1
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1
Change Language

$$\text { Number of integral terms in the expansion of }\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824} \text { is equal to _________. }$$

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2
JEE Main 2024 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

Remainder when $$64^{32^{32}}$$ is divided by 9 is equal to ________.

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3
JEE Main 2024 (Online) 29th January Morning Shift
Numerical
+4
-1
Change Language

$$\text { If } \frac{{ }^{11} C_1}{2}+\frac{{ }^{11} C_2}{3}+\ldots+\frac{{ }^{11} C_9}{10}=\frac{n}{m} \text { with } \operatorname{gcd}(n, m)=1 \text {, then } n+m \text { is equal to }$$ _______.

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4
JEE Main 2024 (Online) 27th January Evening Shift
Numerical
+4
-1
Change Language

The coefficient of $$x^{2012}$$ in the expansion of $$(1-x)^{2008}\left(1+x+x^2\right)^{2007}$$ is equal to _________.

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