The value of c in (0, 2) satisfying the mean value theorem for th

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let f(x) = ex - 12sinxalog1 + x4 for x  0 and f(0) = 12.  If f is continuous at x = 0, then the value of a is equal to

  • 1

  • - 1

  • 2

  • 3


2.

If y = sin-11 - x, then dydx is equal to

  • 11 - x

  • - 121 - x

  • 1x

  • - 12x1 - x


3.

The derivative of sin-12x1 - x2 with respect to sin-13x - 4x is

  • 23

  • 32

  • 12

  • 1


4.

If y = tan-1x + sec-1x + cot-1x + csc-1x, then dydx is equal to

  • x2 - 1x2 + 1

  • π

  • 0

  • 1


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5.

If fx = x - 2 + x + 1 - x, then f'- 10 is equal to

  • - 3

  • - 2

  • - 1

  • 0


6.

If x = a1 + cosθ, y = aθ + sinθ, then d2ydx2 at θ = π2 is

  • 1a

  • 1a

  • - 1

  • - 2


7.

If y = tan-1cosx1 + sinx, then dydx is equal to

  • 12

  • 2

  • - 2

  • 12


8.

The distance between the origin and the normal to the curve y = e2x + x2 at x = 0 is

  • 2

  • 23

  • 25

  • 12


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9.

The value of c in (0, 2) satisfying the mean value theorem for the function f(x) = x(x - 1)2, x [0, 2] is equal to

  • 34

  • 43

  • 13

  • 23


B.

43

Given curve is

f(x) = x(x - 1)2, x  [0,2]

   f'x = x3x - 4 + 1    f'c = c3c - 4 + 1Also, f0 = 0, f2 = 2By mean value theoremf0 - f2 = f'c0 - 2   0 - 2 = c3c - 4 + 1- 2 3c2 - 4c + 1 = 1       c3c - 4 = 0                     c = 0, 43

 


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10.

The point on the curve x2 + y2 = a2, y 0 at which the tangent is parallel to x-axis is

  • (a, 0)

  • (- a, 0)

  • a2, 32a

  • (0, a)


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