The sum of the coefficients of the first terms in the binomial expansion of is equal to:

Explanation: Solution: Binomial expansion mein coefficients ka sum nikalne ke liye hum property ka prayog karte hain: Yahan hai aur humein pehle terms ka sum chahiye, yani se tak: Formula mein values rakhne par ( ): Sahi Answer: (4)

How do I solve JEE 2023 Mathematics questions?

Practice JEE 2023 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

What is the difficulty level of JEE Mathematics questions?

JEE Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Are JEE previous year papers available for free?

Yes. Mathem Solvex provides free access to JEE previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The sum of the coefficients of the first $50$ terms in the binomial expansion of $(1 - x)^{100}$ is equal to:

Choose the correct answer:

Explanation

Solution:

Binomial expansion $(1-x)^n = \sum_{r=0}^{n} (-1)^r {^nC_r} x^r$ mein coefficients ka sum nikalne ke liye hum property ka prayog karte hain:

\sum_{r=0}^{k} (-1)^r {^nC_r} = (-1)^k {^{n-1}C_k}

Yahan $n = 100$ hai aur humein pehle $50$ terms ka sum chahiye, yani $r = 0$ se $r = 49$ tak:

S = \sum_{r=0}^{49} (-1)^r {^{100}C_r}

Formula mein values rakhne par ( $k = 49$ ):

S = (-1)^{49} {^{100-1}C_{49}} = -{^{99}C_{49}}

Sahi Answer: (4) $-{^{99}C_{49}}$