JEE MAIN 2024 Previous Year Questions (PYQs) – Page 2 of 39
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The area (in sq. units) of the region described by $\{(x,y):y^{2}\le2x,\;y\ge4x-1\}$ is:
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Solution
Given that the inverse trigonometric functions assume principal values only.
Let $x,y\in[-1,1]$ such that $\cos^{-1}x-\sin^{-1}y=\alpha$, with $-\dfrac{\pi}{2}\le\alpha\le\pi$.
Then, the minimum value of $x^{2}+y^{2}+2xy\sin\alpha$ is:
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Solution
Let $y=y(x)$ be the solution of the differential equation
$(x^{2}+4)^{2}\,dy+(2x^{3}y+8xy-2)\,dx=0.$
If $y(0)=0$, then $y(2)$ is equal to:
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Solution
The mean of the following probability distribution of a random variable $X$ is $\dfrac{46}{9}$.
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Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin.
Let the line $x+y=2$ intersect the circle $C$ at the points $P$ and $Q$.
Let $MN$ be a chord of $C$ of length $2$ units and slope $-1$.
Then, the distance (in units) between the chord $PQ$ and the chord $MN$ is:
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Solution
Let $PQ$ be a chord of the parabola $y^{2}=12x$ and the midpoint of $PQ$ be at $(4,1)$.
Then, which of the following points lies on the line passing through the points $P$ and $Q$?
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Solution
The area (in sq. units) of the region
$S = \{\, z \in \mathbb{C} : |z - 1| \le 2,\ (z + \bar{z}) + i(z - \bar{z}) \le 2,\ \operatorname{Im}(z) \ge 0 \,\}$
is :
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If $\displaystyle \int_{-1}^{1}\frac{\cos(\alpha x)}{1+3x^{2}},dx=\frac{2}{\pi}$, then a value of $\alpha$ is:
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If $a,b,c$ are in AP and $a+1,; b,; c+3$ are in GP. Given $a>10$ and the arithmetic mean of $a,b,c$ is $8$, then the cube of the geometric mean of $a,b,c$ is:
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Let a relation $R$ on $\mathbb N\times\mathbb N$ be defined by $(x_1,y_1),R,(x_2,y_2)$ iff $x_1\le x_2$ or $y_1\le y_2$. Consider:
(I) $R$ is reflexive but not symmetric.
(II) $R$ is transitive.
Which of the following is true?
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Solution
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