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Sample 1 Mark Book Back Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 20

    Part A

    20 x 1 = 20
  1. If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

    (a)

    \(\frac { 1 }{ 3 } \)

    (b)

    \(\frac { 1 }{ 9 } \)

    (c)

    \(\frac { 1 }{ 4 } \)

    (d)

    1

  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 = 

    (a)

    \(\left[ \begin{matrix} 2 & -5 \\ -3 & 8 \end{matrix} \right] \)

    (b)

    \(\left[ \begin{matrix} 8 & 5 \\ 3 & 2 \end{matrix} \right] \)

    (c)

    \(\left[ \begin{matrix} 3 & 1 \\ 2 & 1 \end{matrix} \right] \)

    (d)

    \(\left[ \begin{matrix} 8 & -5 \\ -3 & 2 \end{matrix} \right] \)

  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

    (a)

    \(\frac { -4 }{ 5 } \)

    (b)

    \(\frac { -3 }{ 5 } \)

    (c)

    \(\frac { 3 }{ 5 } \)

    (d)

    \(\frac { 4 }{ 5 } \)

  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

    (a)

    Only (i)

    (b)

    (ii) and (iii)

    (c)

    (iii) and (iv)

    (d)

    (i), (ii) and (iv)

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

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

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

    (a)

    -2

    (b)

    -1

    (c)

    1

    (d)

    2

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

    (a)

    2

    (b)

    4

    (c)

    1

    (d)

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

    (a)

    \(\frac{-\pi}{10}\)

    (b)

    \(\frac{\pi}{5}\)

    (c)

    \(\frac{\pi}{10}\)

    (d)

    \(-\frac{\pi}{5}\)

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

    (a)

    tan2\(\alpha\)

    (b)

    0

    (c)

    -1

    (d)

    tan2\(\alpha\)

  10. 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) .

    (a)

    \(\frac { 6 }{ 5 } \)

    (b)

    \(\frac { 5 }{ 3 } \)

    (c)

    \(\frac { 10 }{ 5 } \)

    (d)

    \(\frac { 3 }{ 5 } \)

  11. The circle passing through(1,-2) and touching the axis of x at (3,0) passing through the point

    (a)

    (-5,2)

    (b)

    (2,-5)

    (c)

    (5,-2)

    (d)

    (-2,5)

  12. 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

    (a)

    \(\frac { \pi }{ 6 } \)

    (b)

    \(\frac { \pi }{ 4 } \)

    (c)

    \(\frac { \pi }{ 3 } \)

    (d)

    \(\frac { \pi }{ 2 } \)

  13. 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, 

    (a)

    8 cubic units

    (b)

    512 cubic units

    (c)

    64 cubic units

    (d)

    24 cubic units

  14. 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.

    (a)

    \(\cfrac { 3 }{ 25 } radians/sec\)

    (b)

    \(\cfrac { 4 }{ 25 } radians/sec\)

    (c)

    \(\cfrac { 1 }{ 5 } radians/sec\)

    (d)

    \(\cfrac { 1 }{ 3 } radians/sec\)

  15. The maximum slope of the tangent to the curve y = t:r sin x, x ∈ [0, 2π] is at

    (a)

    \(x=\cfrac { \pi }{ 4 } \)

    (b)

    \(x=\cfrac { \pi }{ 2 } \)

    (c)

    \(x=\pi \)

    (d)

    \(x=\cfrac { 3\pi }{ 2 } \)

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

    (a)

    0.3xdx m3

    (b)

    0.03 xm3

    (c)

    0.03.x2 m3

    (d)

    0.03x3m3

  17. 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

    (a)

    3

    (b)

    6

    (c)

    9

    (d)

    5

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

    (a)

    \(y={ ce }^{ \int { pdx } }\)

    (b)

    \(y={ ce }^{ -\int { pdx } }\)

    (c)

    \(x={ ce }^{ -\int { pdx } }\)

    (d)

    \(x{ce }^{ \int { pdx } }\)

  19. 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

    (a)

    \(\cfrac { 19 }{ 6 } \)

    (b)

    \(-\cfrac { 19 }{ 6 } \)

    (c)

    \(\cfrac { 3 }{ 2 } \)

    (d)

    \(-\cfrac { 3 }{ 2 } \)

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

    (a)

    Q+

    (b)

    Z

    (c)

    R

    (d)

    C

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