1
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

The constant term in the expansion of $${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$$ is ___________.

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2
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

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3
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

Let $$x$$ and $$y$$ be distinct integers where $$1 \le x \le 25$$ and $$1 \le y \le 25$$. Then, the number of ways of choosing $$x$$ and $$y$$, such that $$x+y$$ is divisible by 5, is ____________.

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4
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

For some a, b, c $$\in\mathbb{N}$$, let $$f(x) = ax - 3$$ and $$\mathrm{g(x)=x^b+c,x\in\mathbb{R}}$$. If $${(fog)^{ - 1}}(x) = {\left( {{{x - 7} \over 2}} \right)^{1/3}}$$, then $$(fog)(ac) + (gof)(b)$$ is equal to ____________.

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