The HM of two positive numbers whose AM and GM are 16, 8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

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 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)

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

The value of \(\frac { 1 }{ 2! } +\frac { 1 }{ 4! } +\frac { 1 }{ 6! } +....is\)

(a)

\(\frac { { e }^{ 2 }+1 }{ 2e } \)

(b)

\(\frac { { (e+1) }^{ 2 } }{ 2e } \)

(c)

\(\frac { { (e-1) }^{ 2 } }{ 2e } \)

(d)

\(\frac { { e }^{ 2 }+1 }{ 2e } \)

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be ______________

(a)

5

(b)

6

(c)

7

(d)

8

If in an infinite G. P. first term is equal to 10 times the sum of all successive terms, then its common ratio is ______________

(a)

\(\frac { 1 }{ 10 } \)

(b)

\(\frac { 1 }{ 11 } \)

(c)

\(\frac { 1 }{ 9 } \)

(d)

\(\frac { 1 }{ 20 } \)

The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27}}\),\(\infty \) is ______________

(a)

1

(b)

3

(c)

9

(d)

none of these

The series 1+4x+8x² + \(\frac { 32 }{ 3 } { x }^{ 3 }+.....+\infty \ is\) ______________

(a)

e^x

(b)

e^4x

(c)

e^2x

(d)

e^8x

The value of 2 + 4 + 6 + + 2n is

(a)

\(\frac { n\left( n-1 \right) }{ 2 } \)

(b)

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

(c)

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

(d)

n(n + 1)

The sum of the series C₀²- C₁² + C₂² .....+ (- 1)ⁿC²_n where n is an even integer is ______________

(a)

2nC_n

(b)

(-1)ⁿ2nC_n

(c)

(-1)ⁿ2nC_n-1

(d)

(-1)^n/2nC_n/2