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Friday, 16 October

JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2026, Shift 1, Maths Q3

Question 3 of 75 in this shift, Maths question 3 of 25, Section A.

Let e1e_1 and e2e_2 be two distinct roots of the equation x2−ax+2=0x^2-ax+2=0. Let the sets {a∈R:e1\{a\in\mathbb{R}: e_1 and e2e_2 are the eccentricities of hyperbolas}=(α,β)\}=(\alpha,\beta), and {a∈R:e1\{a\in\mathbb{R}: e_1 and e2e_2 are the eccentricities of an ellipse and a hyperbola, respectively}=(γ,∞)\}=(\gamma,\infty). Then α2+β2+γ2\alpha^2+\beta^2+\gamma^2 is equal to:
  1. (1)18
  2. (2)22
  3. (3)26Official answer
  4. (4)34

Official answer

Option 3

NTA final key.

Chapter
Conic Sections
Topic
Location of Roots
Idea tested
Both roots greater than k

Same topic in other shifts

All Location of Roots questions
  1. 4 Apr 2026, Shift 2 · Q5If the quadratic equation (λ+2)x2−3λx+4λ=0(\lambda+2)x^2-3\lambda x+4\lambda=0, λ≠−2\lambda\neq-2, has two positive roots, then the number of possible…MediumSingle correct
  2. 6 Apr 2026, Shift 2 · Q16Let lim⁡x→2(tan⁡(x−2))(rx2+(p−2)x−2p)(x−2)2=5\lim_{x\to2}\frac{(\tan(x-2))\left(rx^2+(p-2)x-2p\right)}{(x-2)^2}=5 for some r,p∈Rr, p\in\mathbf{R}. If the set of all possible values…HardSingle correct
  3. 2 Apr 2025, Shift 2 · Q21If the set of all a∈R−{1}a \in \mathbf{R} - \{1\}, for which the roots of the equation (1−a)x2+2(a−3)x+9=0(1-a)x^2 + 2(a-3)x + 9 = 0 are positive is…MediumNumerical value
  4. 7 Apr 2025, Shift 1 · Q3Let the set of all values of p∈Rp \in \mathbb{R}, for which both the roots of the equation x2−(p+2)x+(2p+9)=0x^2 - (p+2)x + (2p+9) = 0 are negative real…EasySingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.