If fx = xsin1x, x ≠ 00 &nbs

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Divide 10 into two parts such that the sum of double of the first and the square of the second is minimum

  • (6, 4)

  • (7, 3)

  • (8, 2)

  • (9, 1)


2.

If 2x + y + λ = 0 is normal to the parabola y2 = 8x, then λ, is

  • - 24

  • 8

  • - 16

  • 24


3.

If the line lx + my + n = 0 is tangent to the parabola y2 = 4ax, then

  • mn = al2

  • lm = an2

  • ln = am2

  • None of the above


4.

f : R  R, then f(x) = xx will be

  • many-one-onto

  • one-one-onto

  • many-one-into

  • one-one-into


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5.

If f(x) = log1 +2ax - log1 - bxx,  x  0k,                                              x = 0 is contonuous at x = 0, then value of k is

  • b + a

  • b - 2a

  • 2a - b

  • 2a + b


6.

If fx = x - 3, then f'(3) is

  • - 1

  • 1

  • 0

  • does not exist


7.

All the points on the curve y2 = 4ax + asinxa, where the tangent is parallel to the axis of x are lies on

  • circle

  • parabola

  • straight line

  • None of these


8.

The length of normal at any point to the curve y = c coshxc is

  • fixed

  • y2c2

  • y2c

  • yc2


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9.

The height of right circular cylinder of maximum volume inscribed in a sphere of diameter 2a is

  • 23a

  • 3a

  • 2a3

  • a3


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10.

If fx = xsin1x, x  00           , x = 0, then at x = 0 the function f(x) is

  • continuous

  • differentiable

  • continuous but not differentiable

  • None of the above


C.

continuous but not differentiable

Given, fx = xsin1x, x  00           , x = 0For continuity at x = 0,LHL = f0 - 0 = limh0f0 - h       = limh0- hsin- 1h       = 0 × finite quantityRHL = f0 + 0 = limh0hsin1h        = 0 × finite quantity        = 0and f0 = 0   f0 = LHL = RHL  f(x) is continuous at x = 0.For differentiability at x = 0Rf'0 = limh0f0 + h - f0h          = limh0hsin1h - 0h          = limh0sin1h          = a finite quantity persist between - 1 to+ 1          = does not exist

Lf'0 = limh0f0 - h - f0- h          = limh0- hsin- 1h - 0- h          = limh0sin- 1h          = a finite quantity persist between - 1 to+ 1          = does not exist Rf'0  Lf'0 f(x) is not differentiable at x = 0.


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