Total Questions:50 Total Time: 75 Min
Remaining:
Question:Which term of the sequence (-8, +18i), (-6 + 15i); (-4+12i)............... is purely imaginary.
5th
7th
8th
6th
Question:If \({n^{th}}\) terms of two A.P.'s are \(3n + 8\) and \(7n + 15\), then the ratio of their \({12^{th}}\) terms will be
9-Apr
16-Jul
7-Mar
15-Aug
Question:If \({a_1} = {a_2} = 2,\;{a_n} = {a_{n - 1}} - 1\;(n > 2)\), then \({a_5}\)is
1
\( - 1\)
0
\( - 2\)
Question:If \(n\) be odd or even, then the sum of \(n\) terms of the series \(1 - 2 + \) \(3 - \)\(4 + 5 - 6 + ......\) will be
\( - \frac{n}{2}\)
\(\frac{{n - 1}}{2}\)
\(\frac{{n + 1}}{2}\)
\(\frac{{2n + 1}}{2}\)
1 and 3 are correct
Question:If the first, second and last terms of an A.P. be \(a,\;b,\;2a\) respectively, then its sum will be
\(\frac{{ab}}{{b - a}}\)
\(\frac{{ab}}{{2(b - a)}}\)
\(\frac{{3ab}}{{2(b - a)}}\)
\(\frac{{3ab}}{{4(b - a)}}\)
Question:The solution of the equation\((x + 1) + (x + 4) + (x + 7) + ......... + (x + 28) = 155\) is
2
3
4
Question:The sum of all two digit numbers which, when divided by 4, yield unity as a remainder is
1190
1197
1210
None of these
Question:Let \({S_n}\)denotes the sum of \(n\) terms of an A.P. If \({S_{2n}} = 3{S_n}\), then ratio \(\frac{{{S_{3n}}}}{{{S_n}}} = \)
6
8
10
Question:The first term of an A.P. of consecutive integers is \({p^2} + 1\) The sum of \((2p + 1)\) terms of this series can be expressed as
\({(p + 1)^2}\)
\({(p + 1)^3}\)
\((2p + 1){(p + 1)^2}\)
\({p^3} + {(p + 1)^3}\)
Question:If \(f(x + y,x - y) = xy\,,\) then the arithmetic mean of \(f(x,y)\) and \(f(y,x)\) is
\(x\)
\(y\)
Question:If \(\log 2,\;\log ({2^n} - 1)\) and \(\log ({2^n} + 3)\) are in A.P., then n =
2-May
\({\log _2}5\)
\({\log _3}5\)
2-Mar
Question:If \(a,\,b,\,c\) are in G.P., then
\(a({b^2} + {a^2}) = c({b^2} + {c^2})\)
\(a({b^2} + {c^2}) = c({a^2} + {b^2})\)
\({a^2}(b + c) = {c^2}(a + b)\)
Question:\({7^{th}}\) term of the sequence \(\sqrt 2 ,\;\sqrt {10} ,\;5\sqrt 2 ,\;.......\)is
\(125\sqrt {10} \)
\(25\sqrt 2 \)
125
\(125\sqrt 2 \)
Question:The first and last terms of a G.P. are \(a\) and \(l\) respectively; \(r\) being its common ratio; then the number of terms in this G.P. is
\(\frac{{\log l - \log a}}{{\log r}}\)
\(1 - \frac{{\log l - \log a}}{{\log r}}\)
\(\frac{{\log a - \log l}}{{\log r}}\)
\(1 + \frac{{\log l - \log a}}{{\log r}}\)
Question:If \({\log _x}a,\;{a^{x/2}}\) and \({\log _b}x\) are in G.P., then \(x = \)
\( - \log ({\log _b}a)\)
\( - {\log _a}({\log _a}b)\)
\({\log _a}({\log _e}a) - {\log _a}({\log _e}b)\)
\({\log _a}({\log _e}b) - {\log _a}({\log _e}a)\)
Question:If the roots of the cubic equation \(a{x^3} + b{x^2} + cx + d = 0\) are in G.P., then
\({c^3}a = {b^3}d\)
\(c{a^3} = b{d^3}\)
\({a^3}b = {c^3}d\)
\(a{b^3} = c{d^3}\)
Question:If the sum of \(n\) terms of a G.P. is 255 and \({n^{th}}\)terms is 128 and common ratio is 2, then first term will be
7
Question:The sum of \(n\) terms of the following series \(1 + (1 + x) + (1 + x + {x^2}) + ..........\)will be
\(\frac{{1 - {x^n}}}{{1 - x}}\)
\(\frac{{x(1 - {x^n})}}{{1 - x}}\)
\(\frac{{n(1 - x) - x(1 - {x^n})}}{{{{(1 - x)}^2}}}\)
Question:If the sum of first 6 term is 9 times to the sum of first 3 terms of the same G.P., then the common ratio of the series will be
2-Jan
Question:If three geometric means be inserted between 2 and 32, then the third geometric mean will be
16
12
Question:If five G.M.'s are inserted between 486 and 2/3 then fourth G.M. will be
Question:The G.M. of roots of the equation \({x^2} - 18x + 9 = 0\) is
Question:\(0.\mathop {423}\limits^{\,\,\,\, \bullet \,\,\, \bullet \,} = \)
\(\frac{{419}}{{990}}\)
\(\frac{{419}}{{999}}\)
\(\frac{{417}}{{990}}\)
\(\frac{{417}}{{999}}\)
Question:If \(y = x - {x^2} + {x^3} - {x^4} + ......\infty \), then value of x will be
\(y + \frac{1}{y}\)
\(\frac{y}{{1 + y}}\)
\(y - \frac{1}{y}\)
\(\frac{y}{{1 - y}}\)
Question:If \(x = \sum\limits_{n = 0}^\infty {{a^n}} ,\;y = \sum\limits_{n = 0}^\infty {{b^n},\;z = \sum\limits_{n = 0}^\infty {{{(ab)}^n}} } \), where\(a,\;b < 1\), then
\(xyz = x + y + z\)
\(xz + yz = xy + z\)
\(xy + yz = xz + y\)
\(xy + xz = yz + x\)
Question:If in an infinite G.P. first term is equal to the twice of the sum of the remaining terms, then its common ratio is
3-Jan
1/3
Question:If the sum of the series \(1 + \frac{2}{x} + \frac{4}{{{x^2}}} + \frac{8}{{{x^3}}} + ....\infty \) is a finite number, then
\(x > 2\)
\(x > - 2\)
\(x > \frac{1}{2}\)
Question:\(0.5737373...... = \)
\(\frac{{284}}{{497}}\)
\(\frac{{284}}{{495}}\)
\(\frac{{568}}{{990}}\)
\(\frac{{567}}{{990}}\)
Question:If \(a,\;b,\;c\) are three distinct positive real numbers which are in H.P., then \(\frac{{3a + 2b}}{{2a - b}} + \frac{{3c + 2b}}{{2c - b}}\) is
Greater than or equal to 10
Less than or equal to 10
Only equal to 10
Question:If \(a,\;b,\;c,\;d\) are in H.P., then \(ab + bc + cd\) is equal to
\(3ad\)
\((a + b)(c + d)\)
\(3ac\)
Question:If the arithmetic, geometric and harmonic means between two distinct positive real numbers be \(A,\;G\) and \(H\) respectively, then the relation between them is
\(A > G > H\)
\(A > G < H\)
\(H > G > A\)
\(G > A > H\)
Question:If the arithmetic, geometric and harmonic means between two positive real numbers be \(A,\;G\) and \(H\), then
\({A^2} = GH\)
\({H^2} = AG\)
\(G = AH\)
\({G^2} = AH\)
Question:If \(a,\;b,\;c\) are in G.P. and \(x,\,y\) are the arithmetic means between \(a,\;b\) and \(b,\;c\) respectively, then \(\frac{a}{x} + \frac{c}{y}\)is equal to
\(\frac{1}{2}\)
Question:If \(a,\;b,\;c\) are in A.P. and \(a,\;b,\;d\) in G.P., then \(a,\;a - b,\;d - c\) will be in
A.P.
G.P.
H.P.
Question:\(x + y + z = 15\) if \(9,\;x,\;y,\;z,\;a\) are in A.P.; while \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{5}{3}\) if \(9,\;x,\;y,\;z,\;a\) are in H.P., then the value of \(a\) will be
9
Question:If 9 A.M.'s and H.M.'s are inserted between the 2 and 3 and if the harmonic mean \(H\)is corresponding to arithmetic mean \(A\), then \(A + \frac{6}{H} = \)
5
Question:If \(2(y - a)\) is the H.M. between \(y - x\) and \(y - z\), then \(x - a,\;y - a,\;z - a\) are in
Question:If the ratio of A.M. between two positive real numbers \(a\) and \(b\)to their H.M. is \(m:n\), then \(a:b\) is
\(\frac{{\sqrt {m - n} + \sqrt n }}{{\sqrt {m - n} - \sqrt n }}\)
\(\frac{{\sqrt n + \sqrt {m - n} }}{{\sqrt n - \sqrt {m - n} }}\)
\(\frac{{\sqrt m + \sqrt {m - n} }}{{\sqrt m - \sqrt {m - n} }}\)
Question:Three non-zero real numbers form an A.P. and the squares of these numbers taken in the same order form a G.P. Then the number of all possible common ratios of the G.P. is
Question:If \({a^x} = {b^y} = {c^z}\,{\rm{and}}\,\,a,b,c\) are in G.P. then \(x,y,z\) are in
A. P.
G. P.
H. P.
Question:If \(\frac{a}{b},\frac{b}{c},\frac{c}{a}\) are in H.P., then
\({a^2}b,\,{c^2}a,\,{b^2}c\) are in A.P.
\({a^2}b,\,{b^2}c,\,{c^2}a\)are in H.P.
\({a^2}b,\,{b^2}c,\,{c^2}a\)are in G.P.
Question:If A is the A.M. of the roots of the equation \({x^2} - 2ax + b = 0\) and \(G\) is the G.M. of the roots of the equation \({x^2} - 2bx + {a^2} = 0,\) then
\(A > G\)
\(A \ne G\)
\(A = G\)
Question:If \(|x|\, < 1\), then the sum of the series \(1 + 2x + 3{x^2} + 4{x^3} + ...........\infty \) will be
\(\frac{1}{{1 - x}}\)
\(\frac{1}{{1 + x}}\)
\(\frac{1}{{{{(1 + x)}^2}}}\)
\(\frac{1}{{{{(1 - x)}^2}}}\)
Question:\(1 + \frac{3}{2} + \frac{5}{{{2^2}}} + \frac{7}{{{2^3}}} + ......\,\infty \,\)is equal to
Question:If the set of natural numbers is partitioned into subsets \({S_1} = \left\{ 1 \right\},\;{S_2} = \left\{ {2,\;3} \right\},\;{S_3} = \left\{ {4,\;5,\;6} \right\}\) and so on. Then the sum of the terms in \({S_{50}}\) is
62525
25625
62500
Question:The sum of \((n + 1)\) terms of \(\frac{1}{1} + \frac{1}{{1 + 2}} + \frac{1}{{1 + 2 + 3}} + ......\,\,{\rm{is }}\)
\(\frac{n}{{n + 1}}\)
\(\frac{{2n}}{{n + 1}}\)
\(\frac{2}{{n\,(n + 1)}}\)
\(\frac{{2\,(n + 1)}}{{n + 2}}\)
Question:The natural numbers are written as follows \(1\)\(\begin{array}{*{20}{c}} 2 & 3 \\\end{array}\)\(\begin{array}{*{20}{c}} 4 & 5 & 6 \\\end{array}\)\(\begin{array}{*{20}{c}} 7 & 8 & 9 & {10} \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\\end{array}\).The sum of the numbers in the \({n^{th}}\) row is
\(\frac{n}{2}({n^2} - 1)\)
\(\frac{n}{2}({n^2} + 1)\)
\(\frac{2}{n}({n^2} + 1)\)
\(\frac{2}{n}({n^2} - 1)\)
Question:The \({n^{th}}\) term of series \(\frac{1}{1} + \frac{{1 + 2}}{2} + \frac{{1 + 2 + 3}}{3} + .......\) will be
\(\frac{{{n^2} + 1}}{2}\)
\(\frac{{{n^2} - 1}}{2}\)
Question:The sum to infinity of the following series \(\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ...........\) shall be
\(\infty \)
Question:\(\frac{{\frac{1}{2}.\frac{2}{2}}}{{{1^3}}} + \frac{{\frac{2}{2}.\frac{3}{2}}}{{{1^3} + {2^3}}} + \frac{{\frac{3}{2}.\frac{4}{2}}}{{{1^3} + {2^3} + {3^3}}} + .....n\) terms =
\({\left( {\frac{n}{{n + 1}}} \right)^2}\)
\({\left( {\frac{n}{{n + 1}}} \right)^3}\)
\(\left( {\frac{n}{{n + 1}}} \right)\)
\(\left( {\frac{1}{{n + 1}}} \right)\)