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Day 30: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked 5 times: 2 May 2023 S2*, 3 May 2023 S1*, 11 May 2023 S2*, 16 Apr 2026 S2*, 19 May 2026 S1 (* = numbers or wording changed that year) See all 5 times it was asked

    75
    Let f(x)f(x) be a twice differentiable function such that f′′(x)=−f(x)f''(x) = -f(x), and f′(x)=g(x)f'(x) = g(x). Let h(x)={f(x)}2+{g(x)}2h(x) = \{f(x)\}^2 + \{g(x)\}^2. If h(2)=7h(2) = 7, then h(8)h(8) is equal to:

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  2. Question 2

    Vectors. Asked 5 times: 4 May 2023 S1, 10 May 2023 S1, 14 May 2024 S1*, 13 Apr 2026 S1, 18 Apr 2026 S2 (* = numbers or wording changed that year) See all 5 times it was asked

    91
    If ∣aˉ∣=∣bˉ∣=1,∣cˉ∣=2|\bar{a}| = |\bar{b}| = 1, |\bar{c}| = 2 and aˉ×(aˉ×cˉ)+bˉ=0ˉ\bar{a} \times (\bar{a} \times \bar{c}) + \bar{b} = \bar{0}, then the acute angle between aˉ\bar{a} and cˉ\bar{c} is …\ldots

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  3. Question 3

    Pair of Straight Lines. Asked 5 times: 4 May 2023 S2, 9 May 2023 S2*, 10 May 2024 S2*, 13 Apr 2026 S1, 16 Apr 2026 S2 (* = numbers or wording changed that year) See all 5 times it was asked

    57
    The combined equation of the pair of lines passing through the origin and making an angle π4\dfrac{\pi}{4} with the line 3x+y−6=03x + y - 6 = 0 is...

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  4. Question 4

    Sets, Relations and Functions. Asked 5 times: 9 May 2023 S2*, 10 May 2023 S1*, 11 May 2024 S1*, 13 May 2024 S2*, 16 Apr 2026 S2 (* = numbers or wording changed that year) See all 5 times it was asked

    69
    If ex+ef(x)=ee^x + e^{f(x)} = e, then the domain of f(x)f(x) is

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  5. Question 5

    Trigonometric Functions. Asked 5 times: 11 May 2023 S2, 9 May 2024 S2, 19 Apr 2025 S2, 25 Apr 2025 S2, 26 Apr 2025 S2 See all 5 times it was asked

    113
    In a triangle PQR with usual notations, ∠R=π2\angle R =\frac{\pi}{2}. If tan⁡P2\tan\frac{P}{2} and tan⁡Q2\tan\frac{Q}{2} are the roots of the equation ax2+bx+c=0(a≠0)ax^{2}+bx+c= 0(a\neq 0), then

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