Six positive numbers are in GP, such that their product is 1000.

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

61.

The value of

100011 × 2 + 12 ×3 + 13 ×4 + ... + 1999 × 1000

  • 1000

  • 999

  • 1001

  • 1999


Advertisement

62.

Six positive numbers are in GP, such that their product is 1000. If the fourth term is 1, then the last term is

  • 1000

  • 100

  • 1100

  • 11000


C.

1100

Let the six terms of GP are

ar5 , ar3, ar, ar, ar3, ar5Now, according to the question ar5 . ar3 . ar . ar . ar3 . ar5 = 1000

 a6 = 103 a2 = 103         ...(i)Also, given fourth term = ar = 1 a2r2 = 1 r2 = 110          ...(ii)           from Eqs. (i) and (ii)

 Last term = ar2 = a2r251/2                     = 10 × 11051/2    from Eqs. (i) and (ii)                     = 11041/2 = 1100

 


Advertisement
63.

Five numbers are in AP with common difference  0. If the 1st, 3rd and 4th terms are in GP, then

  • the 5th term is always 0.

  • the 1st term is always 0.

  • the middle term is always 0

  • the middle term is always - 2.


64.

The sum of series

11 × 2C025 + 12 × 3C125 + 13 × 4C225 + ... + 126 × 27C2525

is

  • 227 - 126 × 27

  • 227 - 2826 × 27

  • 12226 + 126 × 27

  • 226 - 152


Advertisement
65.

Let f : R  R  be such that f is injective and f(x) f(y) = f(x + y) for all x, y if f(x), f(y) and f(z) are in GP, then x, y and z are in

  • AP always

  • GP always

  • AP depending on the values of x, y and z

  • GP depending on the values of x, y and z


66.

If P = 1 + 12 × 2 + 13 × 22 + ... and Q = 11 × 2 + 13 × 4 + 15 × 6 + ...,

then

  • P = Q

  • 2P =Q

  • P = 2Q

  • P = 4Q


67.

If x = 1 + 12 × 1! + 14 × 2! + 18 × 3! + ... and y = 1 + x21! + x42! + x63! +... Then, the value of logey is

  • e

  • e2

  • 1

  • 1e


68.

The value of the infinite series

12 + 223! + 12 + 22 + 324! + 12 + 22 + 32 +425! + ... is

  • e

  • 5e

  • 5e6 - 12

  • 5e6


Advertisement
69.

The sum of the series 1 + 12C1n + 13C2n + ... + 1n + 1Cnn is equal to

  • 2n + 1 - 1n + 1

  • 32n - 12n

  • 2n + 1n + 1

  • 2n + 12n


70.

The value of r = 21 + 2 + ... + r - 1r!

  • e

  • 2e

  • e2

  • 3e2


Advertisement