The coefficient of the middle term in the binomial expansion in the powers of x of  and of  is the same, if α equals

a)

b)

c)

d)

The coefficient of  in the expansion of  is

a)

b)

c)

d)

If   and    then   is equal to

a)

b)

c)

d)

The number of integer terms in the expansion of  is

a) 32

b) 33

c) 34

d) 35

If x is positive, the first negative term in the expansion of is

a) 7^th term

b) 5^th term

c) 8^th term

d) 6^th term

The coefficient of  is

a) 21

b) 25

c) 26

d) None of these

If  then the coefficient of  in the expansion of
 is

a) n

b) n – 1

c) n + 2

d) n + 1

Let   be coefficients of the expansion of  then the value of  is

a) 0

b) 1

c)

d) None of these

Two consecutive terms in the expansion of whose coefficients are equal are

a) 11, 12

b) 7, 8

c) 30, 31

d) None of these

The area of triangle with vertices (a, b),  and  where  are in geometric progression with common ratio r, and b are in geometric progression with common ratio s is given by

a)

b)

c)

d) None of the above

Let   , , 2, 3 then  is not greater than

a)

b) 1

c) 2

d) 4

The value of is

a)

b)

c)

d) None of these

The value of the sum of the series
 terms is

a) 0

b)

c)

d) None of these

The series  is equal to

a)

b)

c)

d)

The sum of n terms of three arithmetic progressions whose first term is 1 and common differences 1, 2, 3 are  respectively. The true relation is

a)

b)

c)

d)

The arithmetic mean, harmonic mean and geometric mean between two numbers are , 15 and 12 but not necessarily in this order. Then harmonic mean, geometric mean and arithmetic mean respectively are

a) 15, 12,

b) , 12, 15

c) 12, 15,

d) , 15, 12

If  then
 is equal to

a)

b)

c)

d)

Statement 1 : If 3, 6, 12 are in geometric progression then 9, 12, 18 are in harmonic progression
Statement 2 : If middle term is added in three consecutive terms of a geometric progression, resultant will be in harmonic progression

a) Statement 1 is false. Statement 2 is true

b) Statement 1 is true. Statement 2 is true. Statement 2 is correct explanation for statement 1

c) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation for statement 1

d) Statement 1 is true. Statement 2 is false

If  terms of an arithmetic progression are in geometric progression, and m, n, r are in harmonic progression then the value of the ratio of the common difference to the first term of the arithmetic progression is

a)

b)

c)

d)

The coefficient of  in the following expansion  is

a)

b)

c)

d)

The sum of three terms of a strictly increasing geometric progression is αS and the sum of squares of these terms is .  lies in

a)

b)

c)

d) None of these

The sum of three terms of a strictly increasing geometric progression is αS and the sum of the square of these terms is . If  then the greatest value of the middle term is

a) 5

b)

c) 10

d)

The sum of n terms of the following series
  will be

a)

b)

c)

d) None of these