Learn

Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 January 2020, Shift 2, Maths Q56

Question 56 of 75 in this shift, Maths question 6 of 25, Section A.

If α\alpha and β\beta be the coefficients of x4x^4 and x2x^2 respectively in the expansion of (x+x2−1)6+(x−x2−1)6\left(x + \sqrt{x^2 - 1}\right)^6 + \left(x - \sqrt{x^2 - 1}\right)^6, then :
  1. (1)α+β=60\alpha + \beta = 60
  2. (2)α−β=−132\alpha - \beta = -132Official answer
  3. (3)α+β=−30\alpha + \beta = -30
  4. (4)α−β=60\alpha - \beta = 60

Official answer

Option 2

NTA final key (Jan 2020).

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
Difference of Binomial Expansions

Same topic in other shifts

All Binomial Coefficients questions
  1. 2 Apr 2026, Shift 1 · Q7The number of elements in the set…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q6If for 3≤r≤303 \le r \le 30, (30C30−r)+3(30C31−r)+3(30C32−r)+(30C33−r)=mCr\binom{30}{C_{30-r}} + 3\binom{30}{C_{31-r}} + 3\binom{30}{C_{32-r}} + \binom{30}{C_{33-r}} = ^m C_r, then mm…MediumSingle correct
  3. 4 Apr 2026, Shift 1 · Q9Let the smallest value of k∈Nk\in\mathbb{N}, for which the coefficient of x3x^3 in…MediumSingle correct
  4. 5 Apr 2026, Shift 1 · Q23If the sum of the coefficients of x7x^7 and x14x^{14} in the expansion of (1x3−x4)n\left(\frac{1}{x^3} - x^4\right)^n, x≠0x \neq 0, is zero, then…MediumNumerical value
  5. 6 Apr 2026, Shift 1 · Q8If the coefficients of the middle terms in the binomial expansions of (1+αx)26(1+\alpha x)^{26} and (1−αx)28(1-\alpha x)^{28}, α≠0\alpha\neq 0, are…EasySingle correct
  6. 8 Apr 2026, Shift 2 · Q8If…HardSingle 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.