Binomial Theorem_JEE-Main 050424_(S2) - Competishun – Live JEE & NEET Courses and Exam Prep

Competishun Header

JEE Main 2024

05-04-2024 S2

Question

If the constant term in the expansion of $\left(\frac{\sqrt[5]{3}}{x}+\frac{2 x}{\sqrt[3]{5}}\right)^{12}, x \neq 0$, is $\alpha \times 2^8 \times \sqrt[5]{3}$, then $25 \alpha$ is equal to :

Select the correct option:

A

639

B

724

C

693

D

742

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

QJEE Main 20242024

Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius 2 . If the...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $f, \mathrm{~g}: \mathrm{R} \rightarrow \mathrm{R}$ be defined as : $f(\mathrm{x})=|\mathrm{x}-1|$ and $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

If the constant term in the expansion of $\left(\frac{\sqrt[5]{3}}{x}+\frac{2 x}{\sqrt[3]{5}}\right)^{12}, x \neq 0$, is $\alpha \times 2^8 \times \sqrt[5]{3}$, then...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $(\alpha, \beta, \gamma)$ be the point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$. Then $\alpha+\beta+\gamma$ is equal to

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $\mathrm{A}(-1,1)$ and $\mathrm{B}(2,3)$ be two points and P be a variable point above the line $A B$ such that...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Consider three vectors $\vec{a}, \vec{b}, \vec{c}$. Let $|\vec{a}|=2,|\vec{b}|=3$ and $\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}$. If $\alpha \in\left[0, \frac{\pi}{3}\right]$ is the angle between...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $\vec{a}=2 \hat{\imath}+5 \hat{\jmath}-\hat{k}, \vec{b}=2 \hat{\imath}-2 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be three vectors such that $(\vec{c}+\hat{\imath}) \times(\vec{a}+\vec{b}+\hat{\imath})=\vec{a} \times(\vec{c}+\hat{\imath})$. $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

The area enclosed between the curves $y=x|x|$ and $\mathrm{y}=\mathrm{x}-|\mathrm{x}|$ is :

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $S_1=\{z \in C:|z| \leq 5\}, S_2=\left\{z \in C: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}$ and $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

The differential equation of the family of circles passing the origin and having center at the line $\mathrm{y}=\mathrm{x}$ is :

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $f:[-1,2] \rightarrow \mathrm{R}$ be given by $f(\mathrm{x})=2 \mathrm{x}^2+\mathrm{x}+\left[\mathrm{x}^2\right]-[\mathrm{x}]$, where $[\mathrm{t}]$ denotes the greatest integer less than or equal to...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

The current in an inductor is given by I = (3t + 8) where t is in second. The magnitude...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

A wire of resistance $20 \Omega$ is divided into 10 equal parts. A combination of two parts are connected in...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension....

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of...

JEE MainPhysicsEasy

View Solution→