# Progressions Test 2

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:If $${m^{th}}$$ terms of the series $$63 + 65 + 67 + 69 + .........$$ and $$3 + 10 + 17 + 24 + ......$$ be equal, then $$m =$$

11

12

13

15

## Questions 2 of 50

Question:The sum of 24 terms of the following series $$\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + .........$$ is

300

$$300\sqrt 2$$

$$200\sqrt 2$$

None of these

## Questions 3 of 50

Question:Let $${T_r}$$be the $${r^{th}}$$ term of an A.P. for $$r = 1,\;2,\;3,....$$. If for some positive integers $$m,\;n$$ we have $${T_m} = \frac{1}{n}$$ and $${T_n} = \frac{1}{m}$$, then $${T_{mn}}$$ equals

$$\frac{1}{{mn}}$$

$$\frac{1}{m} + \frac{1}{n}$$

1

0

## Questions 4 of 50

Question:If $$1,\,\,{\log _9}({3^{1 - x}} + 2),\,\,{\log _3}({4.3^x} - 1)$$ are in A.P. then x equals

$${\log _3}4$$

$$1 - {\log _3}4$$

$$1 - {\log _4}3$$

$${\log _4}3$$

## Questions 5 of 50

Question:The sum of $$1 + 3 + 5 + 7 + .........$$upto $$n$$ terms is

$${(n + 1)^2}$$

$${(2n)^2}$$

$${n^2}$$

$${(n - 1)^2}$$

## Questions 6 of 50

Question:If the sum of the series $$54 + 51 + 48 + .............$$ is 513, then the number of terms are

18

20

17

None of these

## Questions 7 of 50

Question:The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is

1

8

4

6

## Questions 8 of 50

Question:If the sum of the first 2n terms of $$2,\,5,\,8...$$ is equal to the sum of the first n terms of $$57,\,59,\,61...$$, then n is equal to

10

12

11

13

## Questions 9 of 50

Question:Three number are in A.P. such that their sum is 18 and sum of their squares is 158. The greatest number among them is

10

11

12

None of these

## Questions 10 of 50

Question:If $$\frac{{3 + 5 + 7 + ..........{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + .........{\rm{to}}\;10\;{\rm{terms}}}} = 7$$, then the value of$$n$$ is

35

36

37

40

## Questions 11 of 50

Question:If $${A_1},\,{A_2}$$ be two arithmetic means between $$\frac{1}{3}$$ and $$\frac{1}{{24}}$$ , then their values are

$$\frac{7}{{72}},\,\frac{5}{{36}}$$

$$\frac{{17}}{{72}},\,\frac{5}{{36}}$$

$$\frac{7}{{36}},\,\frac{5}{{72}}$$

$$\frac{5}{{72}},\,\frac{{17}}{{72}}$$

## Questions 12 of 50

Question:If the sum of three numbers of a arithmetic sequence is 15 and the sum of their squares is 83, then the numbers are

4, 5, 6

3, 5, 7

1, 5, 9

2, 5, 8

## Questions 13 of 50

Question:The four arithmetic means between 3 and 23 are

5, 9, 11, 13

7, 11, 15, 19

5, 11, 15, 22

7, 15, 19, 21

## Questions 14 of 50

Question:If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are

21, 17, 13

20, 16, 12

22, 18, 14

24, 20, 16

## Questions 15 of 50

Question:The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is

$$\frac{{1 - \sqrt 5 }}{2}$$

1

$$2\sqrt 5$$

None of these

## Questions 16 of 50

Question:If $$x,\,2x + 2,\,3x + 3,$$ are in G.P., then the fourth term is

27

$$- 27$$

13.5

$$- 13.5$$

## Questions 17 of 50

Question:If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio r is

$$\frac{3}{5}$$

$$\frac{5}{3}$$

$$\frac{2}{3}$$

$$\frac{3}{2}$$

## Questions 18 of 50

Question:Fifth term of a G.P. is 2, then the product of its 9 terms is

256

512

1024

None of these

## Questions 19 of 50

Question:If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is

1:3

3:2

3:4

2:3

## Questions 20 of 50

Question:The sum of the first five terms of the series $$3 + 4\frac{1}{2} + 6\frac{3}{4} + ......$$ will be

$$39\frac{9}{{16}}$$

$$18\frac{3}{{16}}$$

$$39\frac{7}{{16}}$$

$$13\frac{9}{{16}}$$

## Questions 21 of 50

Question:The sum of few terms of any ratio series is 728, if common ratio is 3 and last term is 486, then first term of series will be

2

1

3

4

## Questions 22 of 50

Question:The product of $$n$$ positive numbers is unity. Their sum is

A positive integer

Equal to $$n + \frac{1}{n}$$

Divisible by $$n$$

Never less than

## Questions 23 of 50

Question:Three numbers are in G.P. such that their sum is 38 and their product is 1728. The greatest number among them is

18

16

14

None of these

## Questions 24 of 50

Question:If x, $${G_1}{,_\;}{G_2},\;y$$be the consecutive terms of a G.P., then the value of $${G_1}\,{G_2}$$will be

$$\frac{y}{x}$$

$$\frac{x}{y}$$

$$xy$$

$$\sqrt {xy}$$

## Questions 25 of 50

Question:The sum of 3 numbers in geometric progression is 38 and their product is 1728. The middle number is

12

8

18

6

## Questions 26 of 50

Question:If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be

1, 3, 9

2, 6, 18

3, 9, 27

2, 4, 8

## Questions 27 of 50

Question:The sum of the series $$5.05 + 1.212 + 0.29088 + ...\,\infty$$ is

6.93378

6.87342

6.74384

6.64474

## Questions 28 of 50

Question:The sum of an infinite geometric series is 3. A series, which is formed by squares of its terms, have the sum also 3. First series will be

$$\frac{3}{2},\frac{3}{4},\frac{3}{8},\frac{3}{{16}},.....$$

$$\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{{16}},.....$$

$$\frac{1}{3},\frac{1}{9},\frac{1}{{27}},\frac{1}{{81}},.....$$

$$1, - \frac{1}{3},\,\frac{1}{{{3^2}}}, - \frac{1}{{{3^3}}},.....$$

## Questions 29 of 50

Question:If $${a^2} + a{b^2} + 16{c^2} = 2(3ab + 6bc + 4ac)$$, where $$a,b,c$$ are non-zero numbers. Then $$a,b,c$$are in

A.P

G.P

H.P

None of these

## Questions 30 of 50

Question:The product (32)(32) 1/6(32)1/36 ...... to $$\infty$$ is

16

32

64

0

62

## Questions 31 of 50

Question:If $$H$$ is the harmonic mean between $$p$$ and $$q$$, then the value of $$\frac{H}{p} + \frac{H}{q}$$ is

2

$$\frac{{pq}}{{p + q}}$$

$$\frac{{p + q}}{{pq}}$$

None of these

## Questions 32 of 50

Question:If the harmonic mean between $$a$$ and $$b$$ be $$H$$, then the value of $$\frac{1}{{H - a}} + \frac{1}{{H - b}}$$ is

$$a + b$$

$$ab$$

$$\frac{1}{a} + \frac{1}{b}$$

$$\frac{1}{a} - \frac{1}{b}$$

## Questions 33 of 50

Question:If $${p^{th}},\;{q^{th}},\;{r^{th}}$$ and $${s^{th}}$$ terms of an A.P. be in G.P., then $$(p - q),\;(q - r),\;(r - s)$$ will be in

G.P.

A.P.

H.P.

None of these

## Questions 34 of 50

Question:If the arithmetic and geometric means of a and b be $$A$$ and $$G$$ respectively, then the value of $$A - G$$ will be

$$\frac{{a - b}}{a}$$

$$\frac{{a + b}}{2}$$

$${\left[ {\frac{{\sqrt a - \sqrt b }}{{\sqrt 2 }}} \right]^2}$$

$$\frac{{2ab}}{{a + b}}$$

## Questions 35 of 50

Question:If $$a,\;b,\;c$$are in A.P., $$b,\;c,\;d$$ are in G.P. and $$c,\;d,\;e$$are in H.P., then $$a,\;c,\;e$$ are in

No particular order

A.P.

G.P.

H.P.

## Questions 36 of 50

Question:If $$a,\;b,\;c$$ are in G.P., $$a - b,\;c - a,\;b - c$$are in H.P., then $$a + 4b + c$$is equal to

0

$$1$$

$$- 1$$

None of these

## Questions 37 of 50

Question:If $$\frac{{b + a}}{{b - a}} = \frac{{b + c}}{{b - c}}$$, then$$a,\;b,\;c$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 38 of 50

Question:If the ratio of two numbers be $$9:1$$, then the ratio of geometric and harmonic means between them will be

$$1:9$$

$$5:3$$

$$3:5$$

$$2:5$$

## Questions 39 of 50

Question:If $$a,\;b,\;c$$ are in H.P., then for all $$n \in N$$ the true statement is

$${a^n} + {c^n} < 2{b^n}$$

$${a^n} + {c^n} > 2{b^n}$$

$${a^n} + {c^n} = 2{b^n}$$

None of the above

## Questions 40 of 50

Question:If A.M. of two terms is 9 and H.M. is 36, then G.M. will be

18

12

16

None of the above

## Questions 41 of 50

Question:If $$p,\;q,\;r$$ are in one geometric progression and $$a,\;b,\;c$$ in another geometric progression, then $$cp,\;bq,\;ar$$ are in

A.P.

H.P.

G.P.

None of these

## Questions 42 of 50

Question:If first three terms of sequence $$\frac{1}{{16}},a,b,\frac{1}{6}$$ are in geometric series and last three terms are in harmonic series, then the value of $$a$$ and $$b$$ will be

$$a = - \frac{1}{4},b = 1$$

$$a = \frac{1}{{12}},b = \frac{1}{9}$$

(1) and (2) both are true

None of these

## Questions 43 of 50

Question:If $$(y - x),\,\,2(y - a)$$ and $$(y - z)$$ are in H.P., then $$x - a,$$ $$y - a,$$ $$z - a$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 44 of 50

Question:If $$a,\,b,\,c$$ are in A.P. and $${a^2},\,{b^2},{c^2}$$are in H.P., then

$$a \ne b \ne c$$

$${a^2} = {b^2} = \frac{{{c^2}}}{2}$$

$$a,\,b,\,c$$ are in G.P.

$$\frac{{ - a}}{2},b,c$$are in G.P

## Questions 45 of 50

Question:If $$a,\;b,\;c$$ are in H.P., then which one of the following is true

$$\frac{1}{{b - a}} + \frac{1}{{b - c}} = \frac{1}{b}$$

$$\frac{{ac}}{{a + c}} = b$$

$$\frac{{b + a}}{{b - a}} + \frac{{b + c}}{{b - c}} = 1$$

None of these

## Questions 46 of 50

Question:The sum of the series $$1 + \frac{{1.3}}{6} + \frac{{1.3.5}}{{6.8}} + ....\infty$$is

1

0

$$\infty$$

4

## Questions 47 of 50

Question:The sum 1(1!) + 2(2!) + 3(3!) + ....+n (n!) equals

$$3\,(n\,!)\, + \,n - 3$$

$$(n + 1)!\, - \,(n - 1)!$$

$$(n + 1)\,!\, - 1$$

$$2\,(n\,!) - 2n - 1$$

## Questions 48 of 50

Question:$$\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ........ + .......\frac{1}{{n.(n + 1)}}$$equals

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

$$\frac{n}{{n + 1}}$$

$$\frac{{2n}}{{n + 1}}$$

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

## Questions 49 of 50

Question:Sum of the series $$\frac{2}{3} + \frac{8}{9} + \frac{{26}}{{27}} + \frac{{80}}{{81}} + .....$$ to n terms is

$$n - \frac{1}{2}({3^n} - 1)$$

$$n + \frac{1}{2}({3^n} - 1)$$

$$n + \frac{1}{2}(1 - {3^{ - n}})$$

$$n + \frac{1}{2}({3^{ - n}} - 1)$$

## Questions 50 of 50

Question:$$\sum\limits_{m = 1}^n {{m^2}}$$ is equal to

$$\frac{{m(m + 1)}}{2}$$
$$\frac{{m(m + 1)(2m + 1)}}{6}$$
$$\frac{{n(n + 1)(2n + 1)}}{6}$$
$$\frac{{n(n + 1)}}{2}$$