If ax = by = cz = du and a, b, c, d are in GP, then x, y, z,

Subject

Mathematics

Class

JEE Class 12

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

1.

If F is function such that F (0) = 2, F(1) = 3, F(x + 2)= 2F(x) - F(x + 1) for x > 0, then F(5) is equal to

  • - 7

  • - 3

  • 17

  • 13


2.

Let S be a set containing n elements. Then, number of binary operations on S is

  • nn

  • 2n2

  • nn2

  • n2


3.

The numerically greatest term in the expansion of (3 - 5x)11 when x = 15, is

  • 55 × 39

  • 55 × 36

  • 45 × 39

  • 45 × 36


4.

The number of solutions of the equation sin(ex) = 5x + 5-x,  is

  • 0

  • 1

  • 2

  • infinitely many


Advertisement
Advertisement

5.

If ax = by = cz = du and a, b, c, d are in GP, then x, y, z, u are in

  • AP

  • GP

  • HP

  • None of these


C.

HP

We have,

ax = by = cz = du

Let ax = by = cz = du = k

 a = k1x, b = k1y, c = k1z, d = k1u       ...(i)

Since, a, b, c, d are in GP.

     ba = cb = dc k1yk1x = k1zk1y = k1uk1z           using Eq. (i) k1y - 1x = k1z - 1y = k1u - 1z 1y - 1x = 1z - 1y = 1u - 1z x, y, z, u are in AP. x, y, z, u are in HP.


Advertisement
6.

If z satisfies the equation z - z = 1 + 2i, then z is equal to

  • 32 + 2i

  • 32 - 2i

  • 2 - 32i

  • 2 + 32i


7.

If z = 1 - i31 + i3, then arg (z) is

  • 60°

  • 120°

  • 240°

  • 300°


8.

If f (x) = log10x2. The set of all values of x for which f(x) is real, is

  • [- 1, 1]

  • [1, )

  • (- , - 1]

  • (- , - 1]  [1, )


Advertisement
9.

For what values of m can the expression 2x2 + mxy + 3y2 - 5y - 2 be expressed as the product of two linear factors?

  • 0

  • ± 1

  • ± 7

  • 49


10.

If 3sinθ + 5cosθ, then the value of 5sinθ - 3cosθ is equal to

  • 5

  • 3

  • 4

  • None of these


Advertisement