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Question Bank No: 1

1. If 1 + $\frac{1 + 2}{2}$ + $\frac{1 + 2 + 3}{3}$ , .. to n terms is S, then S is equal to

a)		$\frac{n (n + 3)}{4}$
b)		$\frac{n (n + 2)}{4}$
c)		$\frac{n (n + 1) (n + 2)}{6}$
d)		$n^{2}$

2. The sum to n terms of the series $\frac{1}{2}$ + $\frac{3}{4}$ + $\frac{7}{8}$ + $\frac{15}{16}$ +................ is

a)		$2^{n}$ -1
b)		1 - $2^{- n}$
c)		n + $2^{n}$ - 1
d)		n + $2^{- n}$ - 1

3. The sum of to n terms of the series $\frac{1}{2}$ + $\frac{3}{4}$ + $\frac{7}{8}$ + $\frac{15}{16}$ +............... is

a)		n-1+ $2^{- n}$
b)		1
c)		n-1 - $2^{- n}$
d)		2+ $2^{- n}$

4. The sum of the series 1 + 2.2 + ${3.3}^{2}$ + ${4.2}^{3}$ + ${5.2}^{4}$ + ......... ${100.2}^{99}$ is

a)		${99.2}^{100}$
b)		${100.2}^{100}$
c)		${99.2}^{100}$ +1
d)		${1000.2}^{100}$

5. HM of 2 numbers is 4. Their AM is A and GM is G. If G satisfies 2A + $G^{2}$ = 27, the numbers are:

a)		16 & 9
b)		9 & 12
c)		3 & 6
d)		20 & 8

6. If A, G, H denote respectively the AM, GM and HM between two unequal positive numbers then

a)		A = $G^{2}$ H
b)		$G^{2}$ = AH
c)		$A^{2}$ = GH
d)		A = GH

7. If S is the sum to infinity of a G.P, whose first term is a, then the sum of the first n term is.

a)		S ${(1 - \frac{a}{S})}^{n}$
b)		S $[1 - {(\frac{a}{S})}^{n}]$
c)		a $[1 - {(\frac{a}{S})}^{n}]$
d)		a ${(1 - \frac{a}{S})}^{n}$

8. A ball is dropped from a height of 48 metres and rebounds 2/3 of the distance it falls. If it continue to fall and rebounds in this way, the distance the ball travels before coming to rest is (in Meters)

a)		144
b)		240
c)		120
d)		96

9. The sum of infinite terms of the goemetric progrssion. $\frac{\sqrt{2} + 1}{\sqrt{2} - 1}$ , $\frac{1}{2 - \sqrt{2}}$ , $\frac{1}{2}$ , .......... is

a)		$\sqrt{2}$ $(\sqrt{2}$ + 1 $)^{2}$
b)		$(\sqrt{2} + 1)^{2}$
c)		5 $\sqrt{2}$
d)		3 $\sqrt{2} + \sqrt{5}$

10. The fourth, seventh and tenth terms of a G.P are p,q,r respectively, then

a)		$p^{2}$ = $q^{2}$ + $r^{2}$
b)		$q^{2}$ = p r
c)		$p^{2}$ = q r
d)		p q r + p q + 1 = 0

11. The valve of $\log_{2}$ $\log_{2}$ $\log_{4}$ 256 + 2 $\log_{\sqrt{2}}$ 2 is

a)		1
b)		2
c)		3
d)		5

12. Suppose you are appointed to a post carrying a scale of pay of Rs.800 - 50 - 1200 - 75 - 2100. The total pay that you would draw in a span of 6 yeras is ( assume that there is no allowance)

a)		66660
b)		66000
c)		60000
d)		66600

13. The interior angles of a polygon are in A.P. The smallest angle is $120^{0}$ and the common difference is $5^{0}$ . The number of sides of the polygon is

a)		9
b)		10
c)		16
d)		5

14. If $a_{1}$ , $a_{2}$ , $a_{3}$ , $a_{4}$ , $a_{5}$ , $a_{6}$ are six AM's between 3 & 31 then $a_{6}$ - $a_{5}$ and $a_{1}$ + $a_{6}$ are respectively.

a)		5&34
b)		4&35
c)		4&34
d)		4&36

15. There are 6 AM's between 2 & a such that 3rd mean is 8 then valve of a is

a)		18
b)		20
c)		25
d)		16

16. The valve of n for which the expression $\frac{x^{n + 1} + y^{n + 1}}{x^{n} + y^{n}}$ is arithmetic mean between x and y is

a)		0
b)		1
c)		-1
d)		None of these

17. If $\frac{a^{n + 1} + b^{n + 1}}{a^{n} + b^{n}}$ is the A.M. between a and b then n equals

a)		1
b)		-1
c)		0
d)		5

18. If the progressions 3, 10, 17,..........and 63, 65, 67,........... are such that their nth terms are equal, then n is equal to

a)		13
b)		15
c)		9
d)		8

19. If Sn denotes the sum of n terms of an A.P., then $S_{n + 3}$ - 3 $S_{n + 2}$ + 3 $S_{n + 1}$ - $S_{n}$ =

a)		3
b)		1
c)		1/2
d)		0

20. In an arithmetic progression, the 24th term is 100, then the sum of the first 47 terms of the arithmetic progression is

a)		2300
b)		2350
c)		4700
d)		4600