1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The coefficient of x101 in the expression $${(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + \,\,{x^{500}}$$, x > 0, is

A
501C101 (5)399
B
501C101 (5)400
C
501C100 (5)400
D
500C101 (5)399
2
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
1
B
2
C
3
D
5
3
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder when 32022 is divided by 5 is :

A
1
B
2
C
3
D
4
4
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
$$\sum\limits_{k = 0}^{20} {{{\left( {{}^{20}{C_k}} \right)}^2}} $$ is equal to :
A
$${}^{40}{C_{21}}$$
B
$${}^{40}{C_{19}}$$
C
$${}^{40}{C_{20}}$$
D
$${}^{41}{C_{20}}$$
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