# Progressions Test 3

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:If $$2x,\;x + 8,\;3x + 1$$ are in A.P., then the value of $$x$$will be

3

7

5

2

## Questions 2 of 50

Question:If the sum of $$n$$ terms of an A.P. is $$nA + {n^2}B$$, where $$A,B$$ are constants, then its common difference will be

$$A - B$$

$$A + B$$

$$2A$$

$$2B$$

## Questions 3 of 50

Question:If $$a,b,c,d,e$$are in A.P. then the value of $$a + b + 4c$$ $$- 4d + e$$ in terms of a, if possible is

4a

2a

3

None of these

## Questions 4 of 50

Question:If the ratio of the sum of $$n$$ terms of two A.P.'s be $$(7n + 1):(4n + 27)$$, then the ratio of their $${11^{th}}$$ terms will be

$$2:3$$

$$3:4$$

$$4:3$$

$$5:6$$

## Questions 5 of 50

Question:If the sum of $$n$$ terms of an A.P. is $$2{n^2} + 5n$$, then the $${n^{th}}$$ term will be

$$4n + 3$$

$$4n + 5$$

$$4n + 6$$

$$4n + 7$$

## Questions 6 of 50

Question:The $${n^{th}}$$term of an A.P. is $$3n - 1$$.Choose from the following the sum of its first five terms

14

35

80

40

## Questions 7 of 50

Question:The sum of numbers from 250 to 1000 which are divisible by 3 is

135657

136557

161575

156375

## Questions 8 of 50

Question:$${7^{th}}$$ term of an A.P. is 40, then the sum of first 13 terms is

53

520

1040

2080

## Questions 9 of 50

Question:If $$\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$$ be the A.M. of $$a$$ and $$b$$, then $$n =$$

1

$$- 1$$

0

None of these

## Questions 10 of 50

Question:A number is the reciprocal of the other. If the arithmetic mean of the two numbers be $$\frac{{13}}{{12}}$$, then the numbers are

$$\frac{1}{4},\;\frac{4}{1}$$

$$\frac{3}{4},\;\frac{4}{3}$$

$$\frac{2}{5},\;\frac{5}{2}$$

$$\frac{3}{2},\;\frac{2}{3}$$

## Questions 11 of 50

Question:If $$\frac{1}{{p + q}},\;\frac{1}{{r + p}},\;\frac{1}{{q + r}}$$ are in A.P., then

$$p,\;,q,\;r$$ are in A.P.

$${p^2},\;{q^2},\;{r^2}$$ are in A.P.

$$\frac{1}{p},\;\frac{1}{q},\;\frac{1}{r}$$ are in A.P.

None of these

## Questions 12 of 50

Question:If $$1,\;{\log _y}x,\;{\log _z}y,\; - 15{\log _x}z$$ are in A.P., then

$${z^3} = x$$

$$x = {y^{ - 1}}$$

$${z^{ - 3}} = y$$

$$x = {y^{ - 1}} = {z^3}$$

All the above

## Questions 13 of 50

Question:If $$x,\;y,\;z$$ are in G.P. and $${a^x} = {b^y} = {c^z}$$, then

$${\log _a}c = {\log _b}a$$

$${\log _b}a = {\log _c}b$$

$${\log _c}b = {\log _a}c$$

None of these

## Questions 14 of 50

Question:If the $${p^{th}}$$,$${q^{th}}$$ and $${r^{th}}$$term of a G.P. are $$a,\;b,\;c$$ respectively, then $$2 + 7 + 14 + 23 + 34 + .....$$ is equal to

0

1

$$abc$$

$$pqr$$

## Questions 15 of 50

Question:The sum of 100 terms of the series $$.9 + .09 + .009.........$$will be

$$1 - {\left( {\frac{1}{{10}}} \right)^{100}}$$

$$1 + {\left( {\frac{1}{{10}}} \right)^{100}}$$

$$1 - {\left( {\frac{1}{{10}}} \right)^{106}}$$

$$1 + {\left( {\frac{1}{{10}}} \right)^{100}}$$

## Questions 16 of 50

Question:The value of $$0.\mathop {234}\limits^{\,\,\,\,\,\, \bullet \,\,\,\, \bullet \,\,\,}$$ is

$$\frac{{232}}{{990}}$$

$$\frac{{232}}{{9990}}$$

$$\frac{{232}}{{990}}$$

$$\frac{{232}}{{9909}}$$

## Questions 17 of 50

Question:The sum of the series $$3 + 33 + 333 + ... + n$$ terms is

$$\frac{1}{{27}}({10^{n + 1}} + 9n - 28)$$

$$\frac{1}{{27}}({10^{n + 1}} - 9n - 10)$$

$$\frac{1}{{27}}({10^{n + 1}} + 10n - 9)$$

None of these

## Questions 18 of 50

Question:The first term of a G.P. is 7, the last term is 448 and sum of all terms is 889, then the common ratio is

5

4

3

2

## Questions 19 of 50

Question:The sum of infinity of a geometric progression is $$\frac{4}{3}$$ and the first term is $$\frac{3}{4}$$. The common ratio is

16-Jul

16-Sep

9-Jan

9-Jul

## Questions 20 of 50

Question:If $$3 + 3\alpha + 3{\alpha ^2} + .........\infty = \frac{{45}}{8}$$, then the value of $$\alpha$$ will be

15/23

15-Jul

8-Jul

15/7

## Questions 21 of 50

Question:Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4, then

$$a = \frac{7}{4},\,r = \frac{3}{7}$$

$$a = \frac{3}{2},\,r = \frac{1}{2}$$

$$a = 2,\,r = \frac{3}{8}$$

$$a = 3,\,r = \frac{1}{4}$$

## Questions 22 of 50

Question:The value of $${a^{{{\log }_b}x}}$$, where $$a = 0.2,\;b = \sqrt 5 ,\;x = \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + .........$$to $$\infty$$ is

1

2

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

4

## Questions 23 of 50

Question:The value of $${4^{1/3}}{.4^{1/9}}{.4^{1/27}}...........\infty$$ is

2

3

4

9

## Questions 24 of 50

Question:If the $${m^{th}}$$term of a H.P. be $$n$$ and $${n^{th}}$$ be $$m$$, then the $${r^{th}}$$ term will be

$$\frac{r}{{mn}}$$

$$\frac{{mn}}{{r + 1}}$$

$$\frac{{mn}}{r}$$

$$\frac{{mn}}{{r - 1}}$$

## Questions 25 of 50

Question:Which number should be added to the numbers 13, 15, 19 so that the resulting numbers be the consecutive terms of a H.P.

7

6

$$- 6$$

$$- 7$$

## Questions 26 of 50

Question:The fifth term of the H.P., $$2,\;2\frac{1}{2},\;3\frac{1}{3},.............$$ will be

$$5\frac{1}{5}$$

$$3\frac{1}{5}$$

1/10

10

## Questions 27 of 50

Question:H.M. between the roots of the equation $${x^2} - 10x + 11 = 0$$ is

$$\frac{1}{5}$$

$$\frac{5}{{21}}$$

$$\frac{{21}}{{20}}$$

$$\frac{{11}}{5}$$

## Questions 28 of 50

Question:The harmonic mean of $$\frac{a}{{1 - ab}}$$ and $$\frac{a}{{1 + ab}}$$ is

$$\frac{a}{{\sqrt {1 - {a^2}{b^2}} }}$$

$$\frac{a}{{1 - {a^2}{b^2}}}$$

$$a$$

$$\frac{1}{{1 - {a^2}{b^2}}}$$

## Questions 29 of 50

Question:The sixth H.M. between 3 and $$\frac{6}{{13}}$$ is

$$\frac{{63}}{{120}}$$

$$\frac{{63}}{{12}}$$

$$\frac{{126}}{{105}}$$

$$\frac{{120}}{{63}}$$

## Questions 30 of 50

Question:If $$\frac{1}{{b - c}},\;\frac{1}{{c - a}},\;\frac{1}{{a - b}}$$be consecutive terms of an A.P., then $${(b - c)^2},\;{(c - a)^2},\;{(a - b)^2}$$ will be in

G.P.

A.P.

H.P.

None of these

## Questions 31 of 50

Question:If $${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$$and $$a,\;b,\;c$$ are in G.P., then $$x,\;y,\;z$$ will be in

A.P.

G.P.

H.P.

None of these

## Questions 32 of 50

Question:If the arithmetic mean of two numbers be $$A$$ and geometric mean be$$G$$, then the numbers will be

$$A \pm ({A^2} - {G^2})$$

$$\sqrt A \pm \sqrt {{A^2} - {G^2}}$$

$$A \pm \sqrt {(A + G)(A - G)}$$

$$\frac{{A \pm \sqrt {(A + G)(A - G)} }}{2}$$

## Questions 33 of 50

Question:Given $${a^x} = {b^y} = {c^z} = {d^u}$$ and $$a,\;b,\;c,\;d$$ are in G.P., then $$x,y,z,u$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 34 of 50

Question:If $${A_1},\;{A_2}$$ are the two A.M.'s between two numbers $$a$$and $$b$$and $${G_1},\;{G_2}$$ be two G.M.'s between same two numbers, then $$\frac{{{A_1} + {A_2}}}{{{G_1}.{G_2}}} =$$

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

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

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

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

## Questions 35 of 50

Question:If the A.M. and H.M. of two numbers is 27 and 12 respectively, then G.M. of the two numbers will be

9

18

24

36

## Questions 36 of 50

Question:If $$a,\;b,\;c$$ are in H.P., then $$\frac{a}{{b + c}},\;\frac{b}{{c + a}},\;\frac{c}{{a + b}}$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 37 of 50

Question:If $$\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$$ are in H.P., then $$x,\;y,\;z$$are in

A.P.

G.P.

H.P.

None of these

## Questions 38 of 50

Question:If the first and $${(2n - 1)^{th}}$$ terms of an A.P., G.P. and H.P. are equal and their $${n^{th}}$$ terms are respectively $$a,\;b$$ and $$c$$, then

$$a \ge b \ge c$$

$$a + c = b$$

$$ac - {b^2} = 0$$

(1) and (3) both

## Questions 39 of 50

Question:If $${x^a} = {x^{b/2}}{z^{b/2}} = {z^c}$$, then $$a,b,c$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 40 of 50

Question:If the product of three terms of G.P. is 512. If 8 added to first and 6 added to second term, so that number may be in A.P., then the numbers are

2, 4, 8

4, 8, 16

3, 6, 12

None of these

## Questions 41 of 50

Question:Given $$a + d > b + c$$ where $$a,\;b,\;c,\;d$$ are real numbers, then

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

$$\frac{1}{a},\;\frac{1}{b},\;\frac{1}{c},\;\frac{1}{d}$$ are in A.P.

$$(a + b),\;(b + c),\;(c + d),\;(a + d)$$are in A.P.

$$\frac{1}{{a + b}},\;\frac{1}{{b + c}},\;\frac{1}{{c + d}},\;\frac{1}{{a + d}}$$ are in A.P.

## Questions 42 of 50

Question:If $${A_1},\;{A_2};{G_1},\;{G_2}$$ and $${H_1},\;{H_2}$$ be two A.M.s, G.M.s and H.M.s between two numbers respectively, then $$\frac{{{G_1}{G_2}}}{{{H_1}{H_2}}} \times \frac{{{H_1} + {H_2}}}{{{A_1} + {A_2}}}$$ =

1

0

2

3

## Questions 43 of 50

Question:If $${a_1},{a_2},....{a_n}$$ are positive real numbers whose product is a fixed number c, then the minimum value of $${a_1} + {a_2} + ...$$ $$+ {a_{n - 1}} + 2{a_n}$$is

$$n{(2c)^{1/n}}$$

$$(n + 1)\,{c^{1/n}}$$

$$2n{c^{1/n}}$$

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

## Questions 44 of 50

Question:If arithmetic mean of two positive numbers is $$A$$, their geometric mean is $$G$$ and harmonic mean is $$H$$, then $$H$$is equal to

$$1.2 + 2.3 + 3.4 + 4.5 + .........$$

$$\frac{G}{{{A^2}}}$$

$$\frac{{{A^2}}}{G}$$

$$\frac{A}{{{G^2}}}$$

## Questions 45 of 50

Question:$${n^{th}}$$ term of the series $$2 + 4 + 7 + 11 + .......$$will be

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

$${n^2} + n + 2$$

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

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

## Questions 46 of 50

Question:The sum of the series $$1 + 2x + 3{x^2} + 4{x^3} + .........$$upto $$n$$ terms is

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

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

$${x^{n + 1}}$$

None of these

## Questions 47 of 50

Question:The sum of the series $$3.6 + 4.7 + 5.8 + ........$$upto $$(n - 2)$$ terms

$${n^3} + {n^2} + n + 2$$

$$\frac{1}{6}(2{n^3} + 12{n^2} + 10n - 84)$$

$${n^3} + {n^2} + n$$

None of these

## Questions 48 of 50

Question:If $$\sum\limits_{i = 1}^n {i = \frac{{n(n + 1)}}{2}}$$, then $$\sum\limits_{i = 1}^n {(3i - 2) = }$$

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

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

$$n(3n + 2)$$

$$\frac{{n(3n + 1)}}{4}$$

## Questions 49 of 50

Question:The sum of $$n$$ terms of the following series $$1.2 + 2.3 + 3.4 + 4.5 + .........$$ shall be

$${n^3}$$

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

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

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

## Questions 50 of 50

Question:$${11^3} + {12^3} + .... + {20^3}$$