1
JEE Main 2025 (Online) 3rd April Morning Shift
Numerical
+4
-1
Change Language

Let the product of the focal distances of the point $\mathbf{P}(4,2 \sqrt{3})$ on the hyperbola $\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be 32 . Let the length of the conjugate axis of H be $p$ and the length of its latus rectum be $q$. Then $p^2+q^2$ is equal to__________

Your input ____
2
JEE Main 2025 (Online) 3rd April Morning Shift
Numerical
+4
-1
Change Language

The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, the $x$-axis and the lines $x=-2$ and $x=4$ is equal to__________

Your input ____
3
JEE Main 2025 (Online) 3rd April Morning Shift
Numerical
+4
-1
Change Language

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________

Your input ____
4
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is:

(Take $\gamma=1.5 ; \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

A
300 K
B
600 K
C
327 K
D
522 K
JEE Main Papers
2023
2021
EXAM MAP