JEE Main 2017 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2017 (offline), Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30.

The value of

(^{21}C_1-{}^{10}C_1)+(^{21}C_2-{}^{10}C_2)+(^{21}C_3-{}^{10}C_3)+(^{21}C_4-{}^{10}C_4)+\ldots+(^{21}C_{10}-{}^{10}C_{10})

is :

(1) $2^{21}-2^{10}$
(2) $2^{20}-2^{9}$
(3) $2^{20}-2^{10}$ Official answer
(4) $2^{21}-2^{11}$

Official answer

Option 3

CBSE answer key (25/04/2017, used for result).

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Sum of all Coefficients

Same idea in other shifts

Asked 3× in all

31 Jan 2024, Shift 2 · Q23Let the coefficient of $x^r$ in the expansion of $(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1}$ be $\alpha_r$ . If…HardNumerical value
11 Apr 2023, Shift 1 · Q21The mean of the coefficients of $x, x^2, \ldots, x^7$ in the binomial expansion of $(2+x)^9$ is ______________.MediumNumerical value

Question text from the official JEE Main paper published by NTA (CBSE ran the 2017 exam); 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.