JEE Main 2025 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

The sum of the series

2\times1\times{}^{20}C_4-3\times2\times{}^{20}C_5+4\times3\times{}^{20}C_6-5\times4\times{}^{20}C_7+\ldots+18\times17\times{}^{20}C_{20}

, is equal to ________.

Official answer

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Falling Factorial Polynomial Split

Same topic in other shifts

All Binomial Coefficients questions

2 Apr 2026, Shift 1 · Q7The number of elements in the set…MediumSingle correct
2 Apr 2026, Shift 2 · Q6If for $3 \le r \le 30$ , $\binom{30}{C_{30-r}} + 3\binom{30}{C_{31-r}} + 3\binom{30}{C_{32-r}} + \binom{30}{C_{33-r}} = ^m C_r$ , then $m$ …MediumSingle correct
4 Apr 2026, Shift 1 · Q9Let the smallest value of $k\in\mathbb{N}$ , for which the coefficient of $x^3$ in…MediumSingle correct
5 Apr 2026, Shift 1 · Q23If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3} - x^4\right)^n$ , $x \neq 0$ , is zero, then…MediumNumerical value
6 Apr 2026, Shift 1 · Q8If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}$ , $\alpha\neq 0$ , are…EasySingle correct
8 Apr 2026, Shift 2 · Q8If…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.