JEE Main 2022 (Online) 25th June Morning Shift | Binomial Theorem Question 95 | Mathematics

If $${1 \over {2\,.\,{3^{10}}}} + {1 \over {{2^2}\,.\,{3^9}}} + \,\,.....\,\, + \,\,{1 \over {{2^{10}}\,.\,3}} = {K \over {{2^{10}}\,.\,{3^{10}}}}$$, then the remainder when K is divided by 6 is :

JEE Main 2022 (Online) 24th June Morning Shift

MCQ (Single Correct Answer)

-1

The remainder when 3²⁰²² is divided by 5 is :

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

$$\sum\limits_{k = 0}^{20} {{{\left( {{}^{20}{C_k}} \right)}^2}} $$ is equal to :

$${}^{40}{C_{21}}$$

$${}^{40}{C_{19}}$$

$${}^{40}{C_{20}}$$

$${}^{41}{C_{20}}$$

JEE Main 2021 (Online) 26th August Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $${{}^{20}{C_r}}$$ is the co-efficient of x^r in the expansion of (1 + x)²⁰, then the value of $$\sum\limits_{r = 0}^{20} {{r^2}.{}^{20}{C_r}} $$ is equal to :

$$420 \times {2^{19}}$$

$$380 \times {2^{19}}$$

$$380 \times {2^{18}}$$

$$420 \times {2^{18}}$$

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