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The sum of infinite terms of a decreasing GP is equal to the greatest value of the function in the interval [-2,3] and the difference between the first two terms is f'(0). Then the common ratio of GP is

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If $a, b, c$ are in GP and $log a - log 2b$, $log 2b - log 3c$ and $log 3c - log a$ are in AP, then $a, b, c$are the lengths of the sides of a triangle which
is

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If $a, a, a_2, ., a_{2n-1},b$ are in AP, $a, b_1, b_2,...b_{2n-1}, b $are in GP and $a, c_1, c_2,... c_{2n-1}, b $ are in HP, where a, b are positive, then the
equation $a_n x^2-b_n+c_n$ has its roots

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If $x=1+\sqrt[{6}]{2}+\sqrt[{6}]{4}+\sqrt[{6}]{8}+\sqrt[{6}]{16}+\sqrt[{6}]{32}$ then ${\Bigg{(}1+\frac{1}{x}\Bigg{)}}^{24}$ =

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The number of solutions of ${5}^{1+|\sin x|+|\sin x{|}^2+\ldots}=25$ for $x\in(-\mathrm{\pi},\mathrm{\pi})$ is

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Which term of the series $\frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ...$ is $\frac{\sqrt{5}}{13}$ ?

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In a Harmonic Progression, $p^{th}$ term is $q$ and
the $q^{th}$ term is $p$. Then $pq^{th}$ term is

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Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common ratio?

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Suppose that m and n are fixed numbers such that the mth term am is equal to n and nth term an is equal to m, (m≠n), the the value of (m+n)th term is

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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+G^{2} = 27, then the two numbers are

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Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then resulting numbers are in geometric progression. Then which of the following is not among the three numbers?

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Let the three terms in A.P. be a – d, a, a + d.

given that a – d + a + a + d = 21

a = 7

then the three term in A.P. are 7 – d, 7, 7 + d

According to given condition 9 – d, 9, 21 + d are in G.P.

(9)^{2} = (9 – d) (21 + d)

81 = 189 + 9d – 21d – d^{2}

81 = 189 – 12d – d^{2}

d^{2} + 12d – 108 = 0

d(d + 18) – 6 (d + 18) = 0

(d – 6) (d + 18) = 0

We get, d = 6, –18

Putting d = 6 in the term 7 – d, 7, 7 + d we get 1, 7, 13.

If $H_1,H_2,\ldots,H_n$ are n harmonic means between a and b $(b\ne a)$;,then $\frac{{{H}}_n+a}{{{H}}_n-a}+\frac{{{H}}_n+b}{{{H}}_n-b}$

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If are positive real numbers whose product is a fixed number c, then the minimum of is

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The four geometric means between 2 and 64 are

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An arithmetic progression has 3 as its first term.
Also, the sum of the first 8 terms is twice the sum of
the first 5 terms. Then what is the common
difference?

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The sum of infinite terms of decreasing GP is equal to the greatest value of the function $f(x) = x^3
+ 3x – 9$ in the
interval [–2, 3] and difference between the first two terms is f '(0). Then the common ratio of the GP is

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If a, b, c, d are in HP and arithmetic mean of ab, bc, cd is 9 then which of the following number is the value ofad?

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