Important Questions of Sequences and Series Mathematics | Zigya

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91.

The value of log35 × log2527 × log497log813 is

  • 1

  • 6

  • 23

  • 3


92.

Sum of n terms of the following series 13 + 33 + 53 + 73 + ... is

  • n2(2n2 - 1)

  • n3(n - 1)

  • n3 + 8n + 4

  • 2n4 + 3n2


93.

GM and HM of two numbers are 10 and 8 respectively. The numbers are

  • 5, 20

  • 4, 25

  • 2, 50

  • 1,100


94.

The value of n for which is the xn +1 + yn + 1xn + yn geometric mean of x and y is

  • n = - 12

  • n = 12

  • n = 1

  • n = - 1


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95.

If angles A, B and C are in AP, then a + cb equal to

  • 2sinA - C2

  • 2cosA - C2

  • cosA - C2

  • sinA - C2


96.

The sum of the infinite series

1 + 12! + 1 . 34! + 1 . 3. 56! + ...

  • e

  • e2

  • e

  • 1e


97.

If three positive real numbers a, b, c are in AP and abc = 4, then the minimum possible value of b is 2

  • 232

  • 223

  • 213

  • 252


98.

For what value of m, am + 1 + bm + 1am + bm  is the arithmetic mean of 'a' and 'b' ?

  • 1

  • 0

  • 2

  • None of these


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99.

If i = - 1 and n is a positive integer, then in + in + 1 + in + 3 is equal to

  • 1

  • i

  • in

  • 0


100.

If a, b, c are in GP (a> 1, b > 1, c > 1), then for any real number x (with x > 0, x  1), logax, logbx, logcx are in

  • GP

  • AP

  • HP

  • GP but not in HP


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