For real x, the greatest value of x2 + 2x +&n

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

11.

If f''(0) = k, k  0, then the value of limx0 2f(x) - 3f(2x) +f(4x)x2 is

  • k

  • 2k

  • 3k

  • 4k


12.

If  y = emsin- 1x then 1 - x2d2ydx2 - xdydx - ky = 0, where k is equal to

  • m2

  • 2

  • - 1

  • - m2


13.

Solution of x + y2dydx = a2 ( 'a' being a constant) is

  • x + ya = tany + Ca, C is an arbitrary

  • xy = atanCx, C is an arbitrary

  • xa = tanyC, C is an arbitrary

  • xy = tan(x + C), C is an arbitrary


14.

The integrating factor of the first order differential equation

x2x2 - 1dydx + xx2 + 1y = x2 - 1 is

  • ex

  • x - 1x

  • x + 1x

  • 1x2


Advertisement
15.

Let a and B be the roots of x2 + x + 1 = 0. If n be a positive integer, then αn + βn is

  • 2cos23

  • 2sin23

  • 2cos3

  • 2sin3


Advertisement

16.

For real x, the greatest value of x2 + 2x + 42x2 + 4x + 9 is

  • 1

  • - 1

  • 12

  • 14


C.

12

Let y = x2 + 2x + 42x2 + 4x + 9

 2x2y + 4xy + 9y = x2 + 2x + 4

 2y - 1x2 + 4y - 2x + 9y - 4 = 0

 x = - 4y - 2 ± 4y - 22 - 42y - 19y - 422y - 1

Since, x is a real number.

 4y - 22 - 42y - 19y - 4  0

4 2y - 12 - 42y - 19y - 4  0

 42y - 12y - 1 - 9y + 4  0

 42y - 13 - 7y  0

 2y - 17y - 3  0

 37  y  12

 Maximum value of y = 12


Advertisement
17.

If the solution of the differential equation xdydx + y = xex be xy = exϕ(x) + C, then ϕx is equal to

  • x + 1

  • x - 1

  • 1 - x

  • x


18.

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

  • 2

  • 3

  • 1

  • None of these


Advertisement
19.

General solution of ydydx + by2 = acosx, 0 < x < 1 is

  • y2 = 2a2bsinx + cosx + ce- 2bx

  • 4b2 + 1y2 = 2asinx + 2bcosx + ce- 2bx

  • 4b2 + 1y2 = 2asinx + 2bcosx + ce2bx

  • y2 = 2a2bsinx + cosx + ce- 2bx


20.

The integrating factor of the differential equation

1 + x2dydx + y = etan-1x is

  • tan-1x

  • 1 + x2

  • etan-1x

  • loge1 + x2


Advertisement