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

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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

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