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JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
For k $$\in$$ N, let $${1 \over {\alpha (\alpha + 1)(\alpha + 2).........(\alpha + 20)}} = \sum\limits_{K = 0}^{20} {{{{A_k}} \over {\alpha + k}}} $$, where $$\alpha > 0$$. Then the value of $$100{\left( {{{{A_{14}} + {A_{15}}} \over {{A_{13}}}}} \right)^2}$$ is equal to _____________.
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2
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
Let $$\left\{ {{a_n}} \right\}_{n = 1}^\infty $$ be a sequence such that a1 = 1, a2 = 1 and $${a_{n + 2}} = 2{a_{n + 1}} + {a_n}$$ for all n $$\ge$$ 1. Then the value of $$47\sum\limits_{n = 1}^\infty {{{{a_n}} \over {{2^{3n}}}}} $$ is equal to ______________.
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3
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
Sn(x) = loga1/2x + loga1/3x + loga1/6x + loga1/11x + loga1/18x + loga1/27x + ...... up to n-terms, where a > 1. If S24(x) = 1093 and S12(2x) = 265, then value of a is equal to ____________.
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4
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
Let $${1 \over {16}}$$, a and b be in G.P. and $${1 \over a}$$, $${1 \over b}$$, 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to ___________.
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