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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 August 2021, Shift 1, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

Equation of a plane at a distance 221\sqrt{\frac{2}{21}} from the origin, which contains the line of intersection of the planes x−y−z−1=0x-y-z-1=0 and 2x+y−3z+4=02x+y-3z+4=0, is :
  1. (1)3x−4z+3=03x-4z+3=0
  2. (2)−x+2y+2z−3=0-x+2y+2z-3=0
  3. (3)3x−y−5z+2=03x-y-5z+2=0
  4. (4)4x−y−5z+2=04x-y-5z+2=0Official answer

Official answer

Option 4

NTA final key.

Idea tested
Family of Planes

Same idea in other shifts

Asked 15× in all
  1. 6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes 2x−y+z=32x-y+z=3, 4x−3y+5z+9=04x-3y+5z+9=0 and parallel to the line…MediumSingle correct
  2. 6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane r⃗⋅(i^+j^+k^)=6\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6 and…MediumSingle correct
  3. 13 Apr 2023, Shift 1 · Q8Let the equation of plane passing through the line of intersection of the planes x+2y+az=2x+2y+az=2 and x−y+z=3x-y+z=3 be 5x−11y+bz=6a−15x-11y+bz=6a-1. For…MediumSingle correct
  4. 26 Jul 2022, Shift 2 · Q27The plane passing through the line L:lx−y+3(1−l)z=1, x+2y−z=2L: lx-y+3(1-l)z=1,\ x+2y-z=2 and perpendicular to the plane 3x+2y+z=63x+2y+z=6 is 3x−8y+7z=43x-8y+7z=4. If θ\theta…HardNumerical value
  5. 27 Jul 2022, Shift 1 · Q17If the plane PP passes through the intersection of two mutually perpendicular planes 2x+ky−5z=12x + ky - 5z = 1 and 3kx−ky+z=53kx - ky + z = 5, k<3k < 3…MediumSingle correct
  6. 28 Jun 2022, Shift 1 · Q16The acute angle between the planes P1_1 and P2_2, when P1_1 and P2_2 are the planes passing through the intersection of the planes…MediumSingle correct
  7. 28 Jun 2022, Shift 1 · Q17Let the plane P:r⃗⋅a⃗=dP:\vec{r}\cdot\vec{a}=d contain the line of intersection of two planes…HardSingle correct
  8. 26 Aug 2021, Shift 1 · Q75A plane P contains the line x+2y+3z+1=0=x−y−z−6x+2y+3z+1=0=x-y-z-6, and is perpendicular to the plane −2x+y+z+8=0-2x+y+z+8=0. Then which of the following points…MediumSingle 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.