The numbers $\alpha>\beta>0$ are the roots of the equation $a x^{2}+b x+1=0$, and $\displaystyle \lim_{x\to \frac{1}{\alpha}} \left( \frac{1-\cos!\big(x^{2}+bx+a\big)}{2(1-a x)^{2}} \right)^{\tfrac{1}{2}} = \frac{1}{k}!\left(\frac{1}{\beta}-\frac{1}{\alpha}\right).$ Then $k$ is equal to:
Previous 10 Questions — JEE Main 2023 (8 April Evening Shift)
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If the number of words (with or without meaning) that can be formed using all the letters of the word MATHEMATICS — in …
Topic: JEE Main 2023 (8 April Evening Shift)
The area of the quadrilateral $ABCD$ with vertices $A(2,1,1)$, $B(1,2,5)$, $C(-2,-3,5)$ and $D(1,-6,-7)$ is equal to:
Topic: JEE Main 2023 (8 April Evening Shift)
The absolute difference of the coefficients of $x^{10}$ and $x^{7}$ in the expansion of $\left(2x^{2}+\dfrac{1}{2x}\rig…
Topic: JEE Main 2023 (8 April Evening Shift)
The mean and variance of $12$ observations are $\dfrac{9}{2}$ and $4$ respectively. Later, it was observed that two obs…
Topic: JEE Main 2023 (8 April Evening Shift)
The set $A={1,2,3,4,5,6,7}$. The relation $R={(x,y)\in A\times A:\ x+y=7}$ is:
Topic: JEE Main 2023 (8 April Evening Shift)
The probability that the random variable $X$ takes value $x$ is given by
$P(X = x) = k(x + 1)3^{-x}, \; x = 0, 1, 2, …
Topic: JEE Main 2023 (8 April Evening Shift)
$ \text{The integral } \displaystyle \int \left[ \left(\frac{x}{2}\right)^{x} + \left(\frac{2}{x}\right)^{x} \right] \l…
Topic: JEE Main 2023 (8 April Evening Shift)
$25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by:
Topic: JEE Main 2023 (8 April Evening Shift)
Let $A=\left\{\theta \in(0,2 \pi): \frac{1+2 i \sin \theta}{1-i \sin \theta}\right.$ is purely imaginary $\}$. Then the…
Topic: JEE Main 2023 (8 April Evening Shift)
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The value of $36,(4\cos^{2}9^\circ-1)(4\cos^{2}27^\circ-1)(4\cos^{2}81^\circ-1)(4\cos^{2}243^\circ-1)$ is:
Topic: JEE Main 2023 (8 April Evening Shift)
$A=\left[\begin{array}{cc}1 & 5 \\ \lambda & 10\end{array}\right], \mathrm{A}^{-1}=\alpha \mathrm{A}+\beta \mathrm{I}$ …
Topic: JEE Main 2023 (8 April Evening Shift)
The set $S$ is all values of $\theta\in[-\pi,\pi]$ for which the system
$x+y+\sqrt{3},z=0,\quad -x+(\tan\theta),y+\sqrt…
Topic: JEE Main 2023 (8 April Evening Shift)
