If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

(a)

2

(b)

1

(c)

4

(d)

16

The sequence \(\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } }, \frac { 1 }{ \sqrt { 3 } +2\sqrt { 2 } },...... \)form an 

(a)

AP

(b)

GP

(c)

HP

(d)

AGP

If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n - 2S_n-1 + S_n-2 is

(a)

d

(b)

2d

(c)

4d

(d)

d²

The remainder when 38¹⁵ is divided by 13 is

(a)

12

(b)

1

(c)

11

(d)

5

The n^th term of the sequence 1, 2, 4, 7, 11,... is

(a)

n³ + 3n² + 2n

(b)

n³ - 3n² + 3n

(c)

\(\frac { n(n+1)(n+2) }{ 3 } \)

(d)

\(\frac { { n }^{ 2 }-n+2 }{ 2 } \)

The sum up to n terms of the series \(\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +\)....is 

(a)

\(\sqrt { 2n+1 } \)

(b)

\(\frac { \sqrt { 2n+1 } }{ 2 } \)

(c)

\(\sqrt { 2n+1 } -1\)

(d)

\(\frac { \sqrt { 2n+1 } -1 }{ 2 } \)

The n^th term of the sequence \(\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 } \),......is

(a)

2ⁿ - n - 1

(b)

1 - 2^-n

(c)

2^-n + n - 1

(d)

2^n-1

The sum up to n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\).....is

(a)

\(\frac { n(n+1) }{ 2 } \)

(b)

2n(n+1)

(c)

\(\frac { n(n+1) }{ \sqrt { 2 } } \)

(d)

1

The value of the series\(\frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 16 } +\).....is

(a)

14

(b)

7

(c)

4

(d)

6

The sum of an infinite GP is 18. If the first term is 6, the common ratio is

(a)

\(\frac { 1 }{ 3 } \)

(b)

\(\frac { 2 }{ 3 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

\(\frac { 3 }{ 4 } \)