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Day 483: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 17 Apr 2026 S2

    64
    If sin⁡−1(x−2)+cos⁡−1(x)+tan⁡−1(x+2)+cot⁡−1(x+4)=sec⁡−1(k)−π2\sin^{-1}(x - 2) + \cos^{-1}(x) + \tan^{-1}(x + 2) + \cot^{-1}(x + 4) = \sec^{-1}(\sqrt{k}) - \dfrac{\pi}{2}, then cos⁡(2 csc⁡−1k−1)=…\cos(2\,\mathrm{\csc}^{-1}\sqrt{k - 1}) = \ldots

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  2. Question 2

    Trigonometry - II. Asked once: 22 Apr 2025 S1

    125
    The value of sin⁡25∘+sin⁡210∘+sin⁡215\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15 +.........+sin⁡285∘+sin⁡290∘=+ ......... +\sin^{2}85^{\circ}+\sin^{2}90^{\circ}=

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  3. Question 3

    Vectors. Asked once: 12 May 2026 S1

    93
    Let aˉ=λi^+4j^\bar{a} = \lambda\hat{i} + 4\hat{j} and bˉ=i^+λj^\bar{b} = \hat{i} + \lambda\hat{j} where λ∈Z\lambda \in Z such that ∣aˉ∣<6|\bar{a}| < 6. The number of possible values of λ\lambda for which aˉ\bar{a} and bˉ\bar{b} are non-collinear is ___

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  4. Question 4

    Applications of Derivative. Asked once: 11 Apr 2026 S1

    77
    The equation of the tangent to the curve y=3x3−3x2+xy = 3x^3 - 3x^2 + x at x=1x = 1 is

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  5. Question 5

    Circle. Asked once: May 2021 S1

    108
    The locus of a point which moves such that the ratio of the length of the tangents to the circles x2+y2+4x+3=0x^2+y^2+4x+3=0 and x2+y2−6x+5=0x^2+y^2-6x+5=0 is 2:32:3, is

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