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

Answers Choices:

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

Answers Choices:

\(A - B\)

\(A + B\)

\(2A\)

\(2B\)

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

Answers Choices:

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

Answers Choices:

\(2:3\)

\(3:4\)

\(4:3\)

\(5:6\)

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

Answers Choices:

\(4n + 3\)

\(4n + 5\)

\(4n + 6\)

\(4n + 7\)

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

Answers Choices:

14

35

80

40

Questions 7 of 50

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

Answers Choices:

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

Answers Choices:

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 \(n = \)

Answers Choices:

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

Answers Choices:

\(\frac{1}{4},\;\frac{4}{1}\)

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

\(\frac{2}{5},\;\frac{5}{2}\)

\(\frac{3}{2},\;\frac{2}{3}\)

Questions 11 of 50

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

Answers Choices:

\(p,\;,q,\;r\) 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

Answers Choices:

\({z^3} = x\)

\(x = {y^{ - 1}}\)

\({z^{ - 3}} = y\)

\(x = {y^{ - 1}} = {z^3}\)

All the above

Questions 13 of 50

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

Answers Choices:

\({\log _a}c = {\log _b}a\)

\({\log _b}a = {\log _c}b\)

\({\log _c}b = {\log _a}c\)

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

Answers Choices:

0

1

\(abc\)

\(pqr\)

Questions 15 of 50

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

Answers Choices:

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

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

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

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

Questions 16 of 50

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

Answers Choices:

\(\frac{{232}}{{990}}\)

\(\frac{{232}}{{9990}}\)

\(\frac{{232}}{{990}}\)

\(\frac{{232}}{{9909}}\)

Questions 17 of 50

Question:The sum of the series \(3 + 33 + 333 + ... + n\) terms is

Answers Choices:

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

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

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

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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

\(a = \frac{7}{4},\,r = \frac{3}{7}\)

\(a = \frac{3}{2},\,r = \frac{1}{2}\)

\(a = 2,\,r = \frac{3}{8}\)

\(a = 3,\,r = \frac{1}{4}\)

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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

\(\frac{r}{{mn}}\)

\(\frac{{mn}}{{r + 1}}\)

\(\frac{{mn}}{r}\)

\(\frac{{mn}}{{r - 1}}\)

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.

Answers Choices:

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

Answers Choices:

\(5\frac{1}{5}\)

\(3\frac{1}{5}\)

1/10

10

Questions 27 of 50

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

Answers Choices:

\(\frac{1}{5}\)

\(\frac{5}{{21}}\)

\(\frac{{21}}{{20}}\)

\(\frac{{11}}{5}\)

Questions 28 of 50

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

Answers Choices:

\(\frac{a}{{\sqrt {1 - {a^2}{b^2}} }}\)

\(\frac{a}{{1 - {a^2}{b^2}}}\)

\(a\)

\(\frac{1}{{1 - {a^2}{b^2}}}\)

Questions 29 of 50

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

Answers Choices:

\(\frac{{63}}{{120}}\)

\(\frac{{63}}{{12}}\)

\(\frac{{126}}{{105}}\)

\(\frac{{120}}{{63}}\)

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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

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

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

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

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

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

Answers Choices:

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 \(\frac{{{A_1} + {A_2}}}{{{G_1}.{G_2}}} = \)

Answers Choices:

\(\frac{{a + b}}{{ab}}\)

\(\frac{{a + b}}{{2ab}}\)

\(\frac{{2ab}}{{a + b}}\)

\(\frac{{ab}}{{a + b}}\)

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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

\(a \ge b \ge c\)

\(a + c = b\)

\(ac - {b^2} = 0\)

(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

Answers Choices:

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

Answers Choices:

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

Answers Choices:

\(a,\;b,\;c,\;d\) 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 \(\frac{{{G_1}{G_2}}}{{{H_1}{H_2}}} \times \frac{{{H_1} + {H_2}}}{{{A_1} + {A_2}}}\) =

Answers Choices:

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

Answers Choices:

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

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

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

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

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

Answers Choices:

\(1.2 + 2.3 + 3.4 + 4.5 + .........\)

\(\frac{G}{{{A^2}}}\)

\(\frac{{{A^2}}}{G}\)

\(\frac{A}{{{G^2}}}\)

Questions 45 of 50

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

Answers Choices:

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

\({n^2} + n + 2\)

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

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

Questions 46 of 50

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

Answers Choices:

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

\(\frac{{1 - {x^n}}}{{1 - x}}\)

\({x^{n + 1}}\)

None of these

Questions 47 of 50

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

Answers Choices:

\({n^3} + {n^2} + n + 2\)

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

\({n^3} + {n^2} + n\)

None of these

Questions 48 of 50

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

Answers Choices:

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

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

\(n(3n + 2)\)

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

Questions 49 of 50

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

Answers Choices:

\({n^3}\)

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

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

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

Questions 50 of 50

Question:\({11^3} + {12^3} + .... + {20^3}\)

Answers Choices:

Is divisible by 5

Is an odd integer divisible by 5

Is an even integer which is not divisible by 5

Is an odd integer which is not divisible by 5