Let $f:\mathbf{R}\rightarrow\mathbf{R}$ and $g:\mathbf{R}\rightarrow\mathbf{R}$ be defined as $ f(x)= \begin{cases} \log_e x, & x>0,\\[4pt] e^{-x}, & x\le 0 \end{cases} $ and $ g(x)= \begin{cases} x, & x\ge 0,\\[4pt] e^{x}, & x<0. \end{cases} $ Then, $g\circ f:\mathbf{R}\rightarrow\mathbf{R}$ is :
Previous 10 Questions — JEE Main 2024 (1 February Morning Shift)
Nearest first
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The area enclosed by the curves $xy+4y=16$ and $x+y=6$ is equal to:
Topic: JEE Main 2024 (1 February Morning Shift)
Let $S=\Big\{x\in\mathbb{R}:(\sqrt3+\sqrt2)^{x}+(\sqrt3-\sqrt2)^{x}=10\Big\}$.
Then the number of elements in $S$ is:
Topic: JEE Main 2024 (1 February Morning Shift)
Let $\vec a=-5\hat i+\hat j-3\hat k$, $\vec b=\hat i+2\hat j-4\hat k$ and
$\vec c=\big(((\vec a\times\vec b)\times\hat …
Topic: JEE Main 2024 (1 February Morning Shift)
Let the median and the mean deviation about the median of 7 observations
$170,125,230,190,210,a,b$ be $170$ and $\dfrac…
Topic: JEE Main 2024 (1 February Morning Shift)
Let $S=\left\{\,z\in\mathbb{C}:\ |z-1|=1 \ \text{and}\
\left|(\sqrt2-1)(z+\bar z)-i(z-\bar z)\right|=2\sqrt2\,\right\}$…
Topic: JEE Main 2024 (1 February Morning Shift)
If $n$ is the number of ways five different employees can sit into four indistinguishable
offices where any office may …
Topic: JEE Main 2024 (1 February Morning Shift)
The value of the integral $\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)}$
Topic: JEE Main 2024 (1 February Morning Shift)
If $\tan A=\dfrac{1}{\sqrt{x^{2}+x+1}},\quad \tan B=\dfrac{\sqrt{x}}{\sqrt{x^{2}+x+1}}$ and
$\tan C=\big(x^{-3}+x^{-2}+…
Topic: JEE Main 2024 (1 February Morning Shift)
If $A=\begin{bmatrix}\sqrt2&1\\-1&\sqrt2\end{bmatrix}$, $B=\begin{bmatrix}1&0\\1&1\end{bmatrix}$,
$C=ABA^{\mathrm T}$ a…
Topic: JEE Main 2024 (1 February Morning Shift)
A bag contains 8 balls, whose colours are either white or black. Four balls are drawn at random
without replacement and…
Topic: JEE Main 2024 (1 February Morning Shift)
Next 10 Questions — JEE Main 2024 (1 February Morning Shift)
Ascending by ID
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If the system of equations
$
\begin{aligned}
2x + 3y - z &= 5, \\
x + \alpha y + 3z &= -4, \\
3x - y + \beta z &= …
Topic: JEE Main 2024 (1 February Morning Shift)
Let $f:\mathbf{R}\rightarrow\mathbf{R}$ be defined as
$
f(x)=
\begin{cases}
\dfrac{a - b\cos 2x}{x^2}, & x < 0, \\[6…
Topic: JEE Main 2024 (1 February Morning Shift)
Let $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1,\ a > b$ be an ellipse, whose eccentricity is $\dfrac{1}{\sqrt{2}}$ and
…
Topic: JEE Main 2024 (1 February Morning Shift)
For $0 < \theta < \dfrac{\pi}{2}$, if the eccentricity of the hyperbola
$x^2 - y^2 \csc^2\theta = 5$
is $\sqrt{7}…
Topic: JEE Main 2024 (1 February Morning Shift)
Let $y = y(x)$ be the solution of the differential equation
$\frac{dy}{dx} = 2x(x+y)^3 - x(x+y) - 1, \quad y(0) = 1.…
Topic: JEE Main 2024 (1 February Morning Shift)
Let $3,a,b,c$ be in A.P. and $3,\,a-1,\,b+1,\,c+9$ be in G.P.
Then, the arithmetic mean of $a,b,c$ is:
Topic: JEE Main 2024 (1 February Morning Shift)
Let $C:\ x^{2}+y^{2}=4$ and $C':\ x^{2}+y^{2}-4\lambda x+9=0$ be two circles.
If the set of all values of $\lambda$ for…
Topic: JEE Main 2024 (1 February Morning Shift)
If $5f(x)+4f\!\left(\frac{1}{x}\right)=x^{2}-2,\ \forall x\ne 0$ and $y=9x^{2}f(x)$,
then $y$ is strictly increasing …
Topic: JEE Main 2024 (1 February Morning Shift)
If the shortest distance between the lines
\[
\frac{x-\lambda}{2}=\frac{y-2}{1}=\frac{z-1}{1}
\quad\text{and}\quad
\…
Topic: JEE Main 2024 (1 February Morning Shift)
