The minimum distance from the point (4, 2) to the parabola y2 = 8

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

291.

The function y = 2x3 - 9x2 + 12x - 6 is monotonic decreasing when

  • 1 < x < 2

  • x > 2

  • x < 1

  • None of these


292.

Maximum slope of the curve y = - x3 + 3x2 + 9x - 27 is

  • 0

  • 12

  • 16

  • 32


293.

The points on the curve x2 = 2y which are closest to the point (0, 5) are

  • (2, 2), (- 2, 2)

  • 22, 4, - 22, 4

  • 6, 3, - 63, 3

  • 23, 6, - 23, 6


294.

The point on the curve y = 2x2 - 4x + 5, at which the tangent is parallel to x-axis, will be

  • (1, 3)

  • (- 1, 3)

  • (1, - 3)

  • (- 1, - 3)


Advertisement
295.

The interval, inwhich the function f(x) = x2e-x is an increasing function, will be

  • - , 

  • (- 2, 0)

  • 2, 

  • (0, 2)


Advertisement

296.

The minimum distance from the point (4, 2) to the parabola y2 = 8x is

  • 2

  • 22

  • 2

  • 32


B.

22

y2 = 8xOn comparing with y2 = 4ax4a = 8  a = 2Let (2t2, 4t) is the point on the given parabola.Let d = distance between the point (4, 2) and (2t2, 4t)     d2 = 4 - 2t22 + 2 - 4t2     d2 = 16 + 4t4 - 16t2 + 4 + 16t2 - 16t d2 = 4t4 - 16t + 20      ...iLet    l = 4t4 - 16t + 20 dldt = 16t3 - 16For minimum or maximum of l     dldt = 0 16t3 - 16 = 0 t - 1t2 + 1 + t = 0    t = 1Also, d2ldt2 = 48t2 d2ldt2 at t = 1 = 48 > 0 (min)So, distance 'l' is min at (t = 1)Hence, the min distance from parabola     y2 = 8x to (4, 2) is     d2 = 4 - 22 + 2 - 42 d2 = 4 + 4 = 8   d = 22


Advertisement
297.

A particle moves so that the space described in time t is square root of a quadratic function of t. Then,

  • v  1s

  • acceleration  1s3

  • acceleration  s3

  • None of these


298.

The points at which the tangent to the curve y = x3 + 5 is perpendicular to the line x + 3y = 2 are

  • (6, 1), (- 1, 4)

  • (1, 6), (1, 4)

  • (6, 1), (4, - 1)

  • (1, 6), (- 1, 4)


Advertisement
299.

Let f(x) = a - (x - 3)8/9, then maxima of f(x) is

  • 3

  • a - 3

  • a

  • None of these


300.

If the total cost C(x) in rupees associated with the production of x units of an item is given by C (x) = 3x3 - 2x2 + x + 100. Then, the marginal change in cost, when x = 5, is

  • 200

  • 225

  • 206

  • 226


Advertisement