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Day 19: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. This type asked 7 times: 9 May 2023 S1, 10 May 2024 S1, 13 May 2024 S2, 20 Apr 2025 S2, 15 Apr 2026 S1, 16 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 7 of this type

    56
    The general solution of cos⁡x+sin⁡x=cos⁡2x+sin⁡2x\cos x + \sin x = \cos 2x + \sin 2x is x=npπx = np\pi or x=nqπ3+π6x = \dfrac{nq\pi}{3} + \dfrac{\pi}{6} for n∈Zn \in Z then p:q=p : q =

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  2. Question 2

    Differentiation. This type asked 7 times: 3 May 2023 S2, 9 May 2023 S1, 9 May 2024 S1, 20 Apr 2025 S2, 21 Apr 2025 S1, 26 Apr 2025 S2, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 7 of this type

    74
    The derivative of log⁡10x\log_{10}x with respect to log⁡x10\log_x 10 is

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  3. Question 3

    Indefinite Integration. This type asked 7 times: 2 May 2023 S2, 4 May 2023 S2, 10 May 2023 S2, 10 May 2024 S1, 10 May 2024 S2, 12 May 2024 S2, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 7 of this type

    81
    If ∫dxx7/2(x4+1)3/8=m(x4+1x4)n+c\displaystyle\int\dfrac{dx}{x^{7/2}(x^4 + 1)^{3/8}} = m\left(\dfrac{x^4 + 1}{x^4}\right)^n + c, where cc is a constant of integration, then the value of nm\dfrac{n}{m} is...

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  4. Question 4

    Mathematical Logic. This type asked 7 times: 3 May 2023 S2, 10 May 2024 S1, 12 May 2024 S2, 26 Apr 2025 S1, 16 Apr 2026 S1, 18 Apr 2026 S2, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 7 of this type

    62
    The simplified switching circuit for the following circuit is

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  5. Question 5

    Vectors. This type asked 7 times: 4 May 2023 S1, 15 May 2023 S2, 11 May 2024 S2, 22 Apr 2025 S2, 11 Apr 2026 S2, 13 Apr 2026 S2, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 7 of this type

    91
    The sum of all real values of λ\lambda for which the vectors a⃗=λi^+j^+k^,b⃗=i^+λj^+2k^,c⃗=2i^+3j^+λk^\vec{a} = \lambda\hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{i} + \lambda\hat{j} + 2\hat{k}, \vec{c} = 2\hat{i} + 3\hat{j} + \lambda\hat{k} are coplanar is...

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