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Day 126: MHT-CET Maths

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

  1. Question 1

    Measures of Dispersion. Asked 2 times: 11 May 2024 S2, 14 May 2024 S2 See all 2 times it was asked

    149
    If both mean and variance of 50 observations x1,x2,…,x50x_1, x_2, \ldots, x_{50} are equal to 16 and 256 respectively, then mean of (x1−5)2,(x2−5)2,…,(x50−5)2(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2 is

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  2. Question 2

    Probability Distribution. Asked 2 times: 12 May 2024 S1, 14 May 2024 S2 See all 2 times it was asked

    128
    The p.m.f. of a random variable X is P(x)=2xn(n+1),  x=1,2,…,nP(x) = \frac{2x}{n(n+1)},\; x=1,2,\ldots,n, then E(x)E(x) is

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  3. Question 3

    Straight Line. Asked 2 times: 11 May 2023 S1*, 14 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    143
    Let P(−3,0),Q(0,0)P(-3,0), Q(0,0) and R(3,33)R(3,3\sqrt{3}) be three points. Then the equation of the bisector of the angle PQR is

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  4. Question 4

    Trigonometric Functions. Asked 2 times: 9 May 2024 S1, 14 May 2024 S2 See all 2 times it was asked

    119
    If cos⁡−1x−cos⁡−1y3=α\cos^{-1}x - \cos^{-1}\frac{y}{3} = \alpha, where −1≤x≤1-1\leq x\leq1, −3≤y≤3-3\leq y\leq3, x≤y3x\leq\frac{y}{3}, then for all x,yx,y: 9x2−6xycos⁡α+y29x^2 - 6xy\cos\alpha + y^2 is equal to

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  5. Question 5

    Vectors. Asked 2 times: May 2022 S1*, 14 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    120
    Let a⃗=i^+2j^−k^\vec{a} = \hat{i}+2\hat{j}-\hat{k} and b⃗=i^+j^−k^\vec{b} = \hat{i}+\hat{j}-\hat{k}. If c⃗\vec{c} satisfies b⃗×c⃗=b⃗×a⃗\vec{b}\times\vec{c} = \vec{b}\times\vec{a} and c⃗⋅a⃗=0\vec{c}\cdot\vec{a} = 0, then c⃗⋅b⃗\vec{c}\cdot\vec{b} is

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