JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 28 July 2022, Shift 2, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

1+(2+{}^{49}C_1+{}^{49}C_2+...+{}^{49}C_{49})({}^{50}C_2+{}^{50}C_4+...+{}^{50}C_{50})

is equal to

2^n\cdot m

, where m is odd, then n + m is equal to _______.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 6× in all

27 Jan 2024, Shift 1 · Q6If A denotes the sum of all the coefficients in the expansion of $(1-3x+10x^2)^n$ and B denotes the sum of all the coefficients in the…EasySingle correct
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
13 Apr 2023, Shift 1 · Q23Let $\alpha$ be the constant term in the binomial expansion of $\left(\sqrt{x}-\frac{6}{x^{3/2}}\right)^n$ , $n\leq15$ . If the sum of the…HardNumerical value
2 Apr 2017 (offline) · Q67The value of $(^{21}C_1-{}^{10}C_1)+(^{21}C_2-{}^{10}C_2)+(^{21}C_3-{}^{10}C_3)+(^{21}C_4-{}^{10}C_4)+\ldots+(^{21}C_{10}-{}^{10}C_{10})$ …MediumSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.