1
JEE Main 2025 (Online) 24th January Morning Shift
Numerical
+4
-1
Change Language

Let $S=\left\{p_1, p_2 \ldots, p_{10}\right\}$ be the set of first ten prime numbers. Let $A=S \cup P$, where $P$ is the set of all possible products of distinct elements of $S$. Then the number of all ordered pairs $(x, y), x \in S$, $y \in A$, such that $x$ divides $y$, is ________ .

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2
JEE Main 2025 (Online) 24th January Morning Shift
Numerical
+4
-1
Change Language

If for some $\alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8$ and $\sec ^2\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^2\left(\cot ^{-1} \beta\right)=36$, then $\alpha^2+\beta$ is __________

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3
JEE Main 2025 (Online) 24th January Morning Shift
Numerical
+4
-1
Change Language

The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is _________.

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4
JEE Main 2025 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

An object of mass ' m ' is projected from origin in a vertical xy plane at an angle $45^{\circ}$ with the $\mathrm{x}-$ axis with an initial velocity $\mathrm{v}_0$. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]

A
$\frac{m v_o{ }^3}{2 \sqrt{2} g}$ along negative $z$-axis
B
$\frac{m v_o^3}{2 \sqrt{2} g}$ along positive $z$-axis
C
$\frac{m v_o^3}{4 \sqrt{2} g}$ along positive $z$-axis
D
$\frac{m v_o^3}{4 \sqrt{2} g}$ along negative z-axis
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