If the sum of first 11 terms o

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 Multiple Choice QuestionsMultiple Choice Questions

211.

ln ABC, if the sides a, b, c are in geometric progression and the largest angle exceeds the smallest angle by 60°, then cos(B) is equal to

  • 13 + 14

  • 1 - 134

  • 1

  • 13 - 14


212.

The coefficient of x5 in the expansion of(1 + x)21 + (1 +x)22 + ... + (1 + x)30 is

  • C631 - C621

  • C551

  • C59

  • C530 + C520


213.

If the roots of the equation x2 -7x2 + 14x - 8 = 0 are in geometric progression, then the difference between the largest and the smallest roots is

  • 4

  • 2

  • 12

  • 3


214.

p, x1, x2 , ..., xn and q, y1, y2, ..., yn are two arithmetic progressions with common differences a and b respectively. If α and β are the arithmetic means of x1, x2, ..., xn and y1, y2, ..., yn respectively. Then the locus of P α, β is

  • ax - p = by - q

  • b(x - p) = a(y - q)

  • αx - p = βy - q

  • px - α = qy - β


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215.

The sum of the n terms of 12 . 5 + 15 . 8 +18 . 11 + ... is

  • 3n23n + 2

  • 3n3n + 2

  • n23n + 2

  • n3n + 2


216.

If x = 1 . 33 . 6 + 1 . 3 . 53 . 6.  9 + 1 . 3 . 5 . 73 . 6.  9 . 12 + ... to infinite terms, then 9x2 + 24x = ?

  • 31

  • 11

  • 41

  • 21


217.

The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in

  • - , - 3  9, 

  •  - , - 9  3, 

  • - 3, 

  •  - , 9


218.

If |x| < 1, |y| < 1 and x  y, then the sum to infinity of the following series (x + y) + (x2 + xy + y2) + (x+ x2y + xy2 + y3) + ..... is :

  • x +y + xy1 - x1 - y

  • x + y - xy1 - x1 - y

  • x + y - xy1 - x1 + y

  • x + y + xy1 + x1 + y


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219.

Let S be the sum of the first 9 term of the series :(x + ka} + (x2 + (k + 2)a} + {x3 + (k + 4)a} + {x4 + (k + 6)a} + ........ where a  0 and x  1. If S = x10 - x +45ax - 1x - 1, then k is equal to

  •  - 3

  • 1

  •  - 5

  • 3


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220.

If the sum of first 11 terms of an A.P. , a1, a2, a3 ..... is 0(a1  0), then the sum of the A.P., a1, a3, a5, ..... a23 is ka1, where k is equal to :

  • 12110

  • - 12110

  • - 725

  • 725


C.

- 725

 S11 = 0 a + 5d = 0 Nowa1 + a3 + a5 + ... + a23 = 1222a + 12 - 12d= 12a + 11d= 72d= - 725


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