# Progressions Test 7

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:The number of terms in the series $$101 + 99 + 97 + ..... + 47$$ is

25

28

30

20

## Questions 2 of 50

Question:If the $${p^{th}}$$ term of an A.P. be $$q$$ and $${q^{th}}$$term be p, then its $${r^{th}}$$ term will be

$$p + q + r$$

$$p + q - r$$

$$p + r - q$$

$$p - q - r$$

## Questions 3 of 50

Question:If the numbers $$a,\;b,\;c,\;d,\;e$$form an A.P., then the value of $$a - 4b + 6c - 4d + e$$ is

1

2

0

None of these

## Questions 4 of 50

Question:The sixth term of an A.P. is equal to 2, the value of the common difference of the A.P. which makes the product $${a_1}{a_4}{a_5}$$ least is given by

$$x = \frac{8}{5}$$

$$x = \frac{5}{4}$$

$$x = 2/3$$

None of these

## Questions 5 of 50

Question:The ratio of the sums of first $$n$$even numbers and $$n$$ odd numbers will be

$$1:n$$

$$(n + 1):1$$

$$(n + 1):n$$

$$(n - 1):1$$

## Questions 6 of 50

Question:If $${a_1},\;{a_2},\;{a_3}.......{a_n}$$ are in A.P., where $${a_i} > 0$$ for all $$i$$, then the value of $$\frac{1}{{\sqrt {{a_1}} + \sqrt {{a_2}} }} + \frac{1}{{\sqrt {{a_2}} + \sqrt {{a_3}} }} +$$ $$........ + \frac{1}{{\sqrt {{a_{n - 1}}} + \sqrt {{a_n}} }} =$$

$$\frac{{n - 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}$$

$$\frac{{n + 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}$$

$$\frac{{n - 1}}{{\sqrt {{a_1}} - \sqrt {{a_n}} }}$$

$$\frac{{n + 1}}{{\sqrt {{a_1}} - \sqrt {{a_n}} }}$$

## Questions 7 of 50

Question:If $${S_n}$$ denotes the sum of $$n$$ terms of an arithmetic progression, then the value of $$({S_{2n}} - {S_n})$$is equal to

$$2{S_n}$$

$${S_{3n}}$$

$$\frac{1}{3}{S_{3n}}$$

$$\frac{1}{2}{S_n}$$

## Questions 8 of 50

Question:The solution of $${\log _{\sqrt 3 }}x + {\log _{\sqrt[4]{3}}}x + {\log _{\sqrt[6]{3}}}x + ......... + {\log _{\sqrt[{16}]{3}}}x = 36$$ is

$$x = 3$$

$$x = 4\sqrt 3$$

$$x = 9$$

$$x = \sqrt 3$$

## Questions 9 of 50

Question:The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is

10

11

12

None of these

## Questions 10 of 50

Question:The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is

5

10

12

14

## Questions 11 of 50

Question:If the sum of two extreme numbers of an A.P. with four terms is 8 and product of remaining two middle term is 15, then greatest number of the series will be

5

7

9

11

## Questions 12 of 50

Question:If the sides of a right angled traingle are in A.P., then the sides are proportional to

1:02:03

2:03:04

3:04:05

4:05:06

## Questions 13 of 50

Question:If the $${4^{th}},\;{7^{th}}$$ and $${10^{th}}$$ terms of a G.P. be $$a,\;b,\;c$$ respectively, then the relation between [a,\;b,\;c\)is

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

$${a^2} = bc$$

$${b^2} = ac$$

$${c^2} = ab$$

## Questions 14 of 50

Question:If the first term of a G.P. be 5 and common ratio be $$- 5$$, then which term is 3125

$${6^{th}}$$

$${5^{th}}$$

$${7^{th}}$$

$${8^{th}}$$

## Questions 15 of 50

Question:If the $${10^{th}}$$ term of a geometric progression is 9 and $${4^{th}}$$ term is 4, then its $${7^{th}}$$ term is

6

36

$$\frac{4}{9}$$

$$\frac{9}{4}$$

## Questions 16 of 50

Question:The 6th term of a G.P. is 32 and its 8th term is 128, then the common ratio of the G.P. is

1

2

4

4

## Questions 17 of 50

Question:The number $$111..............1$$ (91 times) is a

Even number

Prime number

Not prime

None of these

## Questions 18 of 50

Question:For a sequence $$< {a_n} > ,\;{a_1} = 2$$ and $$\frac{{{a_{n + 1}}}}{{{a_n}}} = \frac{1}{3}$$. Then $$\sum\limits_{r = 1}^{20} {{a_r}}$$ is

$$\frac{{20}}{2}[4 + 19 \times 3]$$

$$3\left( {1 - \frac{1}{{{3^{20}}}}} \right)$$

$$2(1 - {3^{20}})$$

None of these

## Questions 19 of 50

Question:The G.M. of the numbers $$3,\,{3^2},\,{3^3},....,\,{3^n}$$ is

$${3^{\frac{2}{n}}}$$

$${3^{\frac{{n + 1}}{2}}}$$

$${3^{\frac{n}{2}}}$$

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

## Questions 20 of 50

Question:The product of three geometric means between 4 and $$\frac{1}{4}$$ will be

4

2

$$- 1$$

1

## Questions 21 of 50

Question:The sum of infinite terms of a G.P. is $$x$$ and on squaring the each term of it, the sum will be $$y$$, then the common ratio of this series is

$$\frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$

$$\frac{{{x^2} + {y^2}}}{{{x^2} - {y^2}}}$$

$$\frac{{{x^2} - y}}{{{x^2} + y}}$$

$$\frac{{{x^2} + y}}{{{x^2} - y}}$$

## Questions 22 of 50

Question:If the sum of an infinite G.P. and the sum of square of its terms is 3, then the common ratio of the first series is

1

$$\frac{1}{2}$$

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

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

## Questions 23 of 50

Question:The value of $$\overline {0.037}$$ where, $$\overline {.037}$$ stands for the number 0.037037037........ is

$$\frac{{37}}{{1000}}$$

$$\frac{1}{{27}}$$

$$\frac{1}{{37}}$$

$$\frac{{37}}{{999}}$$

## Questions 24 of 50

Question:If $$x$$ is added to each of numbers 3, 9, 21 so that the resulting numbers may be in G.P., then the value of $$x$$ will be

3

$$\frac{1}{2}$$

2

$$\frac{1}{3}$$

## Questions 25 of 50

Question:If the $${7^{th}}$$ term of a harmonic progression is 8 and the $${8^{th}}$$term is 7, then its $${15^{th}}$$ term is

16

14

$$\frac{{27}}{{14}}$$

$$\frac{{56}}{{15}}$$

## Questions 26 of 50

Question:If the $${7^{th}}$$ term of a H.P. is $$\frac{1}{{10}}$$ and the $${12^{th}}$$ term is $$\frac{1}{{25}}$$, then the $${20^{th}}$$ term is

$$\frac{1}{{37}}$$

$$\frac{1}{{41}}$$

$$\frac{1}{{45}}$$

$$\frac{1}{{49}}$$

## Questions 27 of 50

Question:If sixth term of a H.P. is $$\frac{1}{{61}}$$ and its tenth term is $$\frac{1}{{105}},$$ then first term of that H.P. is

$$\frac{1}{{28}}$$

$$\frac{1}{{39}}$$

$$\frac{1}{6}$$

$$\frac{1}{{17}}$$

## Questions 28 of 50

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

$$ab = cd$$

$$ad = bc$$

$$ac = bd$$

$$abcd = 1$$

## Questions 29 of 50

Question:If $$a,\;b,\;c$$ are in A.P., then$$\frac{a}{{bc}},\;\frac{1}{c},\;\frac{2}{b}$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 30 of 50

Question:If the roots of$$a\,(b - c){x^2} + b\,(c - a)x + c\,(a - b) = 0$$ be equal, then $$a,\;b,\;c$$are in

A.P.

G.P.

H.P.

None of these

## Questions 31 of 50

Question:If $${a^2},\;{b^2},\;{c^2}$$ are in A.P., then $${(b + c)^{ - 1}},\;{(c + a)^{ - 1}}$$ and $${(a + b)^{ - 1}}$$ will be in

H.P.

G.P.

A.P.

None of these

## Questions 32 of 50

Question:If $$a,\;b,\;c$$ are in A.P., then $$\frac{1}{{bc}},\;\frac{1}{{ca}},\;\frac{1}{{ab}}$$ will be in

A.P.

G.P.

H.P.

None of these

## Questions 33 of 50

Question:If $$x,\;1,\;z$$ are in A.P. and $$x,\;2,\;z$$ are in G.P., then $$x,\;4,\;z$$ will be in

A.P.

G.P.

H.P.

None of these

## Questions 34 of 50

Question:If the $${p^{th}},\;{q^{th}}$$ and $${r^{th}}$$term of a G.P. and H.P. are $$a,\;b,\;c$$, then $$a(b - c)\log a + b(c - a)$$ $$\log b + c(a - b)\log c =$$

$$- 1$$

0

1

Does not exist

## Questions 35 of 50

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

$$a = b = c$$

$$2b = 3a + c$$

$${b^2} = \sqrt {(ac/8)}$$

None of these

## Questions 36 of 50

Question:In the four numbers first three are in G.P. and last three are in A.P. whose common difference is 6. If the first and last numbers are same, then first will be

2

4

6

8

## Questions 37 of 50

Question:If $${\log _x}y,\;{\log _z}x,\;{\log _y}z$$ are in G.P. $$xyz = 64$$ and $${x^3},\;{y^3},\;{z^3}$$ are in A.P., then

$$x = y = z$$

$$x = 4$$

$$x,\;y,\,z$$are in G.P.

All the above

## Questions 38 of 50

Question:If three unequal numbers $$p,\;q,\;r$$ are in H.P. and their squares are in A.P., then the ratio $$p:q:r$$ is

$$1 - \sqrt 3 :2:1 + \sqrt 3$$

$$1:\sqrt 2 : - \sqrt 3$$

$$1: - \sqrt 2 :\sqrt 3$$

$$1 \mp \sqrt 3 : - 2:1 \pm \sqrt 3$$

## Questions 39 of 50

Question:If $${G_1}$$ and $${G_2}$$ are two geometric means and A the arithmetic mean inserted between two numbers, then the value of $$\frac{{G_1^2}}{{{G_2}}} + \frac{{G_2^2}}{{{G_1}}}$$ is

$$\frac{A}{2}$$

A

2:00 AM

None of these

## Questions 40 of 50

Question:If $$\log (x + z) + \log (x + z - 2y) = 2\log (x - z),\,$$ then $$x,\,y,\,z$$ are in

H.P.

G.P.

A.P.

None of these

## Questions 41 of 50

Question:If A and G are arithmetic and geometric means and $${x^2} - 2Ax + {G^2} = 0$$, then

$$A = G$$

$$A > G$$

$$A < G$$

$$A = - \,G$$

## Questions 42 of 50

Question:If ln $$(a + c)$$, In $$(c - a)$$, In $$(a - 2b + c)$$ are in A.P., then

$$a,\;b,\;c$$are in A.P.

$${a^2},\;{b^2},\;{c^2}$$are in A.P.

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

$$a,\;b,\;c$$ are in H.P

## Questions 43 of 50

Question:The sum of infinite terms of the following series $$1 + \frac{4}{5} + \frac{7}{{{5^2}}} + \frac{{10}}{{{5^3}}} + .........$$ will be

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

$$\frac{{35}}{8}$$

$$\frac{{35}}{4}$$

$$\frac{{35}}{{16}}$$

## Questions 44 of 50

Question:The sum of the series $$1 + 3x + 6{x^2} + 10{x^3} + ........\infty$$ will be

$$\frac{1}{{{{(1 - x)}^2}}}$$

$$\frac{1}{{1 - x}}$$

$$\frac{1}{{{{(1 + x)}^2}}}$$

$$\frac{1}{{{{(1 - x)}^3}}}$$

## Questions 45 of 50

Question:The sum of $$(n - 1)$$ terms of $$1 + (1 + 3) +$$ $$(1 + 3 + 5) + .......$$ is

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

$$\frac{{{n^2}(n + 1)}}{4}$$

$$\frac{{n\,(n - 1)\,(2n - 1)}}{6}$$

$${n^2}$$

## Questions 46 of 50

Question:The sum of first $$n$$ terms of the given series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ............$$is$$\frac{{n{{(n + 1)}^2}}}{2}$$, when $$n$$ is even. When $$n$$ is odd, the sum will be

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

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

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

None of these

## Questions 47 of 50

Question:The sum of all the products of the first $$n$$ natural numbers taken two at a time is

$$\frac{1}{{24}}n(n - 1)(n + 1)(3n + 2)$$

$$\frac{{{n^2}}}{{48}}(n - 1)(n - 2)$$

$$\frac{1}{6}n(n + 1)(n + 2)(n + 5)$$

None of these

## Questions 48 of 50

Question:The sum of the series $${1.3^2} + {2.5^2} + {3.7^2} + ..........$$upto $$20$$ terms is

188090

189080

199080

None of these

## Questions 49 of 50

Question:If the sum of $$1 + \frac{{1 + 2}}{2} + \frac{{1 + 2 + 3}}{3} + .....$$ to n terms is S, then S is equal to

$$\frac{{n(n + 3)}}{4}$$

$$\frac{{n(n + 2)}}{4}$$

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

$${n^2}$$

## Questions 50 of 50

Question:The nth term of the series $$\frac{2}{{1!}} + \frac{7}{{2\,!}} + \frac{{15}}{{3\,!}} + \frac{{26}}{{4\,!}} + .....$$ is

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