1
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1

If the coefficient of x10 in the binomial expansion of $${\left( {{{\sqrt x } \over {{5^{{1 \over 4}}}}} + {{\sqrt 5 } \over {{x^{{1 \over 3}}}}}} \right)^{60}}$$ is $${5^k}\,.\,l$$, where l, k $$\in$$ N and l is co-prime to 5, then k is equal to _____________.

2
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
If $$\left( {{}^{40}{C_0}} \right) + \left( {{}^{41}{C_1}} \right) + \left( {{}^{42}{C_2}} \right) + \,\,.....\,\, + \,\,\left( {{}^{60}{C_{20}}} \right) = {m \over n}{}^{60}{C_{20}}$$ m and n are coprime, then m + n is equal to ___________.
3
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-1

Let $$A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } }$$ and $$B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } }$$. Then A + B is equal to _____________.

4
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1

If the sum of the co-efficient of all the positive even powers of x in the binomial expansion of $${\left( {2{x^3} + {3 \over x}} \right)^{10}}$$ is $${5^{10}} - \beta \,.\,{3^9}$$, then $$\beta$$ is equal to ____________.

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