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Day 508: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 26 Apr 2025 S1

    145
    The number of positive integral solutions of tan⁡−1x+cos⁡−1(y1+y2)=sin⁡−1(310)\tan^{- 1}x+\cos^{- 1}\left( \frac{y}{\sqrt{1 +y^{2}}} \right)=\sin^{- 1}\left( \frac{3}{\sqrt{10}} \right) are

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  2. Question 2

    Trigonometry - II. Asked once: 9 May 2023 S2

    128
    If A, B, C are the angles of a triangle with tan⁡A2=13,tan⁡B2=23\tan\frac{A}{2} = \frac{1}{3}, \tan\frac{B}{2} = \frac{2}{3} then the value of tan⁡C2\tan\frac{C}{2} is

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  3. Question 3

    Vectors. Asked once: 16 Apr 2026 S2

    89
    If aˉ=4i^+j^+k^,bˉ=2i^+j^+2k^\bar{a} = 4\hat{i} + \hat{j} + \hat{k}, \bar{b} = 2\hat{i} + \hat{j} + 2\hat{k} and cˉ=3i^+4j^+5k^\bar{c} = 3\hat{i} + 4\hat{j} + 5\hat{k}, then (aˉ+bˉ)⋅(bˉ+cˉ)=(\bar{a} + \bar{b})\cdot(\bar{b} + \bar{c}) =

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  4. Question 4

    Applications of Derivative. Asked once: 19 Apr 2025 S1

    135
    A population p(t)p(t) of 1000 bacteria introduced into a nutrient medium grows according to the relation p(t)=1000+1000t100+t2p(t) = 1000 +\frac{1000t}{100 +t^{2}}. The maximum size of this bacterial population is

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  5. Question 5

    Definite Integration. Asked once: 10 May 2023 S2

    121
    ∫0ax−ax+a dx=\displaystyle\int_0^a \frac{x-a}{x+a}\,dx =

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