1
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 ___________.
2
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 _____________.

3
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 ____________.

4
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1 Let Cr denote the binomial coefficient of xr in the expansion of $${(1 + x)^{10}}$$. If for $$\alpha$$, $$\beta$$ $$\in$$ R, $${C_1} + 3.2{C_2} + 5.3{C_3} +$$ ....... upto 10 terms $$= {{\alpha \times {2^{11}}} \over {{2^\beta } - 1}}\left( {{C_0} + {{{C_1}} \over 2} + {{{C_2}} \over 3} + \,\,.....\,\,upto\,10\,terms} \right)$$ then the value of $$\alpha$$ + $$\beta$$ is equal to ___________.

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