JEE Main 2025 (Online) 3rd April Morning Shift | Binomial Theorem Question 9 | Mathematics | JEE Main - ExamSIDE.com

Joint Entrance Examination

Medical

Graduate Aptitude Test in Engineering

Civil Services

Defence

Staff Selection Commission

CBSE

1

JEE Main 2025 (Online) 3rd April Morning Shift

MCQ (Single Correct Answer)

+4

-1

The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is :

A

16923

B

18817

C

3763

D

33845

2

JEE Main 2025 (Online) 3rd April Morning Shift

MCQ (Single Correct Answer)

+4

-1

If $\sum\limits_{r=1}^9\left(\frac{r+3}{2^r}\right) \cdot{ }^9 C_r=\alpha\left(\frac{3}{2}\right)^9-\beta, \alpha, \beta \in \mathbb{N}$, then $(\alpha+\beta)^2$ is equal to

A

27

B

81

C

18

D

9

3

JEE Main 2025 (Online) 2nd April Evening Shift

MCQ (Single Correct Answer)

+4

-1

$$If\,\sum\limits_{r = 0}^{10} {({{{{10}^{r + 1}} - 1} \over {{{10}^r}}}).{}^{11}{C_{r + 1}} = {{{}_\alpha 11 - {{11}^{11}}} \over {{{10}^{10}}}},\,then\,\,\alpha \,\,is\,\,equal\,\,to:} $$

A

11

B

20

C

24

D

15

4

JEE Main 2025 (Online) 2nd April Morning Shift

MCQ (Single Correct Answer)

+4

-1

The largest $\mathrm{n} \in \mathbf{N}$ such that $3^{\mathrm{n}}$ divides 50 ! is :

A

22

B

20

C

21

D

23

JEE Main Subjects

EXAM MAP

Joint Entrance Examination

JEE Main JEE Advanced MHT CET BITSAT COMEDK WB JEE KCET VITEEE AP EAPCET TS EAMCET IAT (IISER)

Medical

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Civil Services

UPSC Civil Service

Defence

Staff Selection Commission

CBSE