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 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)

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

If the sum of n terms of an A. P. be 3n² - n and its common difference is 6, then its first term is ______________

(a)

2

(b)

3

(c)

1

(d)

4

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)

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

If \(\Sigma n=210\) then \(\Sigma { n }^{ 2 }\)= ______________

(a)

2870

(b)

2160

(c)

2970

(d)

none of these

\(\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+...\) is ______________

(a)

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

(b)

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

(c)

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

(d)

none of these

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

3 log 2 + \(\frac{1}{4}-\frac{1}{2}(\frac{1}{4})^2+\frac{1}{3}(\frac{1}{4})^2\)+ . . . = ______________

(a)

log 8

(b)

log 10

(c)

log 2

(d)

log 4

The sum of the coefficients in the expansion of (1 - x)¹⁰ is ______________

(a)

0

(b)

1

(c)

10²

(d)

1024

If an A.P the sum of terms equidistant from the beginning and end is equal to ______________

(a)

first term

(b)

second term

(c)

sum of first and last term

(d)

last term