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Model 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 (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)

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

  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

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  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 
     

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

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

    (a)

    \(\cfrac { -5\pi }{ 6 } \)

    (b)

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

    (c)

    \(\cfrac { -3\pi }{ 4 } \)

    (d)

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

  5. 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)

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

  6. \({ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 } \)is equal to

    (a)

    2\(\pi\)

    (b)

    \(\pi\)

    (c)

    0

    (d)

    tan-1\(\frac{12}{65}\)

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

    (a)

    x2−x−6=0

    (b)

    x2−x−12=0

    (c)

    x2+x−12=0

    (d)

    x2+x−6=0

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

    (a)

    (4,7)

    (b)

    (7,4)

    (c)

    (9,4)

    (d)

    (4,9)

  9. The locus of a point whose distance from (-2,0) is \(\frac { 2 }{ 3 } \) times its distance from the line x = \(\frac { -9 }{ 2 } \) is

    (a)

    a parabola

    (b)

    a hyperbola

    (c)

    an ellipse

    (d)

    a circle

  10. 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

    (a)

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

    (b)

    \(\frac { 3\pi }{ 6 } \)

    (c)

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

    (d)

    \( { \pi }\)

  11. If the length of the perpendicular from the origin to the plane 2x + 3y + λz =1, λ > 0 is \(\frac{1}{5}\) then the value of λ is

    (a)

    \(2\sqrt { 3 } \)

    (b)

    \(3\sqrt { 2 } \)

    (c)

    0

    (d)

    1

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

    (a)

    \(-4\sqrt { 3 } \)

    (b)

    -4

    (c)

    \(\cfrac { \sqrt { 3 } }{ 12 } \)

    (d)

    \(4\sqrt { 3 } \)

  13. 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

  14. The value of \(\frac { (n+2) }{ (n) } =90\) then n is 

    (a)

    10

    (b)

    5

    (c)

    8

    (d)

    9

  15. The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    1

  16. The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { \phi \left( \frac { y }{ x } \right) }{ \phi '\left( \frac { y }{ x } \right) } \)is

    (a)

    \(x\phi \left( \frac { y }{ x } \right) =k\)

    (b)

    \(\phi \left( \frac { y }{ x } \right) =kx\)

    (c)

    \(y\phi \left( \frac { y }{ x } \right) =k\)

    (d)

    \(\phi \left( \frac { y }{ x } \right) =ky\)

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

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  18. Which of the following is a discrete random variable?
    I. The number of cars crossing a particular signal in a day
    II.The number of customers in a queue-to buy train tickets at a moment.
    III.The time taken to complete a telephone call.

    (a)

    I and II

    (b)

    II only

    (c)

    III only

    (d)

    II and III

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

    (a)

    Q+

    (b)

    Z

    (c)

    R

    (d)

    C

  20. Determine the truth value of each of the following statements:
    (a) 4+2=5 and 6+3=9
    (b) 3+2=5 and 6+1=7
    (c) 4+5=9 and1+2= 4
    (d) 3+2=5 and 4+7=11

    (a)
    (a) (b) (c) (d)
    F T T T
    (b)
    (a) (b) (c) (d)
    T F T F
    (c)
    (a) (b) (c) (d)
    T T F F
    (d)
    (a) (b) (c) (d)
    F F T T

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