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Line and Plane

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 13 times: 10 May 2023 S1, 10 May 2023 S2, 11 May 2023 S1, 15 May 2023 S2, 11 May 2024 S2, 14 May 2024 S2, 23 Apr 2025 S1, 11 Apr 2026 S1, 11 Apr 2026 S2, 15 Apr 2026 S2, 17 Apr 2026 S1, 12 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 13 of this type

    94
    If the lines x−11=y−12=z−13\dfrac{x - 1}{1} = \dfrac{y - 1}{2} = \dfrac{z - 1}{3} and x−31=y−k2=z−51\dfrac{x - 3}{1} = \dfrac{y - k}{2} = \dfrac{z - 5}{1} are intersect at the point PP, then the distance (in units) of the point PP from the origin O(0,0,0)O(0, 0, 0) is ...

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  2. Question 2

    This type asked 10 times: 2 May 2023 S1, 3 May 2023 S1, 9 May 2023 S1, 9 May 2023 S2, 10 May 2023 S1, 10 May 2024 S1, 22 Apr 2025 S1, 25 Apr 2025 S2, 12 May 2026 S2, 13 May 2026 S1. This one: 13 May 2026 S1 See all 10 of this type

    93
    Let the line x−23=y−1−5=z+22\dfrac{x - 2}{3} = \dfrac{y - 1}{-5} = \dfrac{z + 2}{2} lie in the plane x+3y−αz+β=0x + 3y - \alpha z + \beta = 0. Then (α,β)(\alpha, \beta) equals

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  3. Question 3

    This type asked 9 times: 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 19 Apr 2025 S2, 20 Apr 2025 S2, 26 Apr 2025 S2, 13 Apr 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 9 of this type

    96
    The equation of a plane passing through the intersection of two planes r⃗⋅(i^−2j^+3k^)=4\vec{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 4 and r⃗⋅(2i^+j^−3k^)=7\vec{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = 7 and parallel to Y-axis is

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  4. Question 4

    This type asked 8 times: 9 May 2023 S1, 9 May 2024 S1, 12 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S1, 17 Apr 2026 S2, 12 May 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 8 of this type

    96
    The distance of the point (1,1,1)(1, 1, 1) from the line passing through the point (2,3,4)(2, 3, 4) whose direction ratios are 2,−3,62, -3, 6 is:

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  5. Question 5

    This type asked 8 times: 10 May 2023 S2, 9 May 2024 S2, 12 May 2024 S2, 21 Apr 2025 S1, 13 Apr 2026 S1, 19 Apr 2026 S1, 19 Apr 2026 S2, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 8 of this type

    94
    The shortest distance between the lines x−33=y−8−1=z−31\dfrac{x - 3}{3} = \dfrac{y - 8}{-1} = \dfrac{z - 3}{1} and x+3−3=y+72=z−64\dfrac{x + 3}{-3} = \dfrac{y + 7}{2} = \dfrac{z - 6}{4} is

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  6. Question 6

    This type asked 8 times: May 2022 S1, 9 May 2023 S2, 9 May 2024 S2, 12 May 2024 S2, 14 May 2024 S2, 20 Apr 2025 S1, 21 Apr 2025 S1, 21 Apr 2025 S2. This one: 21 Apr 2025 S2 See all 8 of this type

    112
    The direction ratios of the line of intersection of the planes x−y+z−5=0x-y+z- 5 = 0 and x−3y−6=0x- 3y- 6 = 0, are

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  7. Question 7

    Asked 7 times: 10 May 2023 S1*, 10 May 2023 S2*, 15 May 2023 S2*, 11 May 2024 S2*, 14 May 2024 S2*, 23 Apr 2025 S1*, 11 Apr 2026 S1 (* = numbers or wording changed that year) See all 7 times it was asked

    94
    If the lines x−12=y+13=z−14\dfrac{x - 1}{2} = \dfrac{y + 1}{3} = \dfrac{z - 1}{4} and x−21=y+m2=z−21\dfrac{x - 2}{1} = \dfrac{y + m}{2} = \dfrac{z - 2}{1} intersect each other, then the value of mm is....

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  8. Question 8

    This type asked 7 times: 4 May 2023 S1, 16 May 2023 S2, 13 May 2024 S2, 17 Apr 2026 S2, 13 May 2026 S1, 13 May 2026 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 7 of this type

    95
    The coordinates of the foot of the perpendicular drawn from the point P(−1,3,2)P(-1, 3, 2) to the line formed by the intersection of the planes x+y+z=1x + y + z = 1 and 2x−y+z=22x - y + z = 2 are:

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  9. Question 9

    This type asked 7 times: 10 May 2024 S2, 11 May 2024 S1, 20 Apr 2025 S2, 23 Apr 2025 S1, 11 Apr 2026 S2, 18 Apr 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 7 of this type

    92
    The equation of the line passing through the point of intersection of the lines x−31=y−52=z−1−1\dfrac{x - 3}{1} = \dfrac{y - 5}{2} = \dfrac{z - 1}{-1} & x−42=y−2−1=z−42\dfrac{x - 4}{2} = \dfrac{y - 2}{-1} = \dfrac{z - 4}{2} and in the direction of i^−2j^+k^\hat{i} - 2\hat{j} + \hat{k} is

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  10. Question 10

    This type asked 7 times: 4 May 2023 S2, 11 May 2023 S1, 10 May 2024 S2, 25 Apr 2025 S1, 11 Apr 2026 S1, 16 Apr 2026 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 7 of this type

    95
    The distance of the point 2i^+j^−k^2\hat{i} + \hat{j} - \hat{k} from the plane rˉ⋅(i^−2j^+4k^)=9\bar{r}\cdot(\hat{i} - 2\hat{j} + 4\hat{k}) = 9, is

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