Total Questions:50 Total Time: 75 Min
Remaining:
Question:If the \({9^{th}}\)term of an A.P. is 35 and \({19^{th}}\) is 75, then its \({20^{th}}\) terms will be
78
79
80
81
Question:The \({9^{th}}\) term of the series \(27 + 9 + 5\frac{2}{5} + 3\frac{6}{7} + ........\) will be
\(1\frac{{10}}{{17}}\)
\(\frac{{10}}{{17}}\)
\(\frac{{16}}{{27}}\)
\(\frac{{17}}{{27}}\)
Question:The sum of the series \(\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ........\)to 9 terms is
\( - \frac{5}{6}\)
\( - \frac{1}{2}\)
1
\( - \frac{3}{2}\)
Question:The interior angles of a polygon are in A.P. If the smallest angle be \({120^o}\)and the common difference be 5o, then the number of sides is
8
10
9
6
Question:If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are
5
15
Question:The maximum sum of the series \(20 + 19\frac{1}{3} + 18\frac{2}{3} + .........\) is
310
300
320
None of these
Question:If \({a_1},\,{a_2},....,{a_{n + 1}}\)are in A.P., then \(\frac{1}{{{a_1}{a_2}}} + \frac{1}{{{a_2}{a_3}}} + ..... + \frac{1}{{{a_n}{a_{n + 1}}}}\) is
\(\frac{{n - 1}}{{{a_1}{a_{n + 1}}}}\)
\(\frac{1}{{{a_1}{a_{n + 1}}}}\)
\(\frac{{n + 1}}{{{a_1}{a_{n + 1}}}}\)
\(\frac{n}{{{a_1}{a_{n + 1}}}}\)
Question:If the sum of the first \(n\)terms of a series be \(5{n^2} + 2n\), then its second term is
7
17
24
42
Question:If \(A\) be an arithmetic mean between two numbers and \(S\) be the sum of \(n\) arithmetic means between the same numbers, then
\(S = n\,A\)
\(A = n\,S\)
\(A = S\)
Question:The arithmetic mean of first n natural number
\(\frac{{n - 1}}{2}\)
\(\frac{{n + 1}}{2}\)
\(\frac{n}{2}\)
\(n\)
Question:The difference between an integer and its cube is divisible by
4
Question:If \(a,\,b,\,c\) are in A.P., then \((a + 2b - c)\)\((2b + c - a)\)\((c + a - b)\) equals
\(\frac{1}{2}abc\)
abc
2 abc
4 abc
Question:If the third term of a G.P. is 4 then the product of its first 5 terms is
\({4^3}\)
\({4^4}\)
\({4^5}\)
Question:If the \({5^{th}}\) term of a G.P. is \(\frac{1}{3}\) and \({9^{th}}\) term is \(\frac{{16}}{{243}}\), then the \({4^{th}}\) term will be
\(\frac{3}{4}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{2}{5}\)
Question:If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is [Roorkee 1972]
\(\frac{3}{2}\)
2
3
Question:The sum of the series \(6 + 66 + 666 + ..........\)upto \(n\) terms is
\(({10^{n - 1}} - 9n + 10)/81\)
\(2({10^{n + 1}} - 9n - 10)/27\)
\(2({10^n} - 9n - 10)/27\)
Question:The sum of a G.P. with common ratio 3 is 364, and last term is 243, then the number of terms is
Question:If \(n\) geometric means be inserted between \(a\) and \(b\)then the \({n^{th}}\) geometric mean will be
\(a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n - 1}}}}\)
\(a\,{\left( {\frac{b}{a}} \right)^{\frac{{n - 1}}{n}}}\)
\(a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n + 1}}}}\)
\(a\,{\left( {\frac{b}{a}} \right)^{\frac{1}{n}}}\)
Question:The sum can be found of a infinite G.P. whose common ratio is \(r\)
For all values of \(r\)
For only positive value of \(r\)
Only for \(0 < r < 1\)
Only for \( - 1 < r < 1(r \ne 0)\)
Question:If \(A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty \), then the value of r will be
\(A{(1 - A)^z}\)
\({\left( {\frac{{A - 1}}{A}} \right)^{1/z}}\)
\({\left( {\frac{1}{A} - 1} \right)^{1/z}}\)
\(A{(1 - A)^{1/z}}\)
Question:If \(y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = \)
\(\frac{y}{{1 + y}}\)
\(\frac{{1 - y}}{y}\)
\(\frac{y}{{1 - y}}\)
Question:If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are
3/2, 1/2
1, Â½
3/2, 2
Question:If \({a_1},\;{a_2},\;{a_3},...............,\;{a_n}\) are in H.P., then \({a_1}{a_2} + {a_2}{a_3} + \) \(.......... + {a_{n - 1}}{a_n}\) will be equal to
\({a_1}{a_n}\)
\(n{a_1}{a_n}\)
\((n - 1){a_1}{a_n}\)
Question:If \(x,\;y,\;z\) are in H.P., then the value of expression \(\log (x + z) + \log (x - 2y + z)\) will be
\(\log (x - z)\)
\(2\log (x - z)\)
\(3\log (x - z)\)
\(4\log (x - z)\)
Question:If \(\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}\) be the harmonic mean between \(a\) and \(b\), then the value of \(n\) is
\( - 1\)
0
Question:If the harmonic mean between \(a\) and \(b\) be \(H\), then \(\frac{{H + a}}{{H - a}} + \frac{{H + b}}{{H - b}} = \)
\(a + b\)
Question:If \(\frac{1}{{b - a}} + \frac{1}{{b - c}} = \frac{1}{a} + \frac{1}{c}\), then \(a,\;b,\;c\) are in
A.P.
G.P.
H.P.
In G.P. and H.P. both
Question:If \(a\) and \(b\) are two different positive real numbers, then which of the following relations is true
\(2\sqrt {ab} > (a + b)\)
\(2\sqrt {ab} < (a + b)\)
\(2\sqrt {ab} = (a + b)\)
Question:If \(a,\;b,\;c\) are in A.P., then \({3^a},\;{3^b},\;{3^c}\) shall be in
Question:If the \({(m + 1)^{th}},\;{(n + 1)^{th}}\) and \({(r + 1)^{th}}\) terms of an A.P. are in G.P. and \(m,\;n,\;r\) are in H.P., then the value of the ratio of the common difference to the first term of the A.P. is
\( - \frac{2}{n}\)
\(\frac{2}{n}\)
\( - \frac{n}{2}\)
Question:An A.P., a G.P. and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in
Question:If \(,a,\;b,\,c\) be in G.P. and \(a + x,\;b + x,\;c + x\) in H.P., then the value of \(x\) is (\(a,\;b,\;c\) are distinct numbers)
\(c\)
\(b\)
\(a\)
Question:If the ratio of H.M. and G.M. between two numbers \(a\) and \(b\) is \(4:5\), then the ratio of the two numbers will be
\(1:2\)
\(2:1\)
\(4:1\)
\(1:4\)
3 and 4 are correct
Question:If the A.M., G.M. and H.M. between two positive numbers \(a\) and \(b\) are equal, then
\(a = b\)
\(ab = 1\)
\(a > b\)
\(a < b\)
Question:If \(a,\;b,\;c\) are in A.P., then \({10^{ax + 10}},\;{10^{bx + 10}},\;{10^{cx + 10}}\) will be in
G.P. only when \(x > 0\)
G.P. for all values of \(x\)
G.P. for \(x < 0\)
Question:The common difference of an A.P. whose first term is unity and whose second, tenth and thirty fourth terms are in G.P., is
\(\frac{1}{5}\)
\(\frac{1}{6}\)
\(\frac{1}{9}\)
Question:Let the positive numbers a, b, c, d be in A.P., then abc, abd acd, bcd are
Not in A.P./G.P./H.P.
In A.P.
In G.P.
In H.P.
Question:If in the equation \(a{x^2} + bx + c = 0,\) the sum of roots is equal to sum of square of their reciprocals, then \(\frac{c}{a},\frac{a}{b},\frac{b}{c}\) are in
Question:The harmonic mean between two numbers is \(14\frac{2}{5}\)and the geometric mean 24 . The greater number them is
72
54
36
Question:When \(\frac{1}{a} + \frac{1}{c} + \frac{1}{{a - b}} + \frac{1}{{c - d}} = 0\) and \(b \ne a \ne c\), then \(a,\;b,\;c\) are
Question:If \({a^2},\,{b^2},\,{c^2}\) be in A.P., then \(\frac{a}{{b + c}},\,\frac{b}{{c + a}},\,\frac{c}{{a + b}}\) will be in
Question:The sum of the first \(n\) terms of the series \(\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{{15}}{{16}} + .........\) is
\({2^n} - n - 1\)
\(1 - {2^{ - n}}\)
\(n + {2^{ - n}} - 1\)
\({2^n} - 1\)
Question:The sum of \(1 + \frac{2}{5} + \frac{3}{{{5^2}}} + \frac{4}{{{5^3}}} + ...........\)upto \(n\) terms is
\(\frac{{25}}{{16}} - \frac{{4n + 5}}{{16 \times {5^{n - 1}}}}\)
\(\frac{3}{4} - \frac{{2n + 5}}{{16 \times {5^{n + 1}}}}\)
\(\frac{3}{7} - \frac{{3n + 5}}{{16 \times {5^{n - 1}}}}\)
\(\frac{1}{2} - \frac{{5n + 1}}{{3 \times {5^{n + 2}}}}\)
Question:\({2^{1/4}}{.4^{1/8}}{.8^{1/16}}{.16^{1/32}}..........\)is equal to
\(\frac{5}{2}\)
Question:The sum of the series \({1^2}.2 + {2^2}.3 + {3^2}.4 + ........\) to n terms is
\(\frac{{{n^3}{{(n + 1)}^3}(2n + 1)}}{{24}}\)
\(\frac{{n(n + 1)(3{n^2} + 7n + 2)}}{{12}}\)
\(\frac{{n(n + 1)}}{6}[n(n + 1) + (2n + 1)]\)
\(\frac{{n(n + 1)}}{{12}}[6n(n + 1) + 2(2n + 1)]\)
Question:The sum of the series \(1.2.3 + 2.3.4 + 3.4.5 + .......\) to n terms is
\(n(n + 1)(n + 2)\)
\((n + 1)(n + 2)(n + 3)\)
\(\frac{1}{4}n(n + 1)(n + 2)(n + 3)\)
\(\frac{1}{4}(n + 1)(n + 2)(n + 3)\)
Question:The sum of \({1^3} + {2^3} + {3^3} + {4^3} + ..... + {15^3}\),is [MP PET 2003]
22000
10,000
14,400
15,000
Question:The sum to \(n\) terms of the infinite series \({1.3^2} + {2.5^2} + {3.7^2} + ..........\infty \) is
\(\frac{n}{6}(n + 1)(6{n^2} + 14n + 7)\)
\(\frac{n}{6}(n + 1)(2n + 1)(3n + 1)\)
\(4{n^3} + 4{n^2} + n\)
Question:If the \({n^{th}}\) term of a series be \(3 + n\,(n - 1)\), then the sum of \(n\) terms of the series is
\(\frac{{{n^2} + n}}{3}\)
\(\frac{{{n^3} + 8n}}{3}\)
\(\frac{{{n^2} + 8n}}{5}\)
\(\frac{{{n^2} - 8n}}{3}\)
Question:The sum to \(n\) terms of \((2n - 1) + 2\,(2n - 3)\) \( + 3\,(2n - 5) + .....\) is
\((n + 1)\,(n + 2)\,(n + 3)/6\)
\(n\,(n + 1)\,(n + 2)/6\)
\(n\,(n + 1)\,(2n + 3)\,\)
\(n\,(n + 1)\,(2n + 1)/6\)