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Day 187: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 16 Apr 2026 S1 (same type asked 7 times) See all 7 of this type

    55
    If 0≤x≤π20 \le x \le \dfrac{\pi}{2} , then the number of values of xx for which sin⁡x−sin⁡2x+sin⁡3x=0\sin x - \sin 2x + \sin 3x = 0 is

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  2. Question 2

    Differentiation. Asked once: 26 Apr 2025 S2 (same type asked 7 times) See all 7 of this type

    136
    If u=log⁡(x−1−x+1)u= \log(\sqrt{x- 1}-\sqrt{x+ 1}) and v=x+1+x−1v=\sqrt{x+ 1}+\sqrt{x- 1} then dudv=\frac{du}{dv}=... .

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  3. Question 3

    Indefinite Integration. Asked once: 12 May 2024 S2 (same type asked 7 times) See all 7 of this type

    105
    If ∫1−x2x4 dx=A(x)(1−x2)m+c\int \frac{\sqrt{1-x^2}}{x^4}\,dx = A(x)\left(1-x^2\right)^m + c for a suitable chosen integer mm and a function A(x)A(x), where cc is a constant of integration, then (A(x))m(A(x))^m equals

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  4. Question 4

    Mathematical Logic. Asked once: 18 Apr 2026 S2 (same type asked 7 times) See all 7 of this type

    61
    The minimum number of switches in the simplified form of the following switching circuit is

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  5. Question 5

    Vectors. Asked once: 13 Apr 2026 S2 (same type asked 7 times) See all 7 of this type

    90
    If aˉ=i^+j^+k^,bˉ=i^,cˉ=c1i^+c2j^+c3k^\bar{a} = \hat{i} + \hat{j} + \hat{k}, \bar{b} = \hat{i}, \bar{c} = c_1\hat{i} + c_2\hat{j} + c_3\hat{k} with c1=1,c2=2c_1 = 1, c_2 = 2, then value of c3c_3 such that aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} are coplanar is ____

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