Total Questions:50 Total Time: 75 Min
Remaining:
Question:If \({m^{th}}\) terms of the series \(63 + 65 + 67 + 69 + .........\) and \(3 + 10 + 17 + 24 + ......\) be equal, then \(m = \)
11
12
13
15
Question:The sum of 24 terms of the following series \(\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + .........\) is
300
\(300\sqrt 2 \)
\(200\sqrt 2 \)
None of these
Question:Let \({T_r}\)be the \({r^{th}}\) term of an A.P. for \(r = 1,\;2,\;3,....\). If for some positive integers \(m,\;n\) we have \({T_m} = \frac{1}{n}\) and \({T_n} = \frac{1}{m}\), then \({T_{mn}}\) equals
\(\frac{1}{{mn}}\)
\(\frac{1}{m} + \frac{1}{n}\)
1
0
Question:If \(1,\,\,{\log _9}({3^{1 - x}} + 2),\,\,{\log _3}({4.3^x} - 1)\) are in A.P. then x equals
\({\log _3}4\)
\(1 - {\log _3}4\)
\(1 - {\log _4}3\)
\({\log _4}3\)
Question:The sum of \(1 + 3 + 5 + 7 + .........\)upto \(n\) terms is
\({(n + 1)^2}\)
\({(2n)^2}\)
\({n^2}\)
\({(n - 1)^2}\)
Question:If the sum of the series \(54 + 51 + 48 + .............\) is 513, then the number of terms are
18
20
17
Question:The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is
8
4
6
Question:If the sum of the first 2n terms of \(2,\,5,\,8...\) is equal to the sum of the first n terms of \(57,\,59,\,61...\), then n is equal to
10
Question:Three number are in A.P. such that their sum is 18 and sum of their squares is 158. The greatest number among them is
Question:If \(\frac{{3 + 5 + 7 + ..........{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + .........{\rm{to}}\;10\;{\rm{terms}}}} = 7\), then the value of\(n\) is
35
36
37
40
Question:If \({A_1},\,{A_2}\) be two arithmetic means between \(\frac{1}{3}\) and \(\frac{1}{{24}}\) , then their values are
\(\frac{7}{{72}},\,\frac{5}{{36}}\)
\(\frac{{17}}{{72}},\,\frac{5}{{36}}\)
\(\frac{7}{{36}},\,\frac{5}{{72}}\)
\(\frac{5}{{72}},\,\frac{{17}}{{72}}\)
Question:If the sum of three numbers of a arithmetic sequence is 15 and the sum of their squares is 83, then the numbers are
4, 5, 6
3, 5, 7
1, 5, 9
2, 5, 8
Question:The four arithmetic means between 3 and 23 are
5, 9, 11, 13
7, 11, 15, 19
5, 11, 15, 22
7, 15, 19, 21
Question:If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are
21, 17, 13
20,Â 16, 12
22, 18, 14
24, 20, 16
Question:The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is
\(\frac{{1 - \sqrt 5 }}{2}\)
\(2\sqrt 5 \)
Question:If \(x,\,2x + 2,\,3x + 3,\) are in G.P., then the fourth term is
27
\( - 27\)
13.5
\( - 13.5\)
Question:If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio r is
\(\frac{3}{5}\)
\(\frac{5}{3}\)
\(\frac{2}{3}\)
\(\frac{3}{2}\)
Question:Fifth term of a G.P. is 2, then the product of its 9 terms is
256
512
1024
Question:If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is
1:3
3:2
3:4
2:3
Question:The sum of the first five terms of the series \(3 + 4\frac{1}{2} + 6\frac{3}{4} + ......\) will be
\(39\frac{9}{{16}}\)
\(18\frac{3}{{16}}\)
\(39\frac{7}{{16}}\)
\(13\frac{9}{{16}}\)
Question:The sum of few terms of any ratio series is 728, if common ratio is 3 and last term is 486, then first term of series will be
2
3
Question:The product of \(n\) positive numbers is unity. Their sum is
A positive integer
Equal to \(n + \frac{1}{n}\)
Divisible by \(n\)
Never less than
Question:Three numbers are in G.P. such that their sum is 38 and their product is 1728. The greatest number among them is
16
14
Question:If x, \({G_1}{,_\;}{G_2},\;y\)be the consecutive terms of a G.P., then the value of \({G_1}\,{G_2}\)will be
\(\frac{y}{x}\)
\(\frac{x}{y}\)
\(xy\)
\(\sqrt {xy} \)
Question:The sum of 3 numbers in geometric progression is 38 and their product is 1728. The middle number is
Question:If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be
1, 3, 9
2, 6, 18
3, 9, 27
2, 4, 8
Question:The sum of the series \(5.05 + 1.212 + 0.29088 + ...\,\infty \) is
6.93378
6.87342
6.74384
6.64474
Question:The sum of an infinite geometric series is 3. A series, which is formed by squares of its terms, have the sum also 3. First series will be
\(\frac{3}{2},\frac{3}{4},\frac{3}{8},\frac{3}{{16}},.....\)
\(\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{{16}},.....\)
\(\frac{1}{3},\frac{1}{9},\frac{1}{{27}},\frac{1}{{81}},.....\)
\(1, - \frac{1}{3},\,\frac{1}{{{3^2}}}, - \frac{1}{{{3^3}}},.....\)
Question:If \({a^2} + a{b^2} + 16{c^2} = 2(3ab + 6bc + 4ac)\), where \(a,b,c\) are non-zero numbers. Then \(a,b,c\)are in
A.P
G.P
H.P
Question:The product (32)(32) 1/6(32)1/36 ...... to \(\infty \) is
32
64
62
Question:If \(H\) is the harmonic mean between \(p\) and \(q\), then the value of \(\frac{H}{p} + \frac{H}{q}\) is
\(\frac{{pq}}{{p + q}}\)
\(\frac{{p + q}}{{pq}}\)
Question:If the harmonic mean between \(a\) and \(b\) be \(H\), then the value of \(\frac{1}{{H - a}} + \frac{1}{{H - b}}\) is
\(a + b\)
\(ab\)
\(\frac{1}{a} + \frac{1}{b}\)
\(\frac{1}{a} - \frac{1}{b}\)
Question:If \({p^{th}},\;{q^{th}},\;{r^{th}}\) and \({s^{th}}\) terms of an A.P. be in G.P., then \((p - q),\;(q - r),\;(r - s)\) will be in
G.P.
A.P.
H.P.
Question:If the arithmetic and geometric means of a and b be \(A\) and \(G\) respectively, then the value of \(A - G\) will be
\(\frac{{a - b}}{a}\)
\(\frac{{a + b}}{2}\)
\({\left[ {\frac{{\sqrt a - \sqrt b }}{{\sqrt 2 }}} \right]^2}\)
\(\frac{{2ab}}{{a + b}}\)
Question:If \(a,\;b,\;c\)are in A.P., \(b,\;c,\;d\) are in G.P. and \(c,\;d,\;e\)are in H.P., then \(a,\;c,\;e\) are in
No particular order
Question:If \(a,\;b,\;c\) are in G.P., \(a - b,\;c - a,\;b - c\)are in H.P., then \(a + 4b + c\)is equal to
\(1\)
\( - 1\)
Question:If \(\frac{{b + a}}{{b - a}} = \frac{{b + c}}{{b - c}}\), then\(a,\;b,\;c\) are in
Question:If the ratio of two numbers be \(9:1\), then the ratio of geometric and harmonic means between them will be
\(1:9\)
\(5:3\)
\(3:5\)
\(2:5\)
Question:If \(a,\;b,\;c\) are in H.P., then for all \(n \in N\) the true statement is
\({a^n} + {c^n} < 2{b^n}\)
\({a^n} + {c^n} > 2{b^n}\)
\({a^n} + {c^n} = 2{b^n}\)
None of the above
Question:If A.M. of two terms is 9 and H.M. is 36, then G.M. will be
Question:If \(p,\;q,\;r\) are in one geometric progression and \(a,\;b,\;c\) in another geometric progression, then \(cp,\;bq,\;ar\) are in
Question:If first three terms of sequence \(\frac{1}{{16}},a,b,\frac{1}{6}\) are in geometric series and last three terms are in harmonic series, then the value of \(a\) and \(b\) will be
\(a = - \frac{1}{4},b = 1\)
\(a = \frac{1}{{12}},b = \frac{1}{9}\)
(1) and (2) both are true
Question:If \((y - x),\,\,2(y - a)\) and \((y - z)\) are in H.P., then \(x - a,\) \(y - a,\) \(z - a\) are in
Question:If \(a,\,b,\,c\) are in A.P. and \({a^2},\,{b^2},{c^2}\)are in H.P., then
\(a \ne b \ne c\)
\({a^2} = {b^2} = \frac{{{c^2}}}{2}\)
\(a,\,b,\,c\) are in G.P.
\(\frac{{ - a}}{2},b,c\)are in G.P
Question:If \(a,\;b,\;c\) are in H.P., then which one of the following is true
\(\frac{1}{{b - a}} + \frac{1}{{b - c}} = \frac{1}{b}\)
\(\frac{{ac}}{{a + c}} = b\)
\(\frac{{b + a}}{{b - a}} + \frac{{b + c}}{{b - c}} = 1\)
Question:The sum of the series \(1 + \frac{{1.3}}{6} + \frac{{1.3.5}}{{6.8}} + ....\infty \)is
\(\infty \)
Question:The sum 1(1!) + 2(2!) + 3(3!) + ....+n (n!) equals
\(3\,(n\,!)\, + \,n - 3\)
\((n + 1)!\, - \,(n - 1)!\)
\((n + 1)\,!\, - 1\)
\(2\,(n\,!) - 2n - 1\)
Question:\(\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ........ + .......\frac{1}{{n.(n + 1)}}\)equals
\(\frac{1}{{n(n + 1)}}\)
\(\frac{n}{{n + 1}}\)
\(\frac{{2n}}{{n + 1}}\)
\(\frac{2}{{n(n + 1)}}\)
Question:Sum of the series \(\frac{2}{3} + \frac{8}{9} + \frac{{26}}{{27}} + \frac{{80}}{{81}} + .....\) to n terms is
\(n - \frac{1}{2}({3^n} - 1)\)
\(n + \frac{1}{2}({3^n} - 1)\)
\(n + \frac{1}{2}(1 - {3^{ - n}})\)
\(n + \frac{1}{2}({3^{ - n}} - 1)\)
Question:\(\sum\limits_{m = 1}^n {{m^2}} \) is equal to
\(\frac{{m(m + 1)}}{2}\)
\(\frac{{m(m + 1)(2m + 1)}}{6}\)
\(\frac{{n(n + 1)(2n + 1)}}{6}\)
\(\frac{{n(n + 1)}}{2}\)