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12th Standard English Medium Maths Subject Book Back 1 Mark Questions with Solution Part -I

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    1 Marks

    25 x 1 = 25
  1. If |adj(adj A)| = |A|9, then the order of the square matrix A is

    (a)

    3

    (b)

    4

    (c)

    2

    (d)

    5

  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

    (a)

    15

    (b)

    12

    (c)

    14

    (d)

    11

  3. If A = \(\left[ \begin{matrix} \cos { \theta } & \sin { \theta } \\ -\sin { \theta } & \cos { \theta } \end{matrix} \right] \) and A(adj A) =  \(\left[ \begin{matrix} k & 0 \\ 0 & k \end{matrix} \right] \), then k =

    (a)

    0

    (b)

    sin θ

    (c)

    cos θ

    (d)

    1

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

    (a)

    0

    (b)

    2n

    (c)

    2n

    (d)

    n2

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

    (a)

    |z| = 1, arg(z) =\(\frac { \pi }{ 4 } \)

    (b)

    |z| = 1, arg(z) = \(\frac { \pi }{ 6 } \)

    (c)

    |z| = \(\frac { \sqrt { 3 } }{ 2 } \), arg(z) = \(\frac { 5\pi }{ 24 } \)

    (d)

    |z| = \(\frac { \sqrt { 3 } }{ 2 } \), arg (z) = tan-1\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

  6. If a = cos θ + i sin θ, then \(\frac { 1+a }{ 1-a } \) = ___________

    (a)

    cot \(\frac { \theta }{ 2 } \)

    (b)

    cot θ

    (c)

    i cot \(\frac { \theta }{ 2 } \)

    (d)

    i tan\(\frac { \theta }{ 2 } \)

  7. According to the rational root theorem, which number is not possible rational zero of 4x+ 2x- 10x- 5?

    (a)

    -1

    (b)

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

    (c)

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

    (d)

    5

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

    (a)

    2

    (b)

    4

    (c)

    1

    (d)

  9. The quadratic equation whose roots are ∝ and β is ___________

    (a)

    (x - ∝)(x -β) = 0

    (b)

    (x - ∝)(x + β) = 0

    (c)

    ∝ + β = \(\frac{b}{a}\)

    (d)

    ∝ β = \(\frac{-c}{a}\)

  10. If f(x) = 0 has n roots, then f'(x) = 0 has __________ roots

    (a)

    n

    (b)

    n -1

    (c)

    n+1

    (d)

    (n-r)

  11. If \({ sin }^{ -1 }x-cos^{ -1 }x=\frac { \pi }{ 6 } \) then ___________

    (a)

    \(\frac { 1 }{ 2 } \)

    (b)

    \(\frac { \sqrt { 3 } }{ 2 } \)

    (c)

    \(\frac { -1 }{ 2 } \)

    (d)

    none of these

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

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    none

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

    (a)

    \([\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]\) = 1

    (b)

    \([\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]\) = -1

    (c)

    \([\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]\) = 0

    (d)

    \([\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]\) = 2

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

    (a)

    \(\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right| \)

    (b)

    \(\frac{1}{3}\)\(\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right| \)

    (c)

    1

    (d)

    -1

  15. 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 \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\overset { \rightarrow }{ p } +\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) .\overset { \rightarrow }{ q } +\left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) .\overset { \rightarrow }{ r } \)= ____________

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  16. 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 __________

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    \(\infty\)

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

    (a)

    t = 0

    (b)

    \(\\ \\ \\ t=\cfrac { 1 }{ 3 } \)

    (c)

    t =1

    (d)

    t = 3

  18. 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

    (a)

    2

    (b)

    2.5

    (c)

    3

    (d)

    3.5

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

    (a)

    <b

    (b)

    ≤b

    (c)

    =b

    (d)

    ≠b

  20. If \(u(x, y)=e^{x^{2}+y^{2}}\),then \(\frac { \partial u }{ \partial x } \) is equal to

    (a)

    \(e^{x^{2}+y^{2}}\)

    (b)

    2xu

    (c)

    x2u

    (d)

    y2u

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

    (a)

    ex + ey

    (b)

    \(\frac{1}{e^x + e^y}\)

    (c)

    2

    (d)

    1

  22. If \(\int _{ 0 }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } } \) then a is

    (a)

    4

    (b)

    1

    (c)

    3

    (d)

    2

  23. The order and degree of the differential equation \(\sqrt { sinx } (dx+dy)=\sqrt { cos x } (dx-dy)\) is

    (a)

    1, 2

    (b)

    2, 2

    (c)

    1, 1

    (d)

    2, 1

  24. A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
    \(f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0< x < l \\ 0 & l <x<2l \end{array}\right.\)
    The mean and variance of the shorter of the two pieces are respectively.

    (a)

    \(\frac { l }{ 2 } ,\frac { { l }^{ 2 } }{ 3 } \)

    (b)

    \( \frac { l }{ 2 } ,\frac { { l }^{ 2 } }{ 6 } \)

    (c)

    \(l,\frac { { l }^{ 2 } }{ 12 } \)

    (d)

    \(\frac { l }{ 2 } ,\frac { { l }^{ 2 } }{ 12 } \)

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

    (a)

    commutative but not associative

    (b)

    associative but not commutative

    (c)

    both commutative and associative

    (d)

    neither commutative nor associative

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