JEE MAIN 2023 Previous Year Questions (PYQs) – Page 21 of 34
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Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola
$16x^{2}-y^{2}+64x+4y+44=0$.
Then the area of the region above the parabola $x^{2}=y+4$, below the transverse axis $T$ and on the right of the conjugate axis $C$ is:
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The set of all $a\in\mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root, is:
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Let the function $f(x)=2x^{3}+(2p-7)x^{2}+3(2p-9)x-6$ have a maxima for some value of $x<0$ and a minima for some value of $x>0$.
Then, the set of all values of $p$ is:
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Evaluate the integral $ \displaystyle \int_{0}^{\infty}\frac{6}{e^{3x}+6e^{2x}+11e^{x}+6},dx $ is equal to:
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Let $z$ be a complex number such that $\left|\dfrac{z-2i}{z+i}\right|=2,\ z\ne -i$.
Then $z$ lies on the circle of radius $2$ and centre:
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Let $s_1,s_2,s_3,\ldots,s_{10}$ respectively be the sum to $12$ terms of $10$ A.P.s whose first terms are $1,2,3,\ldots,10$ and the common differences are $1,3,5,\ldots,19$ respectively. Then $\sum_{i=1}^{10}s_i$ is equal to:
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$ \text{The integral } 16 \int_{1}^{2} \frac{dx}{x^{3}(x^{2}+2)^{2}} \text{ is equal to:}$
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Let $B=\left[\begin{array}{lll}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & 4\end{array}\right], \alpha > 2$ be the adjoint of a matrix $A$ and $|A|=2$. Then $\left[\begin{array}{ccc}\alpha & -2 \alpha & \alpha\end{array}\right] B\left[\begin{array}{c}\alpha \\ -2 \alpha \\ \alpha\end{array}\right]$$ is equal to :
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Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by
$f(x)=\log_{\sqrt{m}}\!\left(\sqrt{2}(\sin x-\cos x)+m-2\right)$, for some $m$, such that the range of $f$ is $[0,2]$.
Then the value of $m$ is ______
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The fractional part of the number $\dfrac{4^{2022}}{15}$ is equal to:
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Solution
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