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Day 393: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 4 May 2023 S1 (same type asked 6 times) See all 6 of this type

    135
    If I=∫esin⁡θ(log⁡sin⁡θ+csc⁡2θ)cos⁡θ dθI=\int e^{\sin\theta}(\log\sin\theta+\csc^2\theta)\cos\theta\,d\theta, then I is equal to

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  2. Question 2

    Complex Numbers. Asked once: 3 May 2023 S2 (same type asked 6 times) See all 6 of this type

    149
    If z2+z+1=0z^{2}+z+1=0 then (z3+1z3)2+(z4+1z4)2=\left(z^{3}+\frac{1}{z^{3}}\right)^{2}+\left(z^{4}+\frac{1}{z^{4}}\right)^{2}= where z=ω=z=\omega= complex cube root of unity

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  3. Question 3

    Trigonometric Functions. Asked once: 4 May 2023 S2 (same type asked 6 times) See all 6 of this type

    116
    The value of tan⁡−1(3)−sec⁡−1(−2)cosec−1(−2)+cos⁡−1(−12)\frac{\tan^{-1}(\sqrt{3})-\sec^{-1}(-2)}{\text{cosec}^{-1}(-\sqrt{2})+\cos^{-1}\left(-\frac{1}{2}\right)} is

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  4. Question 4

    Line and Plane. Asked once: 3 May 2023 S2 (same type asked 6 times) See all 6 of this type

    147
    On which of the following lines lies the point of intersection of the line x−42=y−52=z−31\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1} and the plane x+y+z=2x+y+z=2?

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  5. Question 5

    Mathematical Logic. Asked once: 19 Apr 2026 S1 (same type asked 19 times) See all 19 of this type

    63
    The logical statement (p∨q)∧[(∼p∧q)∨(p∧∼q)]∧∼q(p \vee q) \wedge [(\sim p \wedge q) \vee (p \wedge \sim q)] \wedge \sim q is logically equivalent to ...

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