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

Let the set $$C=\left\{(x, y) \mid x^2-2^y=2023, x, y \in \mathbb{N}\right\}$$. Then $$\sum_\limits{(x, y) \in C}(x+y)$$ is equal to _________.

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2
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1
Change Language

Let $$[\alpha]$$ denote the greatest integer $$\leq \alpha$$. Then $$[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots+[\sqrt{120}]$$ is equal to __________

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3
JEE Main 2023 (Online) 11th April Evening Shift
Numerical
+4
-1
Change Language

The number of points, where the curve $$f(x)=\mathrm{e}^{8 x}-\mathrm{e}^{6 x}-3 \mathrm{e}^{4 x}-\mathrm{e}^{2 x}+1, x \in \mathbb{R}$$ cuts $$x$$-axis, is equal to _________.

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4
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1
Change Language

If $$a$$ and $$b$$ are the roots of the equation $$x^{2}-7 x-1=0$$, then the value of $$\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$$ is equal to _____________.

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