Three rotten apples are mixed accidentally with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the number of rotten apples. If $\mu$ and $\sigma^{2}$ represent the mean and variance of $X$, respectively, then $10(\mu^{2}+\sigma^{2})$ is equal to:
Previous 10 Questions — JEE Main 2023 (29 January Morning Shift)
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Let $B$ and $C$ be the two points on the line $y+x=0$ such that $B$ and $C$ are symmetric with respect to the origin. …
Topic: JEE Main 2023 (29 January Morning Shift)
Let $\lambda\ne 0$ be a real number. Let $\alpha,\beta$ be the roots of the equation $14x^{2}-31x+3\lambda=0$ and $\alp…
Topic: JEE Main 2023 (29 January Morning Shift)
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Let $f(\theta)=3\big(\sin^{4}\!\left(\tfrac{3\pi}{2}-\theta\right)+\sin^{4}\!(3\pi+\theta)\big)-2\big(1-\sin^{2}2\theta…
Topic: JEE Main 2023 (29 January Morning Shift)
Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside.
If the player…
Topic: JEE Main 2023 (29 January Morning Shift)
Let the tangents at the points $A(4,-11)$ and $B(8,-5)$ on the circle $x^{2}+y^{2}-3x+10y-15=0$, intersect at the point…
Topic: JEE Main 2023 (29 January Morning Shift)
Let $f(x)=x+\dfrac{a}{\pi^{2}-4}\sin x+\dfrac{b}{\pi^{2}-4}\cos x,\ x\in\mathbb{R}$ be a function which satisfies
$\d…
Topic: JEE Main 2023 (29 January Morning Shift)
Let $\alpha$ and $\beta$ be real numbers. Consider a $3\times 3$ matrix $A$ such that $A^{2}=3A+\alpha I$.
If $A^{4}=…
Topic: JEE Main 2023 (29 January Morning Shift)
A light ray emits from the origin making an angle $30^\circ$ with the positive $x$-axis.
After getting reflected by t…
Topic: JEE Main 2023 (29 January Morning Shift)
For two non-zero complex numbers $z_{1}$ and $z_{2}$, if $\operatorname{Re}(z_{1}z_{2})=0$ and $\operatorname{Re}(z_{1}…
Topic: JEE Main 2023 (29 January Morning Shift)
Let $\Delta$ be the area of the region $\{(x,y)\in\mathbb{R}^{2}:\ x^{2}+y^{2}\le 21,\ y^{2}\le 4x,\ x\ge 1\}$.
Then …
Topic: JEE Main 2023 (29 January Morning Shift)
The domain of
$$f(x)=\frac{\log_{(x+1)}(x-2)}{e^{2\log_e x}-(2x+3)},\quad x\in\mathbb{R}$$
is:
Topic: JEE Main 2023 (29 January Morning Shift)
Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that
$$f(x)=\frac{x^{2}+2x+1}{x^{2}+1}.$$
Then:
Topic: JEE Main 2023 (29 January Morning Shift)
