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Day 331: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 20 Apr 2025 S1 (same type asked 9 times) See all 9 of this type

    123
    ∫−22∣x2−x−2∣dx=\int_{- 2}^{2} \left| x^{2}-x- 2 \right|dx=

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  2. Question 2

    Mathematical Logic. Asked once: 22 Apr 2025 S1 (same type asked 9 times) See all 9 of this type

    121
    Which of the following statements has the truth value T? (A) cube roots of unity are in Geometric progression and their sum is 1 (B)  4+7>10\ 4 + 7 > 10 iff 2+8<102 + 8 < 10 (C)  ∃x∈N\ \exists x \in \mathbb{N} such that x2−3x+2=0x^{2} - 3x + 2 = 0 and ∃n∈N\exists n \in \mathbb{N} such that n is an odd number (D) 3+i3 + i is a complex number or 2+3=5\sqrt{2} + \sqrt{3} = \sqrt{5}

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  3. Question 3

    Differentiation. Asked once: 15 May 2023 S1 (same type asked 9 times) See all 9 of this type

    115
    If (a+2bcos⁡x)(a−2bcos⁡y)=a2−b2(a+2b\cos x)(a-2b\cos y) = a^{2}-b^{2}, where a>b>0a>b>0, then dxdy\frac{dx}{dy} at (π4,π4)\left(\frac{\pi}{4},\frac{\pi}{4}\right) is

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  4. Question 4

    Vectors. Asked once: 2 May 2023 S2 (same type asked 9 times) See all 9 of this type

    123
    If C is a non-zero scalar and A, B are non-zero vectors with A⃗⊥B⃗\vec{A}\perp\vec{B}, A⃗⋅X⃗=C\vec{A}\cdot\vec{X}=C and A⃗×X⃗=B⃗\vec{A}\times\vec{X}=\vec{B}, then X⃗\vec{X} is given by

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  5. Question 5

    Differentiation. Asked once: 10 May 2024 S2 (same type asked 9 times) See all 9 of this type

    119
    Let f be a differentiable function such that f(1)=2f(1)=2 and f′(x)=f(x)f'(x)=f(x), for all x∈Rx\in\mathbb{R}. If h(x)=f(f(x))h(x)=f(f(x)), then h′(1)h'(1) is equal to

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