JEE MAIN 2022 Previous Year Questions (PYQs) – Page 29 of 31
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The general solution of the differential equation
$(x - y^2),dx + y(5x + y^2),dy = 0$ is:
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Let the locus of the centre $(\alpha,\beta)$, $\beta>0$, of the circle which touches the circle $x^2+(y-1)^2=1$ externally and also touches the $x$-axis be $L$. Then the area bounded by $L$ and the line $y=4$ is:
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Let $ABC$ be a triangle such that $\overrightarrow{BC}=\vec a,\ \overrightarrow{CA}=\vec b,\ \overrightarrow{AB}=\vec c,\ |\vec a|=6\sqrt2,\ |\vec b|=2\sqrt3$ and $\vec b\cdot \vec c=12$. Consider the statements:
(S1): $\ \big|\ \vec a\times\vec b+\vec c\times\vec b\ \big| - |\vec c| = 6(2\sqrt2-1)$
(S2): $\ \angle ACB=\cos^{-1}!\left(\sqrt{\tfrac{2}{3}}\right)$
Then
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If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^2 + \alpha x + \beta > 0$, for all $x \in \mathbb{R}$, is :
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For $z \in \mathbb{C}$ if the minimum value of $\lvert z - 3\sqrt{2}\rvert + \lvert z - p\sqrt{2}i\rvert$ is $5\sqrt{2}$, then a value of $p$ is ________.
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The number of real values of $\lambda$, such that the system of linear equations
$2x - 3y + 5z = 9$
$x + 3y - z = -18$
$3x - y + (\lambda^2 - |\lambda|)z = 16$
has no solutions, is
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The number of bijective functions $f:\{1,3,5,7,\ldots,99\}\to\{2,4,6,8,\ldots,100\}$ such that
$f(3)\ge f(9)\ge f(15)\ge f(21)\ge \cdots \ge f(99)$ is ________.
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The remainder when $(11)^{1011} + (1011)^{11}$ is divided by $9$ is
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$\lim_{x \to \tfrac{\pi}{4}} \dfrac{8\sqrt{2} - (\cos x + \sin x)^7}{\sqrt{2} - \sqrt{2}\sin 2x}$ is equal to
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If $A$ and $B$ are two events such that $P(A) = \tfrac{1}{3},\ P(B) = \tfrac{1}{5}$ and $P(A \cup B) = \tfrac{1}{2}$, then
$P(A \mid B') + P(B \mid A')$ is equal to :
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Solution
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