If y = sin-11 + x + 1 - x2, th

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The solution of equation 

sin-11 - x2 - 2sin-1x2 = π2 is

  • x = 0

  • x = 12

  • x = 0 and 12

  • None of these


2.

Let f(x) = - 2sinx,     - π  x  - π2asinx + b,    - π2  x  π2cosx,                  π2  x  π. If f(x) is continuous on - π, π, then

  • a = 1, b = 1

  • a = - 1, b = - 1

  • a = - 1, b = 1

  • a = 1, b = - 1


3.

If f(x) = x1 + exp1x ,     x  00                     ,     x = 0, then f(x) at x = 0 is

  • continuous

  • not continuous

  • differentiable

  • not differentiable


4.

The maximum value of f(x) = 2sinx + cos2x, 0  x  π2 occurs at x is equal to

  • 0

  • π6

  • π2

  • None of these


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5.

If f(x) = x - 2 and g(x) = f(f(x)), then dgxdx for x > 10 is

  • 1 or - 1

  • 1

  • - 1

  • None of these


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6.

If y = sin-11 + x + 1 - x2, then the value of dydx at x = 0 is

  • 1/2

  • - 1/2

  • 0

  • None of these


B.

- 1/2

Given, y = sin-11 + x + 1 - x2Put      x = cos2θ sin-11 + cos2θ + 1 - cos2θ2             = sin-12cosθ + 2sinθ2             = sin-112sinθ + 12cosθ             = sin-1sinπ4 + θ     y = π4 + θ  dydx = 0 - 121 - x2At       x = 0, dydx = - 12


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7.

The distance (in metre) travelled by a vehicle in time t (in seconds) is given by the equation s = 3t3 + 2t2 + t + 1. The difference in the acceleration between t = 2 and t = 4 is

  • 36 m/s2

  • 38 m/s2

  • 45 m/s2

  • 46 m/s2


8.

The value of 1- tanθ4tanθ411tanθ4- tanθ41-1 is

  • cosθ2sinθ2- sinθ2cosθ2

  • cosθ2- sinθ2sinθ2cosθ2

  • sinθ2cosθ2cosθ2sinθ2

  • sinθ2- cosθ2cosθ2sinθ2


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9.

The value of λ and µ for whichi the simultaneous equation x + y + z = 6, x + 2y + 3z = 10 and x + 2y + λz = µ have a unique solution are

  • λ  3

  • μ = 3 only

  • λ = 3 and μ = 3

  • λ  3 and μ can take any value.


10.

If X is any matrix of order n x p (n and p are integers) and I is an identity matrix of order nxn, then the matrix M = I -  X(X'X)-1X' is

(i) idempotent matrix (ii) MX = 0

Choose the correct answer

  • (i) is correct

  • (ii) is correct

  • (i) is incorrect

  • (ii) is incorrect


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