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Day 460: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 12 May 2026 S1

    79
    If f(x)=∫x2(1−x2)(1+1−x2) dxf(x) = \displaystyle\int\dfrac{x^2}{(1 - x^2)(1 + \sqrt{1 - x^2})}\,dx and f(0)=2f(0) = 2, then f(12)=f\left(\dfrac{1}{2}\right) = ...

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  2. Question 2

    Limits. Asked once: 21 Apr 2025 S1

    103
    lim⁡x→∞ex4−1ex4+1=\lim_{x\rightarrow \infty} \frac{e^{x^{4}}- 1}{e^{x^{4}}+ 1}=

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  3. Question 3

    Line and Plane. Asked once: 19 Apr 2026 S2

    92
    If α,β,γ\alpha, \beta, \gamma are the direction angles of the line x=4z+3x = 4z + 3 and y=2−3zy = 2 - 3z, then the value of cos⁡α+cos⁡β+cos⁡γ\cos\alpha + \cos\beta + \cos\gamma is...

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  4. Question 4

    Pair of Straight Lines. Asked once: 4 May 2023 S2

    109
    If O(0,0),A(1,2)O(0,0), A(1,2) and B(3,4)B(3,4) are the vertices of triangle OAB, then the joint equation of the altitude and median drawn from O is

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  5. Question 5

    Permutations and Combinations. Asked once: 23 Apr 2025 S1

    143
    A family consisting of a mother, father and their 8 children ( 4 boys and 4 girls) are to be seated at a round table in a party. How many ways can this be done if the mother and father sit together and the males and females alternate?

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