12th Standard EM Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 12 Session 2019 - 2020
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Maths Question Papers

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

View all

TN Stateboard Education Study Materials

TN Stateboard Updated Class 12th Maths Syllabus

Application of Matrices and Determinants

Introduction - Inverse of a Non-Singular Square Matrix - Elementary Transformations of a Matrix - Applications of Matrices: Solving System of Linear Equations - Applications of Matrices: Consistency of system of linear equations by rank method

Complex Numbers

Introduction to Complex Numbers - Complex Numbers - Basic Algebraic Properties of Complex Numbers - Conjugate of a Complex Number - Modulus of a Complex Number - Geometry and Locus of Complex Numbers - Polar and Euler form of a Complex Number - de Moivre’s Theorem and its Applications

Theory of Equations

Introduction - Basics of Polynomial Equations - Vieta’s Formulae and Formation of Polynomial Equations - Nature of Roots and Nature of Coefficients of Polynomial Equations - Applications to Geometrical Problems - Roots of Higher Degree Polynomial Equations - Polynomials with Additional Information - Polynomial Equations with no additional information - Descartes Rule

Inverse Trigonometric Functions

Introduction - Some Fundamental Concepts - Sine Function and Inverse Sine Function - The Cosine Function and Inverse Cosine Function - The Tangent Function and the Inverse Tangent Function - The Cosecant Function and the Inverse Cosecant Function - The Secant Function and Inverse Secant Function - The Cotangent Function and the Inverse Cotangent Function - Principal Value of Inverse Trigonometric Functions - Properties of Inverse Trigonometric Functions

Two Dimensional Analytical Geometry-II

Introduction - Circle - Conics - Conic Sections - Parametric form of Conics - Tangents and Normals to Conics - Real life Applications of Conics

Applications of Vector Algebra

Introduction - Geometric Introduction to Vectors - Scalar Product and Vector Product - Scalar triple product - Vector triple product - Jacobi’s Identity and Lagrange’s Identity - Different forms of Equation of a Straight line - Different forms of Equation of a plane - Image of a point in a plane - Meeting point of a line and a plane

TN StateboardStudy Material - Sample Question Papers with Solutions for Class 12 Session 2019 - 2020

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