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Day 210: MHT-CET Maths

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

  1. Question 1

    Circle. Asked once: 12 May 2026 S2 (same type asked 4 times) See all 4 of this type

    60
    The length of the tangent segment drawn from point PP to the circle, x2+y2−2x−2y−2=0x^2 + y^2 - 2x - 2y - 2 = 0 is 424\sqrt{2} units. If λmax\lambda_{max} and λmin\lambda_{min} are the maximum and minimum distances of point PP from the circle, then λmax+λmin\lambda_{max} + \lambda_{min} is equal to....

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  2. Question 2

    Differentiation. Asked once: 25 Apr 2025 S2 (same type asked 4 times) See all 4 of this type

    116
    If y=tan⁡−1(12x−64x31−48x2)y=\tan^{- 1}\left( \frac{12x- 64x^{3}}{1 - 48x^{2}} \right), then dydx=\frac{dy}{dx}=

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  3. Question 3

    Mathematical Logic. Asked once: 17 Apr 2026 S2 (same type asked 4 times) See all 4 of this type

    58
    Which of the following statements is/are False? S1:∃n∈NS_1 : \exists n \in N, such that n2+n+2n^2 + n + 2 is divisible by 4. S2:∃x∈NS_2 : \exists x \in N, such that x−17<20x - 17 < 20. S3:∀n∈N,x2+3x−10=0S_3 : \forall n \in N,\quad x^2 + 3x - 10 = 0. S4:∀n∈N,n2≥1S_4 : \forall n \in N,\quad n^2 \ge 1.

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  4. Question 4

    Trigonometric Functions. Asked once: 21 Apr 2025 S2 (same type asked 4 times) See all 4 of this type

    105
    The value of sin⁡[tan⁡−1(1−x22x)+cos⁡−1(1−x21+x2)]\sin\left\lbrack \tan^{- 1}\left( \frac{1 -x^{2}}{2x} \right)+\cos^{- 1}\left( \frac{1 -x^{2}}{1 +x^{2}} \right) \right\rbrack is

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  5. Question 5

    Trigonometric Functions. Asked once: 20 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    57
    The number of common solutions of the pair of equations 2sin⁡2θ−2cos⁡2θ+1=02\sin^2\theta - 2\cos^2\theta + 1 = 0 and 2sin⁡2θ+3sin⁡θ−2=02\sin^2\theta + 3\sin\theta - 2 = 0 in the interval [0,2π][0, 2\pi], is

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