If the function $f(x) = \left\{ {\matrix{ {(1 + |\cos x|)^{\lambda \over {|\cos x|}}} & , & {0 < x < {\pi \over 2}} \cr \mu & , & {x = {\pi \over 2}} \cr e^{{{\cot 6x} \over {{}\cot 4x}}} & , & {{\pi \over 2} < x < \pi } \cr } } \right.$
is continuous at $x = {\pi \over 2}$, then $9\lambda + 6{\log _e}\mu + {\mu ^6} - {e^{6\lambda }}$ is equal to
Previous 10 Questions — JEE Main 2023 (25 January Evening Shift)
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Let $A,B,C$ be $3\times 3$ matrices such that $A$ is symmetric and $B$ and $C$ are skew-symmetric.
Consider the state…
Topic: JEE Main 2023 (25 January Evening Shift)
Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that
$N-2,\ \sqrt{3N…
Topic: JEE Main 2023 (25 January Evening Shift)
The number of functions
$f:\{1,2,3,4\}\to \{\,a\in \mathbb{Z}\mid |a|\le 8\,\}$
satisfying $f(n)+\dfrac{1}{n}f(n+1)=1…
Topic: JEE Main 2023 (25 January Evening Shift)
The foot of the perpendicular from the point $(2,0,5)$ on the line
$\dfrac{x+1}{2}=\dfrac{y-1}{5}=\dfrac{z+1}{-1}$ is …
Topic: JEE Main 2023 (25 January Evening Shift)
The equations of two sides of a variable triangle are $x=0$ and $y=3$, and its third side is a tangent to the parabola …
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The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is:
Topic: JEE Main 2023 (25 January Evening Shift)
Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola
$16x^{2}-y^{2}+64x+4y+44=0$.
The…
Topic: JEE Main 2023 (25 January Evening Shift)
Let the function $f(x)=2x^{3}+(2p-7)x^{2}+3(2p-9)x-6$ have a maxima for some value of $x0$.
Then, the set of all valu…
Topic: JEE Main 2023 (25 January Evening Shift)
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 ra…
Topic: JEE Main 2023 (25 January Evening Shift)
$ \text{The integral } 16 \int_{1}^{2} \frac{dx}{x^{3}(x^{2}+2)^{2}} \text{ is equal to:}$
Topic: JEE Main 2023 (25 January Evening Shift)
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\righ…
Topic: JEE Main 2023 (25 January Evening Shift)
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition,…
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Let $y=y(t)$ be a solution of the differential equation $\dfrac{dy}{dt}+\alpha y=\gamma e^{-\beta t}$ where $\alpha>0$,…
Topic: JEE Main 2023 (25 January Evening Shift)
Let
$A=\begin{bmatrix}\dfrac{1}{\sqrt{10}} & \dfrac{3}{\sqrt{10}}\\[4pt]-\dfrac{3}{\sqrt{10}} & \dfrac{1}{\sqrt{10}}\e…
Topic: JEE Main 2023 (25 January Evening Shift)
Evaluate the sum:
$\displaystyle \sum_{k=0}^{6} \binom{51-k}{3}$
Topic: JEE Main 2023 (25 January Evening Shift)
