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Day 119: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked 2 times: 12 May 2024 S1*, 25 Apr 2025 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    125
    If the lines 1−x2=7y+42λ=2z−52\frac{1 -x}{2}=\frac{7y+ 4}{2\lambda}=\frac{2z- 5}{2} and 7−7x3λ=y−17=6−z5\frac{7 - 7x}{3\lambda}=\frac{y- 1}{7}=\frac{6 -z}{5} are at right angle, then the value of λ\lambda is

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  2. Question 2

    Pair of Straight Lines. Asked 2 times: 3 May 2023 S2*, 25 Apr 2025 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    145
    The joint equation of the bisector of the angle between the lines 2x2+11xy+3y2=02x^{2}+ 11xy+ 3y^{2}= 0 is

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  3. Question 3

    Probability Distribution. Asked 2 times: 16 May 2023 S1, 25 Apr 2025 S1 See all 2 times it was asked

    146
    If a random variable XX has the following probability distribution of X
    X=xX = xP(X=x)P(X = x)
    00
    1kk
    22k2k
    32k2k
    43k3k
    5k2k^{2}
    62k22k^{2}
    77k2+k7k^{2} + k
    Then P(X≥6)=P(X\geq 6) =

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  4. Question 4

    Sets, Relations and Functions. Asked 2 times: 4 May 2023 S1*, 25 Apr 2025 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    101
    If f(x)=log⁡(1+x1−x)f(x) = \log\left( \frac{1 +x}{1 -x} \right) and g(x)=3x+x31+3x2g(x) =\frac{3x+x^{3}}{1 + 3x^{2}}, then (fog)(x)=(fog)(x) =

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  5. Question 5

    Trigonometric Functions. Asked 2 times: 9 May 2023 S1, 25 Apr 2025 S1 See all 2 times it was asked

    117
    The principal value of cos⁡−1[12(cos⁡9π10−sin⁡9π10)]\cos^{- 1}\left\lbrack \frac{1}{\sqrt{2}}\left( \cos\frac{9\pi}{10}- \sin\frac{9\pi}{10} \right) \right\rbrack is

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