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MCQ (Single Correct Answer)
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Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then
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If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the...
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Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right)...
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The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is
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Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p...
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Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2...
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Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then
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If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}...
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Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b $$ \in $$ R...
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In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of ...
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The value of $${2 \over {3!}} + {4 \over {5!}} + {6 \over {7!}} + $$ ............ is
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If angles A, B and C are in A.P., then $${{a + c} \over b}$$ is equal to
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The value of n for which $${{{x^{n + 1}} + {y^{n + 1}}} \over {{x^n} + {y^n}}}$$ is the geometric mean of x and y is...
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G.M. and H.M. of two numbers are 10 and 8 respectively. The numbers are
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Sum of n terms of the following series 13 + 33 + 53 + 73 ......... is
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If sum of an infinite geometric series is $${4 \over {3}}$$ and its 1st term is $${3 \over {4}}$$, then its common ratio...
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The sum of the infinite series $$1 + {1 \over {2!}} + {{1\,.\,3} \over {4!}} + {{1\,.\,3\,.\,5} \over {6!}} + \,....$$ i...
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The coefficient of xn, where n is any positive integer, in the expansion of (1 + 2x + 3x2 + ....... $$\infty$$)1/2 is...
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For what value of m, $${{{a^{m + 1}} + {b^{m + 1}}} \over {{a^m} + {b^m}}}$$ is the arithmetic mean of a and b?
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If three positive real numbers a, b, c are in A.P. and abc = 4 then the minimum possible value of b is
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If a, b, c are G.P. (a > 1, b > 1, c > 1), then for any real number x (with x > 0, x $$\ne$$ 1) logax, logbx, logcx are ...
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The sum of the infinite series $${\left( {{1 \over 3}} \right)^2} + {1 \over 3}{\left( {{1 \over 3}} \right)^4} + {1 \ov...
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If three real numbers a, b, c are in Harmonic Progression, then which of the following is true?
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If a, b, c be in Arithmetic progression, then the value of $$(a + 2b - c)(2b + c - a)(a + 2b + c)$$ is
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The 5th term of the series $${{10} \over 9},{1 \over 3}\sqrt {{{20} \over 3}} ,{2 \over 3}$$ is
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The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto n terms is
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If the mth term and the nth term of an A.P. are respectively $${1 \over n}$$ and $${1 \over m}$$, then the (mn)th term o...
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MCQ (More than One Correct Answer)
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In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i...
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Let x1, x2 be the roots of $${x^2} - 3x + a = 0$$ and x3, x4 be the roots of $${x^2} - 12x + b = 0$$. If $${x_1} < {x...
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The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G2 = 2...
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Find the sum of the first n terms of the series 0.2 + 0.22 + 0.222 + ......
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