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Day 77: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked 3 times: 3 May 2023 S1*, 11 May 2023 S2*, 15 May 2023 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    138
    Let P(2,1,5) be a point in space and Q be a point on the line r⃗=(i^−j^+2k^)+μ(−3i^+j^+5k^)\vec{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu(-3\hat{i}+\hat{j}+5\hat{k}). Then the value of μ\mu for which the vector PQ is parallel to the plane 3x−y+4z=13x-y+4z=1 is

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  2. Question 2

    Vectors. Asked 3 times: 2 May 2023 S1, 11 May 2023 S2, 15 May 2023 S1 See all 3 times it was asked

    145
    If the vectors a⃗=i^−j^+2k^\vec{a}=\hat{i}-\hat{j}+2\hat{k}, b⃗=2i^+4j^+k^\vec{b}=2\hat{i}+4\hat{j}+\hat{k} and c⃗=pi^+j^+qk^\vec{c}=p\hat{i}+\hat{j}+q\hat{k} are mutually orthogonal, then (p,q)(p,q) is equal to

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  3. Question 3

    Line and Plane. Asked 3 times: 3 May 2023 S1*, 9 May 2023 S1*, 9 May 2023 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    121
    The value of m such that x−41=y−21=z+m2\frac{x-4}{1} = \frac{y-2}{1} = \frac{z+m}{2} lies in the plane 2x−4y+z=72x-4y+z=7 is

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  4. Question 4

    Indefinite Integration. This type asked 3 times: 12 May 2024 S2, 20 Apr 2025 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 3 of this type

    77
    ∫dx(x+2)(x2+1)\int \dfrac{dx}{(x + 2)(x^2 + 1)} is equal to

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  5. Question 5

    Probability Distribution. This type asked 3 times: 15 May 2023 S2, 13 May 2024 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 3 of this type

    100
    Two fair dice are thrown. The probability that the sum of the scores is 77 such that the number on the second die is greater than that on the first die is ...

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