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Day 197: MHT-CET Maths

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

  1. Question 1

    Differential Equations. Asked once: 14 May 2026 S2 (same type asked 5 times) See all 5 of this type

    87
    If the function f(x)f(x) satisfying the equation [f′(x)]2+4f(x)f′(x)+f2(x)=0[f'(x)]^2 + 4f(x)f'(x) + f^2(x) = 0, then f(x)=f(x) = (where cc is constant of integration)

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  2. Question 2

    Trigonometric Functions. Asked once: 19 May 2026 S1 (same type asked 5 times) See all 5 of this type

    67
    If α≤2sin⁡−1x+cos⁡−1x≤β\alpha \le 2\sin^{-1}x + \cos^{-1}x \le \beta, then the values of α\alpha and β\beta are

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  3. Question 3

    Vectors. Asked once: 19 May 2026 S1 (same type asked 5 times) See all 5 of this type

    92
    A(1,2)A(1, 2), B(1,0)B(1, 0) and C(0,2)C(0, 2) are vertices of ΔABC\Delta ABC. The position vector of the point in which the bisector of angle AA cuts BCBC is .....

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  4. Question 4

    Line and Plane. Asked once: 14 May 2026 S2 (same type asked 5 times) See all 5 of this type

    95
    If θ\theta is the angle between the line rˉ=(i^+j^−k^)+λ(i^−j^+k^)\bar{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) and the plane rˉ⋅(i^−2j^+3k^)=5\bar{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 5 then the value of cos⁡2θ\cos^2\theta is

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  5. Question 5

    Line and Plane. Asked once: 11 Apr 2026 S2 (same type asked 5 times) See all 5 of this type

    92
    The vector equation of the plane passing through the point A(−2,7,5)A(-2, 7, 5) and parallel to the vectors 4i^−j^+3k^4\hat{i} - \hat{j} + 3\hat{k} and i^+j^+k^\hat{i} + \hat{j} + \hat{k} is ...

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