If ${}^{2n}C_3 : {}^{n}C_3 = 10:1$, then the ratio $(n^2+3n):(n^2-3n+4)$ is

JEE Main 2023 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 6 April 2023, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

{}^{2n}C_3 : {}^{n}C_3 = 10:1

, then the ratio

(n^2+3n):(n^2-3n+4)

(1) $27:11$
(2) $35:16$
(3) $2:1$ Official answer
(4) $65:37$

Official answer

Option 3

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Basic nCr Properties

Same idea in other shifts

Asked 2× in all

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

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.