JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 26 August 2021, Shift 1, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

^{20}C_r

is the co-efficient of

x^r

in the expansion of

(1+x)^{20}

, then the value of

\sum_{r=0}^{20} r^2\,{}^{20}C_r

is equal to :

(1) $420 \times 2^{19}$
(2) $380 \times 2^{19}$
(3) $380 \times 2^{18}$
(4) $420 \times 2^{18}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Second Derivative Method for Sums

Same idea in other shifts

Asked 3× in all

4 Apr 2025, Shift 2 · Q7If $1^2\cdot({}^{15}C_1)+2^2\cdot({}^{15}C_2)+3^2\cdot({}^{15}C_3)+\ldots+15^2\cdot({}^{15}C_{15})=2^m\cdot3^n\cdot5^k$ , where…MediumSingle correct
8 Apr 2024, Shift 1 · Q24Let $\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r$ and $\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}$ . If…HardNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.