Total Questions:50 Total Time: 75 Min
Remaining:
Question:The number of terms in the series \(101 + 99 + 97 + ..... + 47\) is
25
28
30
20
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
\(p + q + r\)
\(p + q - r\)
\(p + r - q\)
\(p - q - r\)
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
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
\(x = \frac{8}{5}\)
\(x = \frac{5}{4}\)
\(x = 2/3\)
Question:The ratio of the sums of first \(n\)even numbers and \(n\) odd numbers will be
\(1:n\)
\((n + 1):1\)
\((n + 1):n\)
\((n - 1):1\)
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 \(\frac{1}{{\sqrt {{a_1}} + \sqrt {{a_2}} }} + \frac{1}{{\sqrt {{a_2}} + \sqrt {{a_3}} }} + \) \(........ + \frac{1}{{\sqrt {{a_{n - 1}}} + \sqrt {{a_n}} }} = \)
\(\frac{{n - 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}\)
\(\frac{{n + 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}\)
\(\frac{{n - 1}}{{\sqrt {{a_1}} - \sqrt {{a_n}} }}\)
\(\frac{{n + 1}}{{\sqrt {{a_1}} - \sqrt {{a_n}} }}\)
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
\(2{S_n}\)
\({S_{3n}}\)
\(\frac{1}{3}{S_{3n}}\)
\(\frac{1}{2}{S_n}\)
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
\(x = 3\)
\(x = 4\sqrt 3 \)
\(x = 9\)
\(x = \sqrt 3 \)
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
Question:The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is
5
14
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
7
9
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
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
\(b = \frac{{a + c}}{2}\)
\({a^2} = bc\)
\({b^2} = ac\)
\({c^2} = ab\)
Question:If the first term of a G.P. be 5 and common ratio be \( - 5\), then which term is 3125
\({6^{th}}\)
\({5^{th}}\)
\({7^{th}}\)
\({8^{th}}\)
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
\(\frac{4}{9}\)
\(\frac{9}{4}\)
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
4
Question:The number \(111..............1\) (91 times) is a
Even number
Prime number
Not prime
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
\(\frac{{20}}{2}[4 + 19 \times 3]\)
\(3\left( {1 - \frac{1}{{{3^{20}}}}} \right)\)
\(2(1 - {3^{20}})\)
Question:The G.M. of the numbers \(3,\,{3^2},\,{3^3},....,\,{3^n}\) is
\({3^{\frac{2}{n}}}\)
\({3^{\frac{{n + 1}}{2}}}\)
\({3^{\frac{n}{2}}}\)
\({3^{\frac{{n - 1}}{2}}}\)
Question:The product of three geometric means between 4 and \(\frac{1}{4}\) will be
\( - 1\)
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
\(\frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}\)
\(\frac{{{x^2} + {y^2}}}{{{x^2} - {y^2}}}\)
\(\frac{{{x^2} - y}}{{{x^2} + y}}\)
\(\frac{{{x^2} + y}}{{{x^2} - y}}\)
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
\(\frac{1}{2}\)
\(\frac{2}{3}\)
\(\frac{3}{2}\)
Question:The value of \(\overline {0.037} \) where, \(\overline {.037} \) stands for the number 0.037037037........ is
\(\frac{{37}}{{1000}}\)
\(\frac{1}{{27}}\)
\(\frac{1}{{37}}\)
\(\frac{{37}}{{999}}\)
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
\(\frac{1}{3}\)
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
\(\frac{{27}}{{14}}\)
\(\frac{{56}}{{15}}\)
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
\(\frac{1}{{41}}\)
\(\frac{1}{{45}}\)
\(\frac{1}{{49}}\)
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
\(\frac{1}{{28}}\)
\(\frac{1}{{39}}\)
\(\frac{1}{6}\)
\(\frac{1}{{17}}\)
Question:If \(a,\;b,\;c\) be in A.P. and \(b,\;c,\;d\) be in H.P., then
\(ab = cd\)
\(ad = bc\)
\(ac = bd\)
\(abcd = 1\)
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.
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
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
Question:If \(a,\;b,\;c\) are in A.P., then \(\frac{1}{{bc}},\;\frac{1}{{ca}},\;\frac{1}{{ab}}\) will be in
Question:If \(x,\;1,\;z\) are in A.P. and \(x,\;2,\;z\) are in G.P., then \(x,\;4,\;z\) will be in
Question:If the \({p^{th}},\;{q^{th}}\) and \({r^{th}}\)term of a G.P. and H.P. are \(a,\;b,\;c\), then \(a(b - c)\log a + b(c - a)\) \(\log b + c(a - b)\log c = \)
Does not exist
Question:If \(a,\,b,\;c\) are in A.P. and \({a^2},\;{b^2},\;{c^2}\) are in H.P., then
\(a = b = c\)
\(2b = 3a + c\)
\({b^2} = \sqrt {(ac/8)} \)
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
8
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
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
\(1 - \sqrt 3 :2:1 + \sqrt 3 \)
\(1:\sqrt 2 : - \sqrt 3 \)
\(1: - \sqrt 2 :\sqrt 3 \)
\(1 \mp \sqrt 3 : - 2:1 \pm \sqrt 3 \)
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
Question:If \(\log (x + z) + \log (x + z - 2y) = 2\log (x - z),\,\) then \(x,\,y,\,z\) are in
Question:If A and G are arithmetic and geometric means and \({x^2} - 2Ax + {G^2} = 0\), then
\(A = G\)
\(A > G\)
\(A < G\)
\(A = - \,G\)
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
Question:The sum of infinite terms of the following series \(1 + \frac{4}{5} + \frac{7}{{{5^2}}} + \frac{{10}}{{{5^3}}} + .........\) will be
\(\frac{3}{{16}}\)
\(\frac{{35}}{8}\)
\(\frac{{35}}{4}\)
\(\frac{{35}}{{16}}\)
Question:The sum of the series \(1 + 3x + 6{x^2} + 10{x^3} + ........\infty \) will be
\(\frac{1}{{{{(1 - x)}^2}}}\)
\(\frac{1}{{1 - x}}\)
\(\frac{1}{{{{(1 + x)}^2}}}\)
\(\frac{1}{{{{(1 - x)}^3}}}\)
Question:The sum of \((n - 1)\) terms of \(1 + (1 + 3) + \) \((1 + 3 + 5) + .......\) is
\(\frac{{n\,(n + 1)\,(2n + 1)}}{6}\)
\(\frac{{{n^2}(n + 1)}}{4}\)
\(\frac{{n\,(n - 1)\,(2n - 1)}}{6}\)
\({n^2}\)
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
\(\frac{{n{{(n + 1)}^2}}}{2}\)
\(\frac{1}{2}{n^2}(n + 1)\)
\(n{(n + 1)^2}\)
Question:The sum of all the products of the first \(n\) natural numbers taken two at a time is
\(\frac{1}{{24}}n(n - 1)(n + 1)(3n + 2)\)
\(\frac{{{n^2}}}{{48}}(n - 1)(n - 2)\)
\(\frac{1}{6}n(n + 1)(n + 2)(n + 5)\)
Question:The sum of the series \({1.3^2} + {2.5^2} + {3.7^2} + ..........\)upto \(20\) terms is
188090
189080
199080
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
\(\frac{{n(n + 3)}}{4}\)
\(\frac{{n(n + 2)}}{4}\)
\(\frac{{n(n + 1)\,(n + 2)}}{6}\)
Question:The nth term of the series \(\frac{2}{{1!}} + \frac{7}{{2\,!}} + \frac{{15}}{{3\,!}} + \frac{{26}}{{4\,!}} + .....\) is
\(\frac{{n\,(3n - 1)}}{{2(n)\,!}}\)
\(\frac{{n\,(3n + 1)}}{{2\,(n)\,!}}\)
\(\frac{n}{2}\frac{{3n}}{{(n)\,!}}\)