If the function $f(x) = \begin{cases} \dfrac{\log_e(1 - x + x^{2}) + \log_e(1 + x + x^{2})}{\sec x - \cos x}, & x \in \left( -\tfrac{\pi}{2}, \tfrac{\pi}{2} \right) \setminus \{0\} \\ k, & x = 0 \end{cases}$ is continuous at $x=0$, then $k$ is equal to:
Previous 10 Questions — JEE Main 2022 (26 July Morning Shift)
Nearest first
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Consider two G.P.s: $2, 2^{2}, 2^{3}, \ldots$ (of $60$ terms) and $4, 4^{2}, 4^{3}, \ldots$ (of $n$ terms).
If the ge…
Topic: JEE Main 2022 (26 July Morning Shift)
The odd natural number $a$, such that the area of the region bounded by $y=1$, $y=3$, $x=0$, $x=y^{a}$ is $\dfrac{364}{…
Topic: JEE Main 2022 (26 July Morning Shift)
If the system of linear equations
$8x + y + 4z = -2$
$x + y + z = 0$
$\lambda x - 3y = \mu$
has infinitely many sol…
Topic: JEE Main 2022 (26 July Morning Shift)
Let $O$ be the origin and $A$ be the point $z_1 = 1 + 2i$. If $B$ is the point $z_2$, $\mathrm{Re}(z_2) < 0$, such that…
Topic: JEE Main 2022 (26 July Morning Shift)
Let $f:\mathbb{R}\to\mathbb{R}$ be a continuous function such that
$f(3x) - f(x) = x$.
If $f(8) = 7$, then $f(14)$…
Topic: JEE Main 2022 (26 July Morning Shift)
Next 10 Questions — JEE Main 2022 (26 July Morning Shift)
Ascending by ID
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If $f(x)=
\begin{cases}
x+a, & x\le 0\\
|x-4|, & x>0
\end{cases}
\quad\text{and}\quad
g(x)=
\begin{cases}
x+1, & x
Topic: JEE Main 2022 (26 July Morning Shift)
Let $f(x)=
\begin{cases}
x^{3}-x^{2}+10x-7, & x\le 1,\\
-2x+\log_{2}(b^{2}-4), & x>1.
\end{cases}$
Then the set of all…
Topic: JEE Main 2022 (26 July Morning Shift)
If $\dfrac{dy}{dx} + 2y\tan x = \sin x,\ 0 < x < \tfrac{\pi}{2}$ and $y\!\left(\tfrac{\pi}{3}\right)=0$, then the maxim…
Topic: JEE Main 2022 (26 July Morning Shift)
A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$.
Let $f(x,…
Topic: JEE Main 2022 (26 July Morning Shift)
The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the lin…
Topic: JEE Main 2022 (26 July Morning Shift)
Let $\vec{a} = \alpha \hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \alpha \hat{k}$, $\alpha > 0$. …
Topic: JEE Main 2022 (26 July Morning Shift)
Let $E_1, E_2, E_3$ be three mutually exclusive events such that
$P(E_1)=\dfrac{2+3p}{6}$, $P(E_2)=\dfrac{2-p}{8}$ and…
Topic: JEE Main 2022 (26 July Morning Shift)
$\tan\!\left(2\tan^{-1}\!\tfrac{1}{5}+\sec^{-1}\!\tfrac{\sqrt{5}}{2}+2\tan^{-1}\!\tfrac{1}{8}\right)$ is equal to:
Topic: JEE Main 2022 (26 July Morning Shift)
