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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12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - 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)

    in+in+1+in+2+in+3 is

  • 4)

    A zero of x3 + 64 is

  • 5)

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

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - 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 the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

  • 3)

    If A is a non-singular matrix then IA-1|= ______

  • 4)

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

  • 5)

    The principal value of the amplitude of (1+i) is

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Two - 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)

    The rank of the matrix \(\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right] \) is

  • 3)

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

  • 4)

    In a homogeneous system if \(\rho\) (A) =\(\rho\)([A|0]) < the number of unknouns then the system has ________

  • 5)

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

12th Standard Maths English Medium Free Online Test Book Back 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 = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 3)

    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

  • 4)

    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

  • 5)

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

12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - 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)

    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

  • 3)

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

  • 4)

    \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

  • 5)

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

12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Two - 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 \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 
     

  • 3)

    The polynomial x3+2x+3 has

  • 4)

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

  • 5)

    The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point (2,3) .

12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Two - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If sin-1 x+cot-1\((\frac{1}{2})=\frac{\pi}{2}\), then x is equal to

  • 2)

    The eccentricity of the ellipse (x−3)2 +(y−4)2 =\(\frac { { y }^{ 2 } }{ 9 } \) is

  • 3)

    The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

  • 4)

    The maximum value of the function x2 e-2x,

  • 5)

    If w (x, y, z) = x2 (v - z) + y2 (z - x) + z2(x - y), then \(\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z } \) is

12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Three - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    Let C be the circle with centre at(1,1) and radius =1. If T is the circle centered at(0, y)
    passing through the origin and touching the circleC externally, then the radius of T is equal to

  • 2)

    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

  • 3)

    If the distance of the point (1,1,1) from the origin is half of its distance from the plane x + y + z + k =0, then the values of k are

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    The principal value of the amplitude of (1+i) is

  • 3)

    If xr=\(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x1, x2 ... x is

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Three - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

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

  • 3)

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

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

  • 2)

    If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA−1 =A, then λ is

  • 3)

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

  • 4)

    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

  • 5)

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

12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Two - 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 a = 1+i, then a2 equals

  • 3)

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

  • 4)

    ·If \(\alpha ={ tan }^{ -1 }\left( \cfrac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \cfrac { 2x-y }{ \sqrt { 3y } } \right) \) then \(\alpha -\beta \)

  • 5)

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

12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Two - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2. is inconsistent then k is

  • 2)

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

  • 3)

    (1+i)3 = ______

  • 4)

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

  • 5)

    If u = yx then \(\frac { \partial u }{ \partial y } \) = ............

12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Three - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if

  • 2)

    The principal value of the amplitude of (1+i) is

  • 3)

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

  • 4)

    If tan-1(3)+tan-1(x)=tan-1(8)then x= 

  • 5)

    The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is

12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Three - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    Which of the following is not an elementary transformation?

  • 2)

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

  • 3)

    If z1, z2, z3 are the vertices of a parallelogram, then the fourth vertex z4 opposite to z2 is _____

  • 4)

    If ∝, β,૪ are the roots of 9x3-7x+6=0, then ∝ β ૪ 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 Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Four - 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 a = 1+i, then a2 equals

  • 3)

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

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Four - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If ATA−1 is symmetric, then A2 =

  • 2)

    Every homogeneous system ______

  • 3)

    If A is a non-singular matrix then IA-1|= ______

  • 4)

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

  • 5)

    If x + y = 8, then the maximum value of xy is _________

12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Five - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| =

  • 3)

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

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Five - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

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

  • 3)

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

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Volume 1 One Mark Questions 2020 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    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

  • 3)

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

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test Volume 1 One Mark Questions with Answer Key 2020 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    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

  • 3)

    If A is a non-singular matrix then IA-1|= ______

  • 4)

    The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

  • 5)

    If \(\omega \neq 1\) is a cubic root of unity and \(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & { -\omega }^{ 2 } & { \omega }^{ 2 } \\ 1 & { \omega }^{ 2 } & { \omega }^{ 2 } \end{matrix} \right| \) =3k, then k is equal to 

12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions 2020 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    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 ?

  • 2)

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

  • 3)

    In LMV theorem, we have f'(x1) =\(\frac { f(b)-f(a) }{ b-a } \) then a < x1 _________

  • 4)

    If the curves y = 2ex and y =ae-x intersect orthogonally, then a = _________

  • 5)

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

12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 2020 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    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 ?

  • 2)

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

  • 3)

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

  • 4)

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

  • 5)

    If loge4 = 1.3868, then loge4.01 =

12th Standard Maths Application of Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 3)

    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

  • 4)

    If A, B and C are invertible matrices of some order, then which one of the following is not true?

  • 5)

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

12th Standard Maths Application of Matrices and Determinants English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - 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 = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) 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

  • 3)

    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 = 

  • 4)

    If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA−1 =A, then λ is

  • 5)

    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

12th Standard Maths Complex Numbers English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    in+in+1+in+2+in+3 is

  • 2)

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

  • 3)

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

  • 4)

    z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

  • 5)

    The principal argument of (sin 40°+i cos40°)5 is

12th Standard Maths Complex Numbers English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - 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)

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

    The value of \(\left( \cfrac { 1+3\sqrt { i } }{ 1-\sqrt { 3i } } \right) ^{ 10 }\)

12th Standard Maths Theory of Equations English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    A zero of x3 + 64 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)

    Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

12th Standard Maths Theory of Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - 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)

    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)

    The quadratic equation whose roots are ∝ and β is

12th Standard Maths Inverse Trigonometric Functions English Medium Free Online Test One Mark Questions 2020 - 2021 - 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)

    If x=\(\frac{1}{5}\), the valur of cos (cos-1x+2sin-1x) 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)

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

12th Standard Maths Inverse Trigonometric Functions English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - 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 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

  • 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)

    sin-1(2cos2x-1)+cos-1(1-2sin2x)=

12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions 2020 - 2021 - 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 equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
    2x+4y=3 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)

    The equation of the circle passing through the foci of the ellipse  \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\) 1having centre at
    (0,3) is

12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - 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 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)

    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

  • 4)

    Area of the greatest rectangle inscribed in the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.\) is

  • 5)

    The values of m for which the line y=mx+ \(2\sqrt { 5 } \) touches the hyperbola 16x2−9y2=144 are the roots of x2−(a+b)x−4=0, then the value of (a+b) is

12th Standard Maths Applications of Vector Algebra English Medium Free Online Test One Mark Questions 2020 - 2021 - 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 the volume of the parallelepiped with \(\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a } \)  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with \((\vec { a } \times \vec { b } )\times (\vec { b } \times \vec { c } ),(\vec { b } \times \vec { c } )\times (\vec { c } \times \vec { a } )\) and \((\vec { c } \times \vec { a } )\times (\vec { a } \times \vec { b } )\)as coterminous edges is, 

  • 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 Standard Maths Differentials and Partial Derivatives English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

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

  • 3)

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

  • 4)

    If the radius of the sphere is measured as 9 em with an error of 0.03 cm, the approximate error in calculating its volume is

  • 5)

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

12th Standard Maths Applications of Vector Algebra English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    If \(\vec { a } ,\vec { b } ,\vec { c } \) 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

  • 3)

    If the line \(\frac { x-2 }{ 3 } =\frac { y-1 }{ -5 }= \frac { x+2 }{ 2 } \) lies in the plane x + 3y + - αz + β = 0, then (α, β) is

  • 4)

    The vector equation \(\vec { r } =(\hat { i } -2\hat { j } -\hat { k } )+t(6\hat { i } -\hat { k) } \) represents a straight line passing through the points

  • 5)

    Let \(\overset { \rightarrow }{ a } \),\(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \) be three non- coplanar vectors and let \(\overset { \rightarrow }{ p } ,\overset { \rightarrow }{ q } ,\overset { \rightarrow }{ r } \) be the vectors defined by the relations \(\overset { \rightarrow }{ P } =\frac { \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ q } =\frac { \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ r } =\frac { \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } \) Then the value of  \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\overset { \rightarrow }{ p } +\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) .\overset { \rightarrow }{ q } +\left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) .\overset { \rightarrow }{ r } \)=

12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions 2020 - 2021 - 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)

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

  • 3)

    The number given by the Rolle's theorem for the functlon x3-3x2, x∈[0,3] is

  • 4)

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

  • 5)

    If a particle moves in a straight line according to s = t3-6t2-15t, the time interval during which the velocity is negative and acceleration is positive is

12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    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.

  • 2)

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

  • 3)

    The minimum value ofthe function |3-x|+9 is

  • 4)

    The point of inflection of the curve y = (x - 1)3 is

  • 5)

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

12th Standard Maths Differentials and Partial Derivatives English Medium Free Online Test One Mark Questions 2020 - 2021 - 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 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)

    The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

  • 4)

    If w (x, y, z) = x2 (v - z) + y2 (z - x) + z2(x - y), then \(\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z } \) is

  • 5)

    If y = x4 - 10 and if x changes from 2 to 1.99, the approximate change in y is

12th Standard Maths Applications of Integration English Medium Free Online Test One Mark Questions 2020 - 2021 - 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 \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

  • 3)

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

  • 4)

    If \(\int _{ a }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } } \)then a is

  • 5)

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

12th Standard Maths Applications of Integration English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    The value of \(\int _{ 0 }^{ \pi }{ \frac { dx }{ 1+{ 5 }^{ cos\ x } } } \) is

  • 3)

    The volume of solid of revolution of the region bounded by y2 = x(a − x) about x-axis is

  • 4)

    The value of \(\int _{ -1 }^{ 2 }{ |x|dx } \)

  • 5)

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

12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions 2020 - 2021 - 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 of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

  • 3)

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

  • 4)

    The degree of the differential equation y \(y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....\) is

  • 5)

    The solution of the differential equation \(\frac { dy }{ dx } +\frac { 1 }{ \sqrt { 1-{ x }^{ 2 } } } =0\)

12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

    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

  • 5)

    If sin x is the integrating factor of the linear differential equation \(\frac { dy }{ dx } +Pt=Q,\)Then P is

12th Standard Maths Probability Distributions English Medium Free Online Test One Mark Questions 2020 - 2021 - 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 random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

  • 3)

    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?

  • 4)

    Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with probability 0.5. Assume that the results of the flips are independent, and let X equal the total number of heads that result The value of E[X] is

  • 5)

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

12th Standard Maths Probability Distributions Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    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

  • 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)

    On a multiple-choice exam with 3 possible destructives for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is

  • 5)

    If X is a binomial randam variable with expected value 6 and variance 2.4, then P(X=5) is 

12th Standard Maths Discrete Mathematics English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    A binary operation on a set S is a function from

  • 2)

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

  • 3)

    If a*b=\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \) on the real numbers then * is

  • 4)

    Which one is the inverse of the statement (PVq)➝(pΛq)?

  • 5)

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

12th Standard Maths Discrete Mathematics Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    Subtraction is not a binary operation in

  • 2)

    If a compound statement involves 3 simple statements, then the number of rows in the truth table is

  • 3)

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

  • 4)

    The proposition p ∧ (¬p ∨ q) is

  • 5)

    If * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Three - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is

  • 2)

    The domain of cos-1(x2 - 4) is______

  • 3)

    The auxiliary circle of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 } \) = 1 is

  • 4)

    The locus of the point of intersection of perpendicular tangents of the parabola y2 = 4ax is

  • 5)

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

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Two - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

  • 2)

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

  • 3)

    In the system of liner equations with 3 unknowns If \(\rho\)(A) = \(\rho\)([A|B]) =1, the system has ________

  • 4)

    The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

  • 5)

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

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Three - 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, B and C are invertible matrices of some order, then which one of the following is not true?

  • 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 A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA−1 =A, then λ is

  • 5)

    The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Four - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    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

  • 2)

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

  • 3)

    When the eccentricity of a ellipse becomes zero, then it becomes a

  • 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)

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

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Four - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

  • 2)

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

  • 3)

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

  • 4)

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

  • 5)

    The value of tan \(\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right) \) is ______

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Five - 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)

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

  • 3)

    If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

  • 4)

    The circle x2+y2=4x+8y+5intersects the line3x−4y=m at two distinct points if

  • 5)

    The values of m for which the line y=mx+ \(2\sqrt { 5 } \) touches the hyperbola 16x2−9y2=144 are the roots of x2−(a+b)x−4=0, then the value of (a+b) is

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Five - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

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

  • 3)

    The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\)  is a positive integer is

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Six - 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)

    in+in+1+in+2+in+3 is

  • 3)

    If \(\alpha \) and \(\beta \) are the roots of x2+x+1=0, then \({ \alpha }^{ 2020 }+{ \beta }^{ 2020 }\) is

  • 4)

    If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| =

  • 5)

    lf the root of the equation x3 +bx2+cx-1=0 form an lncreasing G.P, then

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Six - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If ATA−1 is symmetric, then A2 =

  • 2)

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

  • 3)

    The product of all four values of \(\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }\) is

  • 4)

    If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

  • 5)

    If x=\(\frac{1}{5}\), the valur of cos (cos-1x+2sin-1x) is

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Seven - 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)

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

  • 3)

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

  • 4)

    The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\)  is a positive integer is

  • 5)

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

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Seven - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

  • 2)

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

  • 3)

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

  • 4)

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

  • 5)

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

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Eight - 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)

    Let A = \(\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right] \) and 4B = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right] \). If B is the inverse of A, then the value of x is

  • 3)

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

  • 4)

    If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| =0\)

  • 5)

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

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Eight - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If x=\(\frac{1}{5}\), the valur of cos (cos-1x+2sin-1x) is

  • 2)

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

  • 3)

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

  • 4)

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

  • 5)

    Area of the greatest rectangle inscribed in the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.\) is

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Nine - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

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

  • 2)

    If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| =0\)

  • 3)

    The equation tan-1 x-cot-1 x=tan-1\(\left( \frac { 1 }{ \sqrt { 3 } } \right) \)has

  • 4)

    In a \(\Delta ABC\)  if C is a right angle, then  \({ tan }^{ -1 }\left( \cfrac { a }{ b+c } \right) +{ tan }^{ -1 }\left( \cfrac { b }{ c+a } \right) =\) 

  • 5)

    If x = r cos θ, y = r sin, then \(\frac { \partial r }{ \partial x } \) = ....................

12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Nine - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    If ATA−1 is symmetric, then A2 =

  • 2)

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

  • 3)

    If a = 1+i, then a2 equals

  • 4)

    If z1, z2, z3 are the vertices of a parallelogram, then the fourth vertex z4 opposite to z2 is _____

  • 5)

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

12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Ten - by Satyadevi - Tiruchirappalli - View & Read

  • 1)

    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

  • 2)

    If A is a matrix of order m x n, then \(\rho\)(A) is

  • 3)

    If z=x+iy is a complex number such that |z+2|=|z−2|, then the locus of z is

  • 4)

    The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 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 English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Ten - 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 z is a complex number such that \(z\varepsilon C/R\quad \)and \(z+\cfrac { 1 }{ z } \epsilon R\) then|z| is

  • 3)

    \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

  • 4)

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

  • 5)

    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

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 \(\begin{matrix} lim \\ (x,y)\rightarrow (0,0) \end{matrix}\) 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.
    \(f(x)=|\frac{1}{x}|, x\in [-1,1]\)

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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