JEE MAIN 2022 Previous Year Questions (PYQs) – Page 12 of 31
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Let $y = y(x)$ be the solution of the differential equation $(x + 1)y' - y = {e^{3x}}{(x + 1)^2}$, with $y(0) = {1 \over 3}$. Then, the point $x = - {4 \over 3}$ for the curve $y = y(x)$ is :
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Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $AB$ is a zero matrix. Then
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If the solution curve $y = y(x)$ of the differential equation ${y^2}dx + ({x^2} - xy + {y^2})dy = 0$, which passes through the point (1, 1) and intersects the line $y = \sqrt 3 x$ at the point $(\alpha ,\sqrt 3 \alpha )$, then value of ${\log _e}(\sqrt 3 \alpha )$ is equal to :
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If
$\dfrac{1}{(20-a)(40-a)} + \dfrac{1}{(40-a)(60-a)} + \cdots + \dfrac{1}{(180-a)(200-a)} = \dfrac{1}{256}$,
then the maximum value of $a$ is :
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Solution
Let $x = 2t$, $y = {{{t^2}} \over 3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $SA \bot BA$, where A is any point on the conic. If k is the ordinate of the centroid of the $\Delta$SAB, then $\mathop {\lim }\limits_{t \to 1} k$ is equal to :
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If
$\lim_{x \to 0} \dfrac{\alpha e^{x^2} + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \dfrac{2}{3}$,
where $\alpha, \beta, \gamma \in \mathbb{R}$, then which of the following is NOT correct?
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Solution
Let a circle C in complex plane pass through the points ${z_1} = 3 + 4i$, ${z_2} = 4 + 3i$ and ${z_3} = 5i$. If $z( \ne {z_1})$ is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then $arg(z)$ is equal to :
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The integral
$\int_{0}^{\tfrac{\pi}{2}} \dfrac{1}{3 + 2 \sin x + \cos x} , dx$
is equal to :
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Solution
Let $A = \{ x \in R:|x + 1| < 2\} $ and $B = \{ x \in R:|x - 1| \ge 2\} $. Then which one of the following statements is NOT true?
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Solution
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