MathsJEE Main 24 Jan 2026, Shift 1·Q14·MCQ·Moderate

Binomial Theorem · Sum of binomial coefficients

Let

S = \dfrac{1}{25!} + \dfrac{1}{3!\,23!} + \dfrac{1}{5!\,21!} + \ldots

up to 13 terms. If

13S = \dfrac{2^k}{n!}

,

k \in \mathbb{N}

, then

n + k

is equal to

(1)51
(2)52
(3)49
(4)50

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.

See the full 24 Jan 2026, Shift 1 paper

More on Sum of binomial coefficients

23 Jan 2026, Shift 1 · Q12The value of 100C5051 + 100C5152 + + 100C100101 is:
28 Jan 2026, Shift 2 · Q2The sum of the coefficients of x499 and x500 in [(1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + + x1000] is
4 Apr 2026, Shift 1 · Q9Let the smallest value of k N, for which the coefficient of x3 in (1 + x)3 + (1 + x)4 + (1 + x)5 + + (1 + x)99 + (1 + kx)100, x 0, is (43n…