Total Questions:50 Total Time: 75 Min
Remaining:
Question:If \(a,\;b,\;c\) are in A.P., then \(\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = \)
1
2
3
4
Question:If \({\log _3}2,\;{\log _3}({2^x} - 5)\) and \({\log _3}\left( {{2^x} - \frac{7}{2}} \right)\) are in A.P., then \(x\) is equal to
\(1,\;\frac{1}{2}\)
\(1,\;\frac{1}{3}\)
\(1,\;\frac{3}{2}\)
None of these
Question:If the \({p^{th}},\;{q^{th}}\) and \({r^{th}}\) term of an arithmetic sequence are a , b and \(c\) respectively, then the value of \([a(q - r)\) + \(b(r - p)\) \( + c(p - q)] = \)
\( - 1\)
0
2-Jan
Question:If the \({p^{th}}\) term of an A.P. be \(\frac{1}{q}\) and \({q^{th}}\) term be\(\frac{1}{p}\), then the sum of its \(p{q^{th}}\)terms will be
\(\frac{{pq - 1}}{2}\)
\(\frac{{1 - pq}}{2}\)
\(\frac{{pq + 1}}{2}\)
\( - \frac{{pq + 1}}{2}\)
Question:The sum of first \(n\) natural numbers is
\(n\,(n - 1)\)
\(\frac{{n\,(n - 1)}}{2}\)
\(n\,(n + 1)\)
\(\frac{{n\,(n + 1)}}{2}\)
Question:The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be
3200
1600
200
2800
Question:The sum of the numbers between 100 and 1000 which is divisible by 9 will be
55350
57228
97015
62140
Question:The ratio of sum of \(m\) and \(n\) terms of an A.P. is \({m^2}:{n^2}\), then the ratio of \({m^{th}}\)and \({n^{th}}\) term will be
\(\frac{{m - 1}}{{n - 1}}\)
\(\frac{{n - 1}}{{m - 1}}\)
\(\frac{{2m - 1}}{{2n - 1}}\)
\(\frac{{2n - 1}}{{2m - 1}}\)
Question:The value of \(\sum\limits_{r = 1}^n {\log \left( {\frac{{{a^r}}}{{{b^{r - 1}}}}} \right)} \) is
\(\frac{n}{2}\log \left( {\frac{{{a^n}}}{{{b^n}}}} \right)\)
\(\frac{n}{2}\log \left( {\frac{{{a^{n + 1}}}}{{{b^n}}}} \right)\)
\(\frac{n}{2}\log \left( {\frac{{{a^{n + 1}}}}{{{b^{n - 1}}}}} \right)\)
\(\frac{n}{2}\log \left( {\frac{{{a^{n + 1}}}}{{{b^{n + 1}}}}} \right)\)
Question:Let the sequence \({a_1},{a_2},{a_3},.............{a_{2n}}\) form an A.P. Then \(a_1^2 - a_2^2 + a_3^3 - ......... + a_{2n - 1}^2 - a_{2n}^2 = \)
\(\frac{n}{{2n - 1}}(a_1^2 - a_{2n}^2)\)
\(\frac{{2n}}{{n - 1}}(a_{2n}^2 - a_1^2)\)
\(\frac{n}{{n + 1}}(a_1^2 + a_{2n}^2)\)
Question:If sum of \(n\) terms of an A.P. is \(3{n^2} + 5n\) and \({T_m} = 164\) then \(m = \)
26
27
28
Question:If \({S_n} = nP + \frac{1}{2}n(n - 1)Q\), where \({S_n}\) denotes the sum of the first \(n\) terms of an A.P., then the common difference is
\(P + Q\)
\(2P + 3Q\)
\(2Q\)
\(Q\)
Question:The sum of \(n\)arithmetic means between \(a\) and \(b\), is
\(\frac{{n(a + b)}}{2}\)
\(n(a + b)\)
\(\frac{{(n + 1)(a + b)}}{2}\)
\((n + 1)(a + b)\)
Question:After inserting \(n\) A.M.'s between 2 and 38, the sum of the resulting progression is 200. The value of \(n\) is
10
8
9
Question:The mean of the series \(a,a + nd,\,\,a + 2nd\) is
\(a + (n - 1)\,d\)
\(a + nd\)
\(a + (n + 1)\,d\)
Question:Four numbers are in arithmetic progression. The sum of first and last term is 8 and the product of both middle terms is 15. The least number of the series is
Question:If twice the 11th term of an A.P. is equal to 7 times of its 21st term, then its 25th term is equal to
24
120
Question:If \(x,y,z\) are in A.P. and \({\tan ^{ - 1}}x,{\tan ^{ - 1}}y\)and \({\tan ^{ - 1}}z\) are also in A.P., then
\(x = y = z\)
\(x = y = - z\)
\(x = 1;y = 2;z = 3\)
\(x = 2;y = 4;z = 6\)
\(x = 2y = 3z\)
Question:The \({20^{th}}\) term of the series \(2 \times 4 + 4 \times 6 + 6 \times 8 + .......\)will be
1680
420
840
Question:If \(a,\;b,\;c\) are \({p^{th}},\;{q^{th}}\) and \({r^{th}}\)terms of a G.P., then \({\left( {\frac{c}{b}} \right)^p}{\left( {\frac{b}{a}} \right)^r}{\left( {\frac{a}{c}} \right)^q}\) is equal to
\({a^P}{b^q}{c^r}\)
\({a^q}{b^r}{c^p}\)
\({a^r}{b^p}{c^q}\)
Question:If every term of a G.P. with positive terms is the sum of its two previous terms, then the common ratio of the series is
\(\frac{2}{{\sqrt 5 }}\)
\(\frac{{\sqrt 5 - 1}}{2}\)
\(\frac{{\sqrt 5 + 1}}{2}\)
Question:The sum of first two terms of a G.P. is 1 and every term of this series is twice of its previous term, then the first term will be
4-Jan
3-Jan
3-Feb
4-Mar
Question:If the geometric mean between \(a\) and \(b\) is \(\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}\), then the value of n is
1/2
Question:If \(G\) be the geometric mean of \(x\) and \(y\), then \(\frac{1}{{{G^2} - {x^2}}} + \frac{1}{{{G^2} - {y^2}}} = \)
\({G^2}\)
\(\frac{1}{{{G^2}}}\)
\(\frac{2}{{{G^2}}}\)
\(3{G^2}\)
Question:\(x = 1 + a + {a^2} + ....\infty \,(a < 1)\), \(y = 1 + b + {b^2}.......\infty \,(b < 1)\). Then the value of \(1 + ab + {a^2}{b^2} + ..........\infty \) is
\(\frac{{xy}}{{x + y - 1}}\)
\(\frac{{xy}}{{x + y + 1}}\)
\(\frac{{xy}}{{x - y - 1}}\)
\(\frac{{xy}}{{x - y + 1}}\)
Question:The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be [MNR 1979; RPET 1992, 95]
6
Question:The sum of infinite terms of the geometric progression \(\frac{{\sqrt 2 + 1}}{{\sqrt 2 - 1}},\frac{1}{{2 - \sqrt 2 }},\frac{1}{2}.....\) is
\(\sqrt 2 {(\sqrt 2 + 1)^2}\)
\({(\sqrt 2 + 1)^2}\)
\(5\sqrt 2 \)
\(3\sqrt 2 + \sqrt 5 \)
Question:Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is
5
5-Mar
5-Aug
5-Jan
Question:If \({5^{th}}\) term of a H.P. is \(\frac{1}{{45}}\)and \({11^{th}}\) term is \(\frac{1}{{69}}\), then its \({16^{th}}\) term will be
Jan-89
Jan-85
Jan-80
Jan-79
Question:The first term of a harmonic progression is 1/7 and the second term is 1/9. The \({12^{th}}\) term is
19-Jan
29-Jan
17-Jan
27-Jan
Question:If \(a,\;b,\;c\) be in H.P., then
\({a^2} + {c^2} > {b^2}\)
\({a^2} + {b^2} > 2{c^2}\)
\({a^2} + {c^2} > 2{b^2}\)
\({a^2} + {b^2} > {c^2}\)
Question:If \(a,\;b,\;c,\;d\) are in H.P., then
\(a + d > b + c\)
\(ad > bc\)
Both (1) and (2)
Question:If \({b^2},\,{a^2},\,{c^2}\) are in A.P., then \(a + b,\,b + c,\,c + a\) will be in
A.P.
G.P.
H.P.
Question:If \(a,\;b,\;c\) are in A.P. as well as in G.P., then
\(a = b \ne c\)
\(a \ne b = c\)
\(a \ne b \ne c\)
\(a = b = c\)
Question:If G.M. = 18 and A.M. = 27, then H.M. is
\(\frac{1}{{18}}\)
\(\frac{1}{{12}}\)
12
\(9\sqrt 6 \)
Question:If the A.M. is twice the G.M. of the numbers \(a\) and \(b\), then \(a:b\)will be
\(\frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }}\)
\(\frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }}\)
\(\frac{{\sqrt 3 - 2}}{{\sqrt 3 + 2}}\)
\(\frac{{\sqrt 3 + 2}}{{\sqrt 3 - 2}}\)
Question:If \(\frac{{a + b}}{{1 - ab}},\;b,\;\frac{{b + c}}{{1 - bc}}\) are in A.P., then \(a,\;\frac{1}{b},\;c\) are in
Question:If all the terms of an A.P. are squared, then new series will be in
Question:If \(a,\;b,\;c\), d are any four consecutive coefficients of any expanded binomial, then \(\frac{{a + b}}{a},\;\frac{{b + c}}{b},\;\frac{{c + d}}{c}\) are in
None of the above
Question:\({\log _3}2,\;{\log _6}2,\;{\log _{12}}2\)are in
Question:If a,b,c are in A.P., then \({2^{ax + 1}},{2^{bx + 1}},\,{2^{cx + 1}},x \ne 0\) are in
G.P. only when \(x > {\rm{0}}\)
G.P. if \(x < 0\)
G.P. for all \(x \ne 0\)
Question:If \(b + c,\) \(c + a,\) \(a + b\) are in H.P., then \(\frac{a}{{b + c}},\frac{b}{{c + a}},\frac{c}{{a + b}}\) are in
Question:If p,q,r are in G.P and \({\tan ^{ - 1}}p\), \({\tan ^{ - 1}}q,{\tan ^{ - 1}}r\)are in A.P. then p, q, r are satisfies the relation
\(p = q = r\)
\(p \ne q \ne r\)
\(p + q = r\)
Question:If A.M and G.M of x and y are in the ratio p : q, then x : y is
\(p - \sqrt {{p^2} + {q^2}} \):\(p + \sqrt {{p^2} + {q^2}} \)
\(p + \sqrt {{p^2} - {q^2}} \):\(p - \sqrt {{p^2} - {q^2}} \)
\(p:q\)
\(p + \sqrt {{p^2} + {q^2}} \):\(p - \sqrt {{p^2} + {q^2}} \)
\(q + \sqrt {{p^2} - {q^2}} \):\(q - \sqrt {{p^2} - {q^2}} \)
Question:The sum of \(i - 2 - 3i + 4 + .........\)upto 100 terms, where \(i = \sqrt { - 1} \) is
\(50(1 - i)\)
\(25i\)
\(25(1 + i)\)
\(100(1 - i)\)
Question:\({99^{th}}\) term of the series \(2 + 7 + 14 + 23 + 34 + .....\) is
9998
9999
10000
100000
Question:Sum of the squares of first \(n\) natural numbers exceeds their sum by 330, then \(n = \)
15
20
Question:Sum of first \(n\) terms in the following series \({\cot ^{ - 1}}3 + {\cot ^{ - 1}}7 + {\cot ^{ - 1}}13 + {\cot ^{ - 1}}21 + .............\) is given by
\({\tan ^{ - 1}}\left( {\frac{n}{{n + 2}}} \right)\)
\({\cot ^{ - 1}}\left( {\frac{{n + 2}}{n}} \right)\)
\({\tan ^{ - 1}}(n + 1) - {\tan ^{ - 1}}1\)
All of these
Question:First term of the \({11^{th}}\) group in the following groups (1),(2, 3, 4), (5, 6, 7, 8, 9), .................is
89
97
101
123
Question:\({11^2} + {12^2} + {13^2} + {.......20^2} = \)
2481
2483
2485
2487