1
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y=y(x)$$ is the solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=\sin (2 x), y(0)=\frac{3}{4}$$, then $$y\left(\frac{\pi}{8}\right)$$ is equal to :

A
$$\mathrm{e}^{-\pi / 8}$$
B
$$\mathrm{e}^{\pi / 4}$$
C
$$\mathrm{e}^{-\pi / 4}$$
D
$$\mathrm{e}^{\pi / 8}$$
2
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

The area of the region enclosed by the parabolas $$y=x^2-5 x$$ and $$y=7 x-x^2$$ is ________.

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3
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable $$X$$ denote the number of defective items in the sample. If the variance of $$X$$ is $$\sigma^2$$, then $$96 \sigma^2$$ is equal to __________.

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4
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

Suppose $$\mathrm{AB}$$ is a focal chord of the parabola $$y^2=12 x$$ of length $$l$$ and slope $$\mathrm{m}<\sqrt{3}$$. If the distance of the chord $$\mathrm{AB}$$ from the origin is $$\mathrm{d}$$, then $$l \mathrm{~d}^2$$ is equal to _________.

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