Suppose that the equation f (x) = x2 + bx + c = 0 has two distinc

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

21.

let y = y(x) be the solution of the differential equation sin x dydx + y cos x = 4x, x (0, π). If y = π2 = 0, then yπ6 is equal to:

  • -49π2

  • 493π2

  • -893π2

  • -89π2


22.

If the line ax + by + c = 0, ab  0, is a tangent to the curve xy = 1- 2x, then

  • a> 0, b < 0

  • a>0, b> 0

  • a< 0, b > 0

  • a< 0, b < 0


23.

Time period T of a simple pendulum of length l is given by T = 2π1g. If the length is increased by 2%, then an approximate change in the time period is

  • 2 %

  • 1 %

  • 12 %

  • None of these


24.

The number of values of k, for which the equation x2 - 3x + k=0 has two distinct roots lying in the interval (0, 1), are

  • three

  • two

  • infinitely many

  • no value of k satisfies the requirement


Advertisement
25.

The smallest positive root of the equation tan(x) - x = 0 lies in

  • 0, π2

  • π2, π

  • π, 3π2

  • 3π2, 2π


26.

Let y =  ex2 and y = ex2sinx be two given curves. Then, angle between the tangents to the curves at any point of their intersection is

  • 0

  • π

  • π2

  • π4


Advertisement

27.

Suppose that the equation f (x) = x2 + bx + c = 0 has two distinct real roots α and β. The angle between the tangent to the curve y = f (x) at the point α + β2, fα + β2 and the positive direction of the x-axis is

  • 30°

  • 60°

  • 90°


A.

Since α and β are the roots of f(x) = x2 + bx + c α + β = - b and αβ = c fα + β2 = α + β22 + bα + β2 + c                     = - b22 + b- b2 + cNow, dydx = f'(x) = 2x + bAt point α + β2, fα + β2,i . e - b2, - b24 + c,dydx = 2- b2 + b = 0

Hence, the slope of the tangent to the curve and the positive direction of x-axis is 0°.


Advertisement
28.

The angle of intersection between the curves y = sinx + cosx and x2 + y2 = 10, where [x] denotes the greatest integer  x, is

  • tan-13

  • tan-1- 3

  • tan-13

  • tan-11/3


Advertisement
29.

For the curve x2 + 4xy + 8y = 64 the tangents are parallel to the x-axis only at the points

  • 0, 22 and 0, - 22

  • (8, - 4) and (- 8, 4)

  • 82, - 22 and - 82, 22

  • (9, 0) and (- 8, 0)


30.

Let exp (x) denote the exponential function ex. If f (x) = expx1x, x > 0, then the minimum value off in the interval [2, 5] is

  • expe1e

  • exp212

  • exp515

  • exp313


Advertisement