1
JEE Main 2025 (Online) 2nd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The term independent of $x$ in the expansion of $\left(\frac{(x+1)}{\left(x^{2 / 3}+1-x^{1 / 3}\right)}-\frac{(x-1)}{\left(x-x^{1 / 2}\right)}\right)^{10}, x>1$, is :

A
240
B
120
C
150
D
210
2
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder, when $7^{103}$ is divided by 23, is equal to:

A

9

B

6

C

14

D

17

3
JEE Main 2025 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The least value of n for which the number of integral terms in the Binomial expansion of $(\sqrt[3]{7}+\sqrt[12]{11})^n$ is 183, is :

A

2184

B

2172

C

2196

D

2148

4
JEE Main 2025 (Online) 28th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the coefficients of three consecutive terms $T_r$, $T_{r+1}$ and $T_{r+2}$ in the binomial expansion of $(a + b)^{12}$ be in a G.P. and let $p$ be the number of all possible values of $r$. Let $q$ be the sum of all rational terms in the binomial expansion of $(\sqrt[4]{3}+\sqrt[3]{4})^{12}$. Then $p + q$ is equal to:

A

295

B

283

C

299

D

287

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