JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 September 2020, Shift 2, Maths Q67

Question 67 of 75 in this shift, Maths question 17 of 25.

A plane passing through the point

(3,\,1,\,1)

contains two lines whose direction ratios are

1,\,-2,\,2

and

2,\,3,\,-1

respectively. If this plane also passes through the point

(\alpha,\,-3,\,5)

, then

\alpha

is equal to :

(1) $10$
(2) $-5$
(3) $5$ Official answer
(4) $-10$

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Containing Two Lines

Same idea in other shifts

Asked 4× in all

26 Jul 2022, Shift 2 · Q22The largest value of $a$ , for which the perpendicular distance of the plane containing the lines…HardNumerical value
26 Jun 2022, Shift 2 · Q15If the lines $\vec{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{j} - \hat{k})$ and…MediumSingle correct
3 Sep 2020, Shift 2 · Q75Let a plane P contain two lines $\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$ , $\lambda \in \mathbf{R}$ and…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.