If cos-1x - cos-1y2 = α, where&nbs

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

211.

The domain of sin-1(log3(x)) is :

  • [- 1, 1]

  • [0, 1]

  • [0, ]

  • 13, 3


212.

The value of cos2tan-1- 7 is :

  • 4950

  • - 4950

  • 2425

  • - 2425


213.

Let x1 and x2 be solutions of the equation sin-1x2 - 3x + 52 = π6. Then, the value of x12 + x22 is :

  • 4

  • 5

  • 52

  • 6


214.

If α = cos-135, β = tan-113, where 0 < α, β < π2, then α - β is equal to :

  • tan-19510

  • tan-1914

  • sin-19510

  • cos-19510


Advertisement
Advertisement

215.

If cos-1x - cos-1y2 = α, where - 1  x  1- 2  y  2, x  y2 then for all x, y, 4x2 - 4xycosα + y2 is equal to

  • 4sin2α

  • 2sin2α

  • 4cos2α +2x2y2

  • 4sin2α - 2x2y2


A.

4sin2α

cos-1x - cos-1y2 = αLet cos-1x = A, cos-1y2 = Bx = cosA, y2 = cosBsinA = 1 - x2, sinB = 1 - y24xy2 + 1 +x21 - y24 = cosα1 - x2 - y24 + x2y24 = x2y24 + cos2α - xycosα4 - 4x2 - y2 = 4cos2α - 4 + 4cosα4x2 - 4xycosα + y2 = 4sin2α


Advertisement
216.

y = logtanx2 + sin-1cosx, then dy/dx is

  • csc(x) - 1

  • cs(x)

  • csc(x) + 1

  • x


217.

If 2tan-1cosx = tan-12cscx, then sinx + cosx is equal to

  • 22

  • 2

  • 12

  • 12


218.

tan-13 - sec-1- 2csc-1- 2 + cos-1- 12 is equal to

  • 45

  • - 45

  • 35

  • 0


Advertisement
219.

If α and β are roots of the equation x2 + 5x - 6 = 0, then the value of tan-1α - tan-1β is

  • π2

  • 0

  • π

  • π4


220.

The value of cos-1cotπ2 + cos-1sin2π3 is

  • 2π3

  • π3

  • π2

  • π


Advertisement