The function f (x) = x2 e- 2x, x > 0. Then the maximum value o

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

Advertisement

61.

The function f (x) = x2 e- 2x, x > 0. Then the maximum value of f (x) is :

  • 1e

  • 12e

  • 1e2

  • 4e4


C.

1e2

  fx = x2e- 2x f'(x) = 2xe-2x - 2x2e- 2x            = 2x1 - xe- 2xPut f'(x) = 0 for maxima or minima, we get2x1 - xe- 2x = 0                     x = 0, 1Now, f''(x) = 2x(- 1)e- 2x + 21 - xe- 2x        f''(0) = 0 +2e0 = 2and  f''(1) = - 2e- 2 + 0 - 0 = - 2e2 < 0 f(x) is maximum at x = 1.Thus, maximum value of f(x) = 1 . e- 2 = 1e2


Advertisement
62.

The angle between the tangents at those points on the curve x = t2 + 1 and y = t2 - t - 6 where it meets x-axis is :

  • ±tan-1429

  • ±tan-1549

  • ±tan-11049

  • ±tan-1829


63.

If θ is semi vertical angle of a cone of maximum volume and given slant height, then tan(θ) is equal to

  • 2

  • 1

  • 2

  • 3


64.

A man of 2 m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at which the length of his shadow increase, is

  • 2 km/h

  • 1 km/ h

  • 3 km/h

  • 6 km/h


Advertisement
65.

If y = 4x-5 is a tangent to the curve y2 = px3 + q at (2, 3), then

  • p = 2, q = - 7

  • p = - 2, q = 7

  • p = - 2, q = - 7

  • p = 2, q = 7


66.

A missile is fired from the fround level rises x metre vertically upwards in t second, where x = 100t - 252t2. The maximum height recahed is

  • 200 m

  • 125 m

  • 160 m

  • 190 m


67.

If the curves x2 = 9A(9 - y) and x2 = A(y + 1) intersect orthogonally, then the value of A is

  • 3

  • 4

  • 5

  • 7


68.

If f (x) = 3x4 + 4x3 - 12x2 + 12, then f(x) is

  • increasing in (- , - 2) and in (0, 1)

  • increasing in (- 2, 0) and in (1, )

  • decreasing in (- 2, 0) and in (0, 1)

  • decreasing in (- , - 2) and in (1, )


Advertisement
69.

Gas is being pumped into a spherical balloon at the rate of 30 ft3/min. Then, the rate at which the radius increases when it reaches the value 15 ft is

  • 115π ft/min

  • 130π ft/min

  • 120 ft/min

  • 125 ft/min


70.

A point on curve xy2 = 1 which is at minimum distance from the origin is

  • (1, 1)

  • (1/4, 2)

  • (21/6, 2- 1/3)

  • (2- 1/3, 21/6)


Advertisement