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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 26 August 2021, Shift 2, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

A hall has a square floor of dimension 10 m×10 m10\ \mathrm{m}\times10\ \mathrm{m} (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is cos⁡−115\cos^{-1}\frac{1}{5}, then the height of the hall (in meters) is :

The figure, in words

A cuboid drawn in perspective with vertices labelled E, F, H, G (top face), A, B, D, C (bottom face); diagonals AG and BH drawn, meeting at point P with the angle GPH marked by an arc; bottom edges DC and CB labelled 10 m each.
  1. (1)525\sqrt{2}Official answer
  2. (2)535\sqrt{3}
  3. (3)55
  4. (4)2102\sqrt{10}

Official answer

Option 1

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Angle Between Lines
Idea tested
Angle via Direction Ratios

Same topic in other shifts

All Angle Between Lines questions
  1. 6 Apr 2026, Shift 1 · Q16Let a line L be perpendicular to both the lines L1:x+13=y+35=z+57\mathrm{L}_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7} and…MediumSingle correct
  2. 11 Apr 2023, Shift 2 · Q28Let the line l:x=1−y−2=z−3λl : x = \frac{1-y}{-2} = \frac{z-3}{\lambda}, λ∈R\lambda \in \mathbb{R} meet the plane P:x+2y+3z=4P : x + 2y + 3z = 4 at the point…HardNumerical value
  3. 26 Jun 2022, Shift 1 · Q14If the two lines l1:x−23=y+1−2,z=2l_1 : \frac{x-2}{3} = \frac{y+1}{-2}, z = 2 and l2:x−11=2y+3α=z+52l_2 : \frac{x-1}{1} = \frac{2y+3}{\alpha} = \frac{z+5}{2} are…MediumSingle correct
  4. 27 Jun 2022, Shift 1 · Q14If two straight lines whose direction cosines are given by the relations l+m−n=0l+m-n=0, 3l2+m2+cnl=03l^2+m^2+cnl=0 are parallel, then the positive value…MediumSingle correct
  5. 3 Aug 2021, Shift 2 · Q76Let L1L_1 and L2L_2 be two lines passing through the points P(b−c,c−a,a−b)P(b-c, c-a, a-b) and Q(1l,1m,1n)Q\left(\frac{1}{l}, \frac{1}{m}, \frac{1}{n}\right)…HardSingle correct
  6. 4 Aug 2021, Shift 1 · Q87Maximum number of lines, through the origin which make equal angles with the three coordinate axes in XYZ-space, is ________.EasyNumerical 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. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.