Total Questions:50 Total Time: 75 Min
Remaining:
Question:If \(2x,\;x + 8,\;3x + 1\) are in A.P., then the value of \(x\)will be
3
7
5
2
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
\(A - B\)
\(A + B\)
\(2A\)
\(2B\)
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
None of these
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
\(2:3\)
\(3:4\)
\(4:3\)
\(5:6\)
Question:If the sum of \(n\) terms of an A.P. is \(2{n^2} + 5n\), then the \({n^{th}}\) term will be
\(4n + 3\)
\(4n + 5\)
\(4n + 6\)
\(4n + 7\)
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
Question:The sum of numbers from 250 to 1000 which are divisible by 3 is
135657
136557
161575
156375
Question:\({7^{th}}\) term of an A.P. is 40, then the sum of first 13 terms is
53
520
1040
2080
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
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
\(\frac{1}{4},\;\frac{4}{1}\)
\(\frac{3}{4},\;\frac{4}{3}\)
\(\frac{2}{5},\;\frac{5}{2}\)
\(\frac{3}{2},\;\frac{2}{3}\)
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.
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
Question:If \(x,\;y,\;z\) are in G.P. and \({a^x} = {b^y} = {c^z}\), then
\({\log _a}c = {\log _b}a\)
\({\log _b}a = {\log _c}b\)
\({\log _c}b = {\log _a}c\)
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
\(abc\)
\(pqr\)
Question:The sum of 100 terms of the series \(.9 + .09 + .009.........\)will be
\(1 - {\left( {\frac{1}{{10}}} \right)^{100}}\)
\(1 + {\left( {\frac{1}{{10}}} \right)^{100}}\)
\(\)\(1 - {\left( {\frac{1}{{10}}} \right)^{106}}\)
Question:The value of \(0.\mathop {234}\limits^{\,\,\,\,\,\, \bullet \,\,\,\, \bullet \,\,\,} \) is
\(\frac{{232}}{{990}}\)
\(\frac{{232}}{{9990}}\)
\(\frac{{232}}{{9909}}\)
Question:The sum of the series \(3 + 33 + 333 + ... + n\) terms is
\(\frac{1}{{27}}({10^{n + 1}} + 9n - 28)\)
\(\frac{1}{{27}}({10^{n + 1}} - 9n - 10)\)
\(\frac{1}{{27}}({10^{n + 1}} + 10n - 9)\)
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
4
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
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
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
\(a = \frac{7}{4},\,r = \frac{3}{7}\)
\(a = \frac{3}{2},\,r = \frac{1}{2}\)
\(a = 2,\,r = \frac{3}{8}\)
\(a = 3,\,r = \frac{1}{4}\)
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
\(\frac{1}{2}\)
Question:The value of \({4^{1/3}}{.4^{1/9}}{.4^{1/27}}...........\infty \) is
9
Question:If the \({m^{th}}\)term of a H.P. be \(n\) and \({n^{th}}\) be \(m\), then the \({r^{th}}\) term will be
\(\frac{r}{{mn}}\)
\(\frac{{mn}}{{r + 1}}\)
\(\frac{{mn}}{r}\)
\(\frac{{mn}}{{r - 1}}\)
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.
6
\( - 6\)
\( - 7\)
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
Question:H.M. between the roots of the equation \({x^2} - 10x + 11 = 0\) is
\(\frac{1}{5}\)
\(\frac{5}{{21}}\)
\(\frac{{21}}{{20}}\)
\(\frac{{11}}{5}\)
Question:The harmonic mean of \(\frac{a}{{1 - ab}}\) and \(\frac{a}{{1 + ab}}\) is
\(\frac{a}{{\sqrt {1 - {a^2}{b^2}} }}\)
\(\frac{a}{{1 - {a^2}{b^2}}}\)
\(a\)
\(\frac{1}{{1 - {a^2}{b^2}}}\)
Question:The sixth H.M. between 3 and \(\frac{6}{{13}}\) is
\(\frac{{63}}{{120}}\)
\(\frac{{63}}{{12}}\)
\(\frac{{126}}{{105}}\)
\(\frac{{120}}{{63}}\)
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.
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
Question:If the arithmetic mean of two numbers be \(A\) and geometric mean be\(G\), then the numbers will be
\(A \pm ({A^2} - {G^2})\)
\(\sqrt A \pm \sqrt {{A^2} - {G^2}} \)
\(A \pm \sqrt {(A + G)(A - G)} \)
\(\frac{{A \pm \sqrt {(A + G)(A - G)} }}{2}\)
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
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 \(\frac{{{A_1} + {A_2}}}{{{G_1}.{G_2}}} = \)
\(\frac{{a + b}}{{ab}}\)
\(\frac{{a + b}}{{2ab}}\)
\(\frac{{2ab}}{{a + b}}\)
\(\frac{{ab}}{{a + b}}\)
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
18
24
36
Question:If \(a,\;b,\;c\) are in H.P., then \(\frac{a}{{b + c}},\;\frac{b}{{c + a}},\;\frac{c}{{a + b}}\) are in
Question:If \(\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}\) are in H.P., then \(x,\;y,\;z\)are in
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
Question:If \({x^a} = {x^{b/2}}{z^{b/2}} = {z^c}\), then \(a,b,c\) are in
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
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.
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 \(\frac{{{G_1}{G_2}}}{{{H_1}{H_2}}} \times \frac{{{H_1} + {H_2}}}{{{A_1} + {A_2}}}\) =
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
\(n{(2c)^{1/n}}\)
\((n + 1)\,{c^{1/n}}\)
\(2n{c^{1/n}}\)
\((n + 1){(2c)^{1/n}}\)
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
\(1.2 + 2.3 + 3.4 + 4.5 + .........\)
\(\frac{G}{{{A^2}}}\)
\(\frac{{{A^2}}}{G}\)
\(\frac{A}{{{G^2}}}\)
Question:\({n^{th}}\) term of the series \(2 + 4 + 7 + 11 + .......\)will be
\(\frac{{{n^2} + n + 1}}{2}\)
\({n^2} + n + 2\)
\(\frac{{{n^2} + n + 2}}{2}\)
\(\frac{{{n^2} + 2n + 2}}{2}\)
Question:The sum of the series \(1 + 2x + 3{x^2} + 4{x^3} + .........\)upto \(n\) terms is
\(\frac{{1 - (n + 1){x^n} + n{x^{n + 1}}}}{{{{(1 - x)}^2}}}\)
\(\frac{{1 - {x^n}}}{{1 - x}}\)
\({x^{n + 1}}\)
Question:The sum of the series \(3.6 + 4.7 + 5.8 + ........\)upto \((n - 2)\) terms
\({n^3} + {n^2} + n + 2\)
\(\frac{1}{6}(2{n^3} + 12{n^2} + 10n - 84)\)
\({n^3} + {n^2} + n\)
Question:If \(\sum\limits_{i = 1}^n {i = \frac{{n(n + 1)}}{2}} \), then \(\sum\limits_{i = 1}^n {(3i - 2) = } \)
\(\frac{{n(3n - 1)}}{2}\)
\(\frac{{n(3n + 1)}}{2}\)
\(n(3n + 2)\)
\(\frac{{n(3n + 1)}}{4}\)
Question:The sum of \(n\) terms of the following series \(1.2 + 2.3 + 3.4 + 4.5 + .........\) shall be
\({n^3}\)
\(\frac{1}{3}n\,(n + 1)(n + 2)\)
\(\frac{1}{6}n\,(n + 1)(n + 2)\)
\(\frac{1}{3}n\,(n + 1)(2n + 1)\)
Question:\({11^3} + {12^3} + .... + {20^3}\)
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