All the points on the curve y2 = 4ax + asinxa, where th

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


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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


B.

parabola

           y2 = 4ax +asinxa    ...i 2ydydx = 4a1 + cosxa    ...iiIf tangent is parallel to x-axis, then         dydx = 0So, from Eq. (i), we get    cosxa = - 1 sinxa = 0On putting this value in Eq. (i), we get             y2 = 4ax + 0  y2 = 4axSo, all the points on the curve             y2 = 4ax + asinxawhere the tangent is parallel to the x-axis are lies on parabola.


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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


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


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