JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let

\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 coefficients of the remaining terms in the expansion is 649 and the coefficient of

x^{-n}

\lambda\alpha

, then

\lambda

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
28 Jul 2022, Shift 2 · Q84If $1+(2+{}^{49}C_1+{}^{49}C_2+...+{}^{49}C_{49})({}^{50}C_2+{}^{50}C_4+...+{}^{50}C_{50})$ is equal to $2^n\cdot m$ , where m is odd, then…MediumNumerical 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.