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Day 140: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked 2 times: 3 May 2023 S2, 16 May 2023 S1 See all 2 times it was asked

    129
    If the vectors AB→=3i^+4k^\overrightarrow{AB} = 3\hat{i} + 4\hat{k} and AC→=5i^−2j^+4k^\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k} are the sides of the triangle ABC, then the length of the median, through A, is

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  2. Question 2

    Indefinite Integration. Asked 2 times: 4 May 2023 S1, 15 May 2023 S2 See all 2 times it was asked

    119
    ∫(1+x−1x)ex+1x dx\int\left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}\,dx is equal to

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  3. Question 3

    Limits. Asked 2 times: 11 May 2023 S1*, 15 May 2023 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    146
    lim⁡x→23x+33−x−1233−x−3x/2=\lim_{x\to 2}\frac{3^x+3^{3-x}-12}{3^{3-x}-3^{x/2}} =

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  4. Question 4

    Trigonometric Functions. Asked 2 times: 3 May 2023 S2, 15 May 2023 S2 See all 2 times it was asked

    138
    If 0<x<10 < x < 1, then 1+x2[{xcos⁡(cot⁡−1x)+sin⁡(cot⁡−1x)}2−1]1/2\sqrt{1+x^{2}}\left[\left\{x\cos\left(\cot^{-1}x\right)+\sin\left(\cot^{-1}x\right)\right\}^{2}-1\right]^{1/2} is equal to

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  5. Question 5

    Binomial Distribution. Asked 2 times: 4 May 2023 S1, 15 May 2023 S1 See all 2 times it was asked

    129
    A multiple-choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

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