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Day 389: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. Asked once: 25 Apr 2025 S2 (same type asked 8 times) See all 8 of this type

    102
    A doctor assumes that patient has one of three diseases d1, d2 or d3. Before any test he assumes an equal probability for each disease. He carries out a test that will be positive with probability 0.7 if the patient has disease d1,0.5d1,0.5 if the patient has disease d 2 and 0.8 if the patient has disease d3. Given that the outcome of the test was positive then probability that patient has disease d2 is

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  2. Question 2

    Trigonometric Functions. Asked once: 13 Apr 2026 S1 (same type asked 8 times) See all 8 of this type

    63
    In a triangle ABC, with usual notations if s−a11=s−b12=s−c13\dfrac{s - a}{11} = \dfrac{s - b}{12} = \dfrac{s - c}{13} and λtan⁡2A2=455\lambda\tan^2\dfrac{A}{2} = 455, then λ=\lambda =

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  3. Question 3

    Line and Plane. Asked once: 10 May 2023 S2 (same type asked 8 times) See all 8 of this type

    113
    The shortest distance between lines r⃗=(i^+2j^−k^)+λ(2i^+j^−3k^)\vec{r} = (\hat{i}+2\hat{j}-\hat{k}) + \lambda(2\hat{i}+\hat{j}-3\hat{k}) and r⃗=(2i^−j^+2k^)+μ(i^−j^+k^)\vec{r} = (2\hat{i}-\hat{j}+2\hat{k}) + \mu(\hat{i}-\hat{j}+\hat{k}) is

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  4. Question 4

    Differentiation. Asked once: 2 May 2023 S2 (same type asked 8 times) See all 8 of this type

    134
    If f(x)=sin⁡−1 ⁣(2⋅3x1+9x)f(x) = \sin^{-1}\!\left(\frac{2\cdot3^x}{1+9^x}\right), then f′ ⁣(12)f'\!\left(\frac{1}{2}\right) equals

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  5. Question 5

    Trigonometric Functions. Asked once: 10 May 2023 S2 (same type asked 8 times) See all 8 of this type

    143
    If tan⁡−1(x+2)+tan⁡−1(x−2)−tan⁡−112=0\tan^{-1}(x+2)+\tan^{-1}(x-2)-\tan^{-1}\frac{1}{2}=0, then one value of x is

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