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Day 498: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 13 Apr 2026 S2

    96
    If a line makes angles α,β,γ\alpha, \beta, \gamma with the coordinate axes, then the sum of values of sin⁡2α+sin⁡2β+sin⁡2γ\sin^2\alpha + \sin^2\beta + \sin^2\gamma and cos⁡2α+cos⁡2β+cos⁡2γ\cos 2\alpha + \cos 2\beta + \cos 2\gamma is ...

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  2. Question 2

    Probability Distribution. Asked once: 11 May 2024 S1

    110
    Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals

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  3. Question 3

    Straight Line. Asked once: 9 May 2023 S2

    136
    A line 4x+y=14x+y=1 passes through the point A(2,-7) meets the line BC whose equation is 3x−4y+1=03x-4y+1=0 at the point B. The equation of the line AC so that AB=AC is

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  4. Question 4

    Trigonometric Functions. Asked once: 15 Apr 2026 S2

    70
    The value of tan⁡−1(cos⁡(19π4)−1sin⁡(π4))\tan^{-1}\left(\dfrac{\cos\left(\frac{19\pi}{4}\right) - 1}{\sin\left(\frac{\pi}{4}\right)}\right) is equal to

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  5. Question 5

    Trigonometry - II. Asked once: 12 May 2024 S1

    129
    If tan⁡θ=sin⁡α−cos⁡αsin⁡α+cos⁡α\tan\theta=\frac{\sin\alpha-\cos\alpha}{\sin\alpha+\cos\alpha}, 0≤α≤π20\leq\alpha\leq\frac{\pi}{2}, then the value of cos⁡2θ\cos2\theta is

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