Binomial Theorem

JEE Main 2025 (Online) 24th January Evening ShiftMCQMedium📈 Topic in 21% papers+4−1

Ques. 1JEE Main 2025, 24 January (Evening Shift)

Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)2n-1. If 2A=5B, then n is equal to:

Answer

(4) 21

Solution

N=2n-1, T30= N29x29, T12= N11x11, so 2 N29=5 N11.

Use N29= NN-29. Take N=41: 4129= 4112

4112 4111= 41-1112= 3012= 52 ✓

The ratio N29 N11 increases with N, so N=41 is the only value.

2n-1=41 n=21

Answer: (4)

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Ques. 2JEE Main 2025, 23 January (Morning Shift)

The sum of all rational terms in the expansion of (1+21/3+31/2 )6 is equal to .

Ques. 3JEE Main 2025, 23 January (Evening Shift)

If in the expansion of (1+x)p(1-x)q, the coefficients of x and x2 are 1 and -2, respectively, then p2+q2 is equal to :

Ques. 4JEE Main 2025, 22 January (Morning Shift)

If r=05 11C2r+12r+2= mn, (m,n)=1, then m-n is equal to .

Ques. 5JEE Main 2025, 22 January (Evening Shift)

Let , , and be the coefficients of x7,x5,x3 and x respectively in the expansion of (x+ x3-1 )5+ (x- x3-1 )5, x>1. If u and v satisfy the equations u+ v=18, u+ v=20, then u+v equals :

Ques. 6JEE Main 2025, 22 January (Evening Shift)

If r=130 r2 (30Cr )230Cr-1= 229, then is equal to .

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