1
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1

Let the coefficients of x$$-$$1 and x$$-$$3 in the expansion of $${\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5}}}}}} \right)^{15}},x > 0$$, be m and n respectively. If r is a positive integer such that $$m{n^2} = {}^{15}{C_r}\,.\,{2^r}$$, then the value of r is equal to __________.

2
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1

The number of positive integers k such that the constant term in the binomial expansion of $${\left( {2{x^3} + {3 \over {{x^k}}}} \right)^{12}}$$, x $$\ne$$ 0 is 28 . l, where l is an odd integer, is ______________.

3
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1

If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of $${\left( {{x^n} + {2 \over {{x^5}}}} \right)^7}$$ is 939, then the sum of all the possible integral values of n is _________.

4
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 _____________.

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