PYQ Vault

Circle

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 5 times: 2 May 2023 S2, 9 May 2024 S1, 25 Apr 2025 S1, 26 Apr 2025 S2, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 5 of this type

    56
    Let PA and PB be the tangent segments drawn from point P(6,8)P(6, 8) to the circle with the centre at origin O. The radius of circle for which the area of quadrilateral PAOB is maximum, is...

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  2. Question 2

    This type asked 5 times: 3 May 2023 S1, 4 May 2023 S2, 9 May 2023 S2, 16 May 2023 S1, 13 Apr 2026 S2. This one: 13 Apr 2026 S2 See all 5 of this type

    59
    The equation of the circle concentric with circle x2+y2−6x+7=0x^2 + y^2 - 6x + 7 = 0 and which touches the line x+y+3=0x + y + 3 = 0 is ....

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  3. Question 3

    This type asked 4 times: 21 Apr 2025 S1, 26 Apr 2025 S1, 12 May 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 4 of this type

    59
    The coordinates of the point on the curve x2+y2=8x^2 + y^2 = 8 which are nearest to the point (2,0)(2, 0) are:

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  4. Question 4

    This type asked 4 times: 3 May 2023 S2, 19 Apr 2025 S2, 18 Apr 2026 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 4 of this type

    63
    If the tangent to the circle x2+y2=5x^2 + y^2 = 5 at point (1,−2)(1, -2) also touches the circle x2+y2−8x+6y+k=0x^2 + y^2 - 8x + 6y + k = 0, then k5=⋯⋯⋯\dfrac{k}{5} = \cdots\cdots\cdots

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  5. Question 5

    This type asked 4 times: 11 May 2023 S2, 10 May 2024 S2, 12 May 2026 S1, 13 May 2026 S1. This one: 13 May 2026 S1 See all 4 of this type

    60
    The Cartesian coordinates of a point P with parameter θ=5π6\theta = \dfrac{5\pi}{6} on the circle x2+y2−2x+4y+1=0x^2 + y^2 - 2x + 4y + 1 = 0 are...

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  6. Question 6

    This type asked 4 times: May 2021 S1, 15 May 2023 S1, 11 May 2024 S1, 19 Apr 2025 S1. This one: 19 Apr 2025 S1 See all 4 of this type

    120
    The number of common tangents that can be drawn to the circles x2+y2−6x=0x^{2}+y^{2}- 6x= 0 and x2+y2+6x+2y+1=0x^{2}+y^{2}+ 6x+ 2y+ 1 = 0 is .

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  7. Question 7

    Asked 3 times: 11 May 2023 S2*, 10 May 2024 S2*, 12 May 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    61
    The standard parametric equations of the circle x2+y2−4x−6y−12=0x^2 + y^2 - 4x - 6y - 12 = 0 are ...

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  8. Question 8

    Asked 3 times: 11 Apr 2026 S1, 17 Apr 2026 S1, 20 Apr 2026 S1 See all 3 times it was asked

    60
    The equation of the circle which passes through the points (2,3)(2, 3) and (4,5)(4, 5) and whose centre lies on a straight line 4x−y−3=04x - y - 3 = 0, is

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  9. Question 9

    Asked 3 times: 2 May 2023 S2*, 9 May 2024 S1, 26 Apr 2025 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    130
    Two tangents to the circle x2+y2=4x^{2}+y^{2}= 4 at the points A and B meet at P(−4,0)P( - 4,0). Then the area of quadrilateral PAOB, where ' O ' is the origin is

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  10. Question 10

    This type asked 3 times: 21 Apr 2025 S2, 15 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 3 of this type

    60
    The angle between the tangents drawn from the point (1,1)(1, 1) to the circle 2x2+2y2−8x+4y+5=02x^2 + 2y^2 - 8x + 4y + 5 = 0 is …\ldots

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