The point on the curve x2 + y2 = a2, y ≥ 0 at which the tangen

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 Multiple Choice QuestionsMultiple Choice Questions

81.

The angle between the curves y = ax and y = bx is equal to

  • tan-1a - b1 + ab

  • tan-1a + b1 - ab

  • tan-1logb - loga1 + logalogb

  • tan-1loga - logb1 + logalogb


82.

Let f(x) = (x - 7)2(x - 2)7, x  [2, 7].  The value of θ  2, 7 such that f'θ = 0 is equal to

  • 494

  • 539

  • 537

  • 499


83.

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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84.

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)


D.

(0, a)

Given curve is

x2 + y2 = a2, y  0           ...iDifferentiating w.r.t. x on both sides 2x + 2ydydx = 0 dydx = - xy The tangent is parallel to x-axis. dydx = 0    x = 0Putting x = 0 in Eq. (i), we get    y2 = a2 y = ± a Required point= (0, a)


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85.

An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube will increase when the edge is 5 cm long?

  • 750 cm3/ s

  • 75 cm3/ s

  • 300 cm3/ s

  • 150 cm3/ s


86.

The minimum value of f(x) = 3 - x + 7 is

  • 0

  • 6

  • 7

  • 8


87.

The total revenue in rupees received from the sale of x units of a product is given by R(x) = 13x2 + 26x + 15. Then, the marginal revenue in rupees, when x = 15 is

  • 116

  • 126

  • 136

  • 416


88.

If a tangent of the curve y = 2 + 4x + 1 has slope 25 at a point, then the point is

  • (0, 2)

  • 34, 4

  • (2, 5)

  • (6, 7)


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89.

The points on the graph y = x3 - 3x at which the tangent is parallel to x-axis are

  • (2, 2) and (1, - 2)

  • (- 1, 2) and (- 2, - 2)

  • (2, 2) and (- 1, 2)

  • (1, - 2) and (- 1, 2)


90.

The slope of the normal to the curve y2 - xy - 8 = 0 at the point (0, 2) is equal to

  • - 3

  • - 6

  • 3

  • 6


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