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12th Standard English Medium Maths Reduced syllabus One Mark Important Questions With Answer Key - 2021(Public Exam )

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Multiple Choice Questions


    50 x 1 = 50
  1. If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

    (a)

    A-1

    (b)

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

    (c)

    3A-1

    (d)

    2A-1

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

    (a)

    adj A = |A|A-1

    (b)

    adj(AB) = (adj A)(adj B)

    (c)

    det A-1 = (det A)-1

    (d)

    (ABC)-1 = C-1B-1A-1

  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 = 

    (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)

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

  4. If xayb = em, xcyd = en, Δ1 = \(\left| \begin{matrix} m & b \\ n & d \end{matrix} \right| \), Δ2 = \(\left| \begin{matrix} a & m \\ c & n \end{matrix} \right| \), Δ3 = \(\left| \begin{matrix} a & b \\ c & d \end{matrix} \right| \), then the values of x and y are respectively,

    (a)

    e21), e31)

    (b)

    log (Δ13), log (Δ23)

    (c)

    log (Δ21), log(Δ31)

    (d)

    e(Δ13),e(Δ23)

  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

    (a)

    Only (i)

    (b)

    (ii) and (iii)

    (c)

    (iii) and (iv)

    (d)

    (i), (ii) and (iv)

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

    (a)

    k ≠ 0

    (b)

    -1 < k < 1

    (c)

    -2 < k < 2

    (d)

    k=0

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

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

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

    (a)

    −110°

    (b)

    −70°

    (c)

    70°

    (d)

    110°

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

    (a)

    1

    (b)

    i

    (c)

    x2+y2

    (d)

    1+n2

  10. 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\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

  11. If zn =\(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z1, z2 ..... z6 is

    (a)

    1

    (b)

    -1

    (c)

    i

    (d)

    -i

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

    (a)

    -\(\frac { q }{ r } \)

    (b)

    \(\frac { p }{ r } \)

    (c)

    \(\frac { q }{ r } \)

    (d)

    -\(\frac { q }{ p } \)

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

    (a)

    -1

    (b)

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

    (c)

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

    (d)

    5

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

    (a)

    no solution

    (b)

    one solution

    (c)

    two solution

    (d)

    more than one solution

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

    (a)

    b2-4ac=0

    (b)

    b2 - 4ac <0

    (c)

    b2 - 4ac >0

    (d)

    b2 - 4ac≥0

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

    (a)

    [1,2]

    (b)

    [-1,1]

    (c)

    [0,1]

    (d)

    [-1,0]

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

    (a)

    \(-\sqrt { \frac { 24 }{ 25 } } \)

    (b)

    \(\sqrt { \frac { 24 }{ 25 } } \)

    (c)

    \(\frac{1}{5}\)

    (d)

    -\(\frac{1}{5}\)

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

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    infinte

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

    (a)

    4(a2+b2)

    (b)

    2(a2+b2)

    (c)

    a2 +b2

    (d)

    \(\frac { 1 }{ 2 } \)(a2+b2)

  20. 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

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    4

  21. 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)

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

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

    (a)

    0

    (b)

    1

    (c)

    6

    (d)

    3

  23. 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

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

    (a)

    \(\left| \overset { \rightarrow }{ d } \right| \)

    (b)

    \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)

    (c)

    \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ 0 } \)

    (d)

    a, b, c are coplanar

  25. The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is

    (a)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (b)

    \(\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \)

    (c)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (d)

    \({ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }\)

  26. The straight lines \(\frac { x-3 }{ 2 } =\frac { y+5 }{ 4 } =\frac { z-1 }{ -13 } \) and \(\frac { x+1 }{ 3 } =\frac { y-4 }{ 5 } =\frac { z+2 }{ 2 } \) are

    (a)

    parallel

    (b)

    perpendicular

    (c)

    inclined at 45o

    (d)

    none

  27. For any three vectors \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \)\(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) \times \left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) \) is

    (a)

    0

    (b)

    \(\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] \)

    (c)

    2\(\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] \)

    (d)

    \({ \left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] }^{ 2 }\)

  28. If \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are mutually 丄r unit vectors, then \(\left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right| \) is _______________ 

    (a)

    3

    (b)

    9

    (c)

    \(\sqrt { 3 } \)

    (d)

    \(\sqrt { 3 } \)

  29. 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)

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

  30. The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

    (a)

    -2

    (b)

    2

    (c)

    1

    (d)

    -1

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

    (a)

    \(\frac{1}{31}\)

    (b)

    \(\frac15\)

    (c)

    5

    (d)

    31

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

    (a)

     ex2+y2

    (b)

    2xu

    (c)

    x2u

    (d)

    y2u

  33. 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

    (a)

    9.72 cm3

    (b)

    0.972 cm3

    (c)

    0.972π cm3

    (d)

    9.72π cm3

  34. If loge4 = 1.3868, then loge4.01 =

    (a)

    1.3968

    (b)

    1.3898

    (c)

    1.3893

    (d)

    none

  35. The percentage error in the 11th root of the number 28 is approximately .......... times the percentage error in 28.

    (a)

    \(\frac{1}{28}\)

    (b)

    \(\frac{1}{11}\)

    (c)

    11

    (d)

    28

  36. If u = \((\frac{y}{x})\) then x \(x\frac { \partial u }{ \partial x } +y\frac { \partial u }{ \partial y } \) = .....................

    (a)

    0

    (b)

    1

    (c)

    2u

    (d)

    u

  37. If \(\int _{ 0 }^{ x }{ f(t)dt=x+\int _{ x }^{ 1 }{ tf } (t)dt } \) then the value of f (1) is

    (a)

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

    (b)

    2

    (c)

    1

    (d)

    \(\frac{3}{4}\)

  38. The area bounded by the parabola y = x2 and the line y = 2x is

    (a)

    \(\frac43\)

    (b)

    \(\frac23\)

    (c)

    \(\frac{51}{3}\)

    (d)

    \(\frac{30}{3}\)

  39. The area of the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\)

    (a)

    (b)

    36π

    (c)

    2

    (d)

    36π2

  40. The differential equation of the family of parabolas y2=4ax is

    (a)

    \(2y=x\left( \frac { dy }{ dx } \right) \)

    (b)

    \(y=2x\left( \frac { dy }{ dx } \right) \)

    (c)

    \(y={ 2x }^{ 2 }\left( \frac { dy }{ dx } \right) \)

    (d)

    \({ y }^{ 2 }=2x\left( \frac { dy }{ dx } \right) \)

  41. The general solution of \(4\frac{d^2 y}{dx^2}\)+y=0 is

    (a)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } +B\quad sin\frac { x }{ 2 } \right] \)

    (b)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } -B\quad sin\frac { x }{ 2 } \right] \)

    (c)

    \(y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 } \)

    (d)

    \(t={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }\)

  42. The I.F. of (1+y2)dx=(tan-1-t-x)dy is ________.

    (a)

    etan-1 y

    (b)

    etan-1 x

    (c)

    tan-1 y

    (d)

    tan-1x

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

    (a)

    \(\frac { dy }{ dx } =\frac { -x }{ y } \)

    (b)

    \(\frac { dy }{ dx } =\frac { -y }{ x } \)

    (c)

    \(\frac { dy }{ dx } =\frac { x }{ y } \)

    (d)

    \(\frac { dy }{ dx } =\frac { y }{ x } \)

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

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  45. The variance of a binomial distribution is________.

    (a)

    equal to its mean

    (b)

    less than its mean

    (c)

    greater than its mean

    (d)

    none

  46. If X is a continuous random variable then \(p(a<x<b)=\) ________

    (a)

    \(P(a<x<b)\)

    (b)

    \(P(a\le X\le b)\)

    (c)

    \(P\left( X>a \right) \)

    (d)

    \(1-P\left( X\le a-1 \right) \)

  47. A binary operation on a set S is a function from

    (a)

    S ⟶ S

    (b)

    (SxS) ⟶ S

    (c)

    S⟶ (SxS)

    (d)

    (SxS) ⟶ (SxS)

  48. The binary operation * defined on a set s is said to be commutative if

    (a)

    a*b \(\in \) S ∀ a, b \(\in \) S

    (b)

    a*b = b*a ∀ a, b \(\in \) S

    (c)

    (a*b) * c = a*(b*c) ∀ a, b \(\in \) S

    (d)

    a*b = e ∀ a, b \(\in \) S

  49. '+' is not a binary operation on

    (a)

    ~

    (b)

    z

    (c)

    c

    (d)

    Q- {0}

  50. Which of the following is a statement?

    (a)

    7+2<10

    (b)

    Wish you all success

    (c)

    All the best

    (d)

    How old are you?

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