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Day 76: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked 3 times: 9 May 2023 S1*, 11 May 2023 S2*, 10 May 2024 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    138
    Number of solutions of tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2\cos x in [0,2π][0,2\pi]

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  2. Question 2

    Vectors. Asked 3 times: May 2022 S1*, 15 May 2023 S1*, 10 May 2024 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    135
    If a⃗=i^+2j^+k^\vec{a}=\hat{i}+2\hat{j}+\hat{k}, b⃗=i^−j^+k^\vec{b}=\hat{i}-\hat{j}+\hat{k} and c⃗=i^+j^−k^\vec{c}=\hat{i}+\hat{j}-\hat{k}, then a vector in the plane of a⃗\vec{a} and b⃗\vec{b}, whose projection on c⃗\vec{c} is 13\frac{1}{\sqrt{3}}, is

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  3. Question 3

    Line and Plane. Asked 3 times: 4 May 2023 S2*, 10 May 2023 S2, 16 May 2023 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    139
    The equation of plane through the point (2,−1,−3)(2,-1,-3) and parallel to lines x−13=y+22=z−4\frac{x-1}{3} = \frac{y+2}{2} = \frac{z}{-4} and x2=y−1−3=z−22\frac{x}{2} = \frac{y-1}{-3} = \frac{z-2}{2} is

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  4. Question 4

    Measures of Dispersion. Asked 3 times: 4 May 2023 S2*, 10 May 2023 S2*, 16 May 2023 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    118
    The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14, then the product of remaining two observations is

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  5. Question 5

    Vectors. Asked 3 times: 2 May 2023 S1, 10 May 2023 S2*, 16 May 2023 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    131
    If a⃗=2i^+2j^+3k^\vec{a} = 2\hat{i}+2\hat{j}+3\hat{k}, b⃗=−i^+2j^+k^\vec{b} = -\hat{i}+2\hat{j}+\hat{k} and c⃗=3i^+j^\vec{c} = 3\hat{i}+\hat{j} are vectors such that a⃗+λb⃗\vec{a}+\lambda\vec{b} is perpendicular to c⃗\vec{c}, then value of λ\lambda is

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