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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 28 July 2022, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

A plane P is parallel to two lines whose direction ratios are −2, 1, −3-2,\ 1,\ -3 and −1, 2, −2-1,\ 2,\ -2 and it contains the point (2, 2, −2)(2,\ 2,\ -2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts α, β, γ\alpha,\ \beta,\ \gamma. If V is the volume of the tetrahedron OABC, where O is the origin, and p=α+β+γp=\alpha+\beta+\gamma, then the ordered pair (V, p) is equal to :
  1. (1)(48,−13)(48,-13)
  2. (2)(24,−13)(24,-13)Official answer
  3. (3)(48,11)(48,11)
  4. (4)(24,−5)(24,-5)

Official answer

Option 2

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Planes in 3D
Idea tested
Plane Through Point Parallel to Two Vectors

Same idea in other shifts

Asked 2× in all
  1. 25 Jun 2022, Shift 1 · Q28Let the lines L1\mathrm{L_1} : r⃗=λ(i^+2j^+3k^)\vec{r}=\lambda\left(\hat{i}+2\hat{j}+3\hat{k}\right), λ∈R\lambda\in\mathbf{R} L2\mathrm{L_2} :…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 108 of the 174 JEE Main shifts held from 2017 to 2026.