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Day 105: MHT-CET Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Line and Plane. Asked 2 times: 17 Apr 2026 S2*, 19 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    94
    From a point P (a,b,c)(a, b, c), perpendiculars PA and PB are drawn to XY plane and ZX plane respectively. If O is the origin, then the equation of plane OAB is

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  2. Question 2

    Permutations and Combinations. Asked 2 times: 19 Apr 2025 S1*, 19 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    53
    Four men and three women are to be arranged at a round table. The number of arrangements in which no two women are together is ....

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  3. Question 3

    Permutations and Combinations. Asked 2 times: 17 Apr 2026 S2*, 18 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    52
    In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is …\ldots

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  4. Question 4

    Circle. Asked 2 times: 22 Apr 2025 S1*, 18 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    56
    The area of the region (in sq. unit) bounded by x-axis, the tangent and normal to the circle x2+y2=4x^2 + y^2 = 4, drawn at a point (1,3)(1, \sqrt{3}) is

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  5. Question 5

    Differentiation. Asked 2 times: 10 May 2024 S2*, 18 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    69
    If y=tan⁡−1(log⁡(ex3)log⁡ex3)+tan⁡−1(log⁡(e4x3)log⁡(ex12)),x∈(e−13,e112)y = \tan^{-1}\left(\dfrac{\log\left(\frac{e}{x^3}\right)}{\log ex^3}\right) + \tan^{-1}\left(\dfrac{\log(e^4x^3)}{\log\left(\frac{e}{x^{12}}\right)}\right), x \in \left(e^{-\frac{1}{3}}, e^{\frac{1}{12}}\right) then dydx\dfrac{dy}{dx} is equal to...

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