Competishun Header

Report Issue

JEE MAIN 2025
07-04-2025 SHIFT-1
Question
$\mathop {\lim }\limits_{x \to {0^ + }} \frac{{\tan \left( {5{{(x)}^{\frac{1}{3}}}} \right){{\log }_e}\left( {1 + 3{x^2}} \right)}}{{{{\left( {{{\tan }^{ - 1}}3\sqrt x } \right)}^2}\left( {{e^{5{{(x)}^{\frac{4}{3}}}}} - 1} \right)}}$ is equal to
Select the correct option:
A
$\frac{5}{3}$
B
$\frac{1}{{15}}$
C
1
D
$\frac{1}{3}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\mathop {\lim }\limits_{x \to {0^ + }} \left( {\frac{{\tan \left( {5{x^{1/3}}} \right)}}{{5{x^{1/3}}}}} \right) \cdot \left( {\frac{{{{(3\sqrt x )}^2}}}{{{{\left( {{{\tan }^{ - 1}}3\sqrt x } \right)}^2}}}} \right)\left( {\frac{{\ell \left( {1 + 3{x^2}} \right)}}{{3{x^2}}}} \right)\left( {\frac{{5{x^{4/3}}}}{{{e^{5{x^{\frac{4}{3}}}}} - 1}}} \right) \times \frac{{5{x^{1/3}} \cdot 3{x^2}}}{{5{x^{4/3}} \cdot 9x}}$ $ = \frac{1}{3}$
Question Tags
JEE Main
Mathematics
Easy
Start Preparing for JEE with Competishun
Video Solution
BY competishun
Video Solution
Watch Solution
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE Main 20242024
A 2 kg brick begins to slide over a surface which is inclined at an angle of 45° with respect...
JEE MainPhysicsEasy
View Solution
QJEE-Main 20242024
The $20^{\text {th }}$ term from the end of the progression $20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots,-129 \frac{1}{4}$ is...
JEE MainMathematicsEasy
View Solution
QJEE-Main 20242024
Let R be the interior region between the lines $3 x-y+1=0$ and $x+2 y-5=0$ containing the origin. The set of...
JEE MainMathematicsMedium
View Solution
QJEE-Main 20242024
Let the image of the point $(1,0,7)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ be the point $(\alpha, \beta, \gamma)$. Then which one...
JEE MainMathematicsHard
View Solution
QJEE-Main 20242024
Consider the function $\mathrm{f}:(0,2) \rightarrow \mathrm{R}$ defined by $f(x)=\frac{x}{2}+\frac{2}{x}$ and the function $g(x)$ defined by $g(x)= \left\{\begin{array}{cc}\min \{f(t)\}, & 0
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
An electric bulb rated 50 W – 200 V is connected across a 100 V supply. The power dissipation of...
JEE MainPhysicsEasy
View Solution
QJEE Main 20242024
The equivalent resistance between A and B is:
JEE MainPhysicsMedium
View Solution
QJEE-Main 20242024
Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $...
JEE MainMathematicsEasy
View Solution
QJee Main 20242024
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty...
JEE MainMathematicsHard
View Solution
QJEE Main 20242024
Given below are two statements :
Statement I : The contact angle between a solid and a liquid is...
JEE MainPhysicsEasy
View Solution
QJee Main 20242024
Let $A=\left[\begin{array}{ccc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$ and $...
JEE MainMathematicsHard
View Solution
QJEE Main 20242024
Correct formula for height of a satellite from earths surface is :
JEE MainPhysicsEasy
View Solution
QJEE Main 20242024
Let $\vec{a}=\hat{\imath}+\alpha \hat{\jmath}+\beta \hat{k}, \alpha, \beta \in R$. Let a vector $\vec{b}$ be such that the angle between $\vec{a}$ and...
JEE MainMathematicsEasy
View Solution
Q JEE Main 20242024
A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the...
JEE MainPhysicsEasy
View Solution
QJEE Main 20242024
One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text {th }}$ division of main...
JEE MainPhysicsMedium
View Solution
QJEE MAIN 20242024
Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5 x+7 y=50$. Let the point $P$ divide...
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
The number of solutions of the equation $...
JEE MainMathematicsEasy
View Solution
Q JEE MAIN 20242024
For $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number k be such that $...
JEE MainMathematicsEasy
View Solution
Check this project | Best Developer Portfolio