end{matrix} \right] \), show that [F(\(\alpha\))]-1 = F(-\(\alpha\)).

  • 2)

    If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A2 - 3A - 7I2 = O2. Hence find A−1.

  • 3)

    If A = \(\frac { 1 }{ 9 } \left[ \begin{matrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{matrix} \right] \), prove that A−1 = AT.

  • 4)

    If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)-1 = B-1A-1

  • 5)

    If adj(A) = \(\left[ \begin{matrix} 2 & -4 & 2 \\ -3 & 12 & -7 \\ -2 & 0 & 2 \end{matrix} \right] \), find A.