1
JEE Main 2024 (Online) 5th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
724
B
742
C
693
D
639
2
JEE Main 2024 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

If the coefficients of $$x^4, x^5$$ and $$x^6$$ in the expansion of $$(1+x)^n$$ are in the arithmetic progression, then the maximum value of $$n$$ is:

A
28
B
21
C
7
D
14
3
JEE Main 2024 (Online) 4th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

The sum of all rational terms in the expansion of $$\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$$ is equal to :

A
633
B
6131
C
3133
D
931
4
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $m$ and $n$ be the coefficients of seventh and thirteenth terms respectively

in the expansion of $\left(\frac{1}{3} x^{\frac{1}{3}}+\frac{1}{2 x^{\frac{2}{3}}}\right)^{18}$. Then $\left(\frac{\mathrm{n}}{\mathrm{m}}\right)^{\frac{1}{3}}$ is :
A
$\frac{1}{9}$
B
$\frac{1}{4}$
C
$\frac{4}{9}$
D
$\frac{9}{4}$
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