Let be a function satisfying for all|Modulus| JEE Main 2024

Competishun Header

JEE MAIN 2024

30-01-2024

Question

Let $\mathrm{f}: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$ be a function satisfying $f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}$ for all $x, y, f(y) \neq 0$. If $f^{\prime}(1)=2024$, then

Select the correct option:

A

$x f^{\prime}(x)-2024 f(x)=0$

B

$x f^{\prime}(x)+2024 f(x)=0$

C

$x f^{\prime}(x)+f(x)=2024$

D

$x f^{\prime}(x)-2023 f(x)=0$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

QJEE MAIN 20242024

Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of...

JEE MainMathematicsEasy

View Solution→

QJEE MAIN 20242024

The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{I}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to...

JEE MainMathematicsEasy

View Solution→

Q JEE MAIN 20242024

Let $\vec{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \vec{b}=-\hat{\imath}-8 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}=4 \hat{\imath}+\mathrm{c}_2 \hat{\jmath}+\mathrm{c}_3 \hat{\mathrm{k}}$ be three vectors such that $\vec{b} \times \vec{a}=\vec{c} \times \vec{a}$....

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let C be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersects the...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

If $\lambda>0$, let $\theta$ be the angle between the vectors $\vec{a}=\hat{\imath}+\lambda \hat{\jmath}-3 \hat{k}$ and $\vec{b}=3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$. If the vectors...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

If the function $f(x)=\left\{\begin{array}{ll}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ \log _e 2 \log _e 3 & , x=0\end{array}\right.$...

JEE MainMathematicsEasy

View Solution→

QJEE MAIN 20242024

If $y=\frac{(\sqrt{x}+1)\left(x^2-\sqrt{x}\right)}{x \sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left(3 \cos ^2 x-5\right) \cos ^3 x$, then $96 y^{\prime}\left(\frac{\pi}{6}\right)$ is equal to :

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and  electrons is__

JEE MainChemistryEasy

View Solution→

QJEE MAIN 20242024

Let $f:(0, \infty) \rightarrow R$ and $F(x)=\int_0^x t f(t) d t$. If $F\left(x^2\right)=\mathrm{x}^4+\mathrm{x}^5$, then $\sum_{\mathrm{r}=1}^{12} \mathrm{f}\left(\mathrm{r}^2\right)$ is equal to :

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

2.7 Kg of each of water and acetic acid are mixed, The freezing point of the solution will be $...

JEE MainChemistryEasy

View Solution→

QJEE MAIN 20242024

Let $A=I_2-2 M^{\mathrm{T}}$, where M is real matrix of order $2 \times 1$ such that the relation $\mathrm{M}^{\mathrm{T}} \mathrm{M}=\mathrm{I}_1$ holds....

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high temperature forms oxides of...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

The total number of 'sigma' and 'Pi' bonds in 2-oxohex-4-ynoic acid is____.

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Consider the following reaction, the rate expression of which is given below
$...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

From 6.55 g of aniline, the maximum amount of acetanilide that can be prepared will be $\_\_\_\_$ $\times 10^{-1} \mathrm{~g}$.

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using constant pressure of 5...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

Number of compounds/species from the following with non-zero dipole moment is $\_\_\_\_$ $...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

The maximum number of orbitals which can identified with $\mathrm{n}=4$ and $\mathrm{m}_l=0$ is $\_\_\_\_$

JEE MainChemistryEasy

View Solution→