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JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
The number of rational terms in the binomial expansion of $${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$$ is _______________.
2
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
The term independent of x in the expansion of

$${\left[ {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over {x - {x^{1/2}}}}} \right]^{10}}$$, x $$\ne$$ 1, is equal to ____________.
3
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Let $${}^n{C_r}$$ denote the binomial coefficient of xr in the expansion of (1 + x)n. If $$\sum\limits_{k = 0}^{10} {({2^2} + 3k)} {}^{10}{C_k} = \alpha {.3^{10}} + \beta {.2^{10}},\alpha ,\beta \in R$$, then $$\alpha$$ + $$\beta$$ is equal to ___________.
Let the coefficients of third, fourth and fifth terms in the expansion of $${\left( {x + {a \over {{x^2}}}} \right)^n},x \ne 0$$, be in the ratio 12 : 8 : 3. Then the term independent of x in the expansion, is equal to ___________.