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QUESTION: 1

The first term of an A.P. of consecutive integer is p^{2} + 1. The sum of (2p + 1) terms of this series can be expressed as

Solution:

QUESTION: 2

If a_{1}, a_{2}, a_{3},........ are in A.P. such that a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225, then a_{1} + a_{2} + a_{3} + ......+ a_{23} + a_{24} is equal to

Solution:

QUESTION: 3

If x ∈ R, the numbers 5^{1+x} + 5^{1-x}, a/2, 25^{x} + 25^{-x} form an A.P. then `a' must lie in the interval;

Solution:

QUESTION: 4

The third term of a G.P. is 4. The product of the first five terms is

Solution:

QUESTION: 5

If S is the sum of infinity of a G.P. whose first term is `a', then the sum of the first n terms is

Solution:

QUESTION: 6

The sum of the series + + + ....... + is

Solution:

QUESTION: 7

For a sequence {a_{n}}, a_{1 }= 2 and . Then is

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QUESTION: 8

a, b be the roots of the equation x^{2 –} 3x + a = 0 and g, d the roots of x^{2} – 12x + b = 0 and numbers a, b, g, d (in this order) form an increasing G.P., then

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QUESTION: 9

If 3 + 1/4 (3 + d) + 1/4^{2} (3 + 2d) + .... + upto ∞ = 8, then the value of d is

Solution:

QUESTION: 10

The sum is equal to

Solution:

QUESTION: 11

In a G.P. of positive terms, any term is equal to the sum of the next two terms. The common ratio of the G.P. is

Solution:

QUESTION: 12

If + ...... up to ∞ =, then + ..... =

Solution:

QUESTION: 13

Sum of the series S = 1^{2} – 2^{2} + 3^{2} – 4^{2} + ..... – 2002^{2} + 2003^{2} is

Solution:

QUESTION: 14

If x =, y =, z =where a, b, c are in AP and |a| < 1, |b| < 1, |c| < 1, then x, y, z are in

Solution:

QUESTION: 15

The sum to n term of the series 1(1!) + 2(2!) + 3(3!) + ....

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QUESTION: 16

The sum to 10 terms of the series is

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QUESTION: 17

If p is positive, then the sum to infinity of the series, is

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QUESTION: 18

The positive integer n for which 2 × 2^{2} + 3 × 2^{3} + 4 × 2^{4} + ..... + n × 2^{n} = 2^{n + 10} is

Solution:

QUESTION: 19

If x > 0, and log_{2} x + log_{2} + log_{2} + log_{2} + log_{2} + ....= 4, then x equals

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QUESTION: 20

If a, b, c are in A.P. p, q, r are in H.P. and ap, bq, cr are in G.P., then is equal to

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QUESTION: 21

1^{2} + 2^{2} + ......+ n^{2} = 1015, then value of n is

Solution:

QUESTION: 22

If a and b are p^{th} and q^{th} terms of an AP, then the sum of its (p + q) terms is

Solution:

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