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Mathematics Test - 26
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Mathematics Test - 26

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  • Question 1/10
    3 / -1

    If the sum of two of the roots of x3 + px2 + qx + r = 0 is zero, then pq =

    Solutions

  • Question 2/10
    3 / -1

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  • Question 3/10
    3 / -1

    Solutions

  • Question 4/10
    3 / -1

    sin-1 (sin 10 ) =

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  • Question 5/10
    3 / -1

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  • Question 6/10
    3 / -1

    Solutions

  • Question 7/10
    3 / -1

    Solutions

  • Question 8/10
    3 / -1

    If f(x)=x, g(x)=ex−1, and ∫fog(x)dx=Afog(x)+Btan−1(fog(x))+C, then A+B is equal to:

    Solutions

    It is given that, f(x)=x and g(x)=ex−1

    Therefore, fog(x)=f(g(x))=ex−1

    Now, it is also given that,

    ∫fog(x)dx=Afog(x)+Btan−1(fog(x))+C ----(1)

    Therefore,

    ⇒∫fog(x) dx=∫ex−1 dx ----(2)

    Let t=ex−1

    ⇒t2=ex−1

    Differentiating both sides, we get,

    ⇒2t dt=ex dx

    ⇒2t dt=t2+1 dx(∵t2=ex−1)

    ⇒2tt2+1 dt=dx

    Substituting this value in equation (2), we get,

    ⇒∫t.2tt2+1 dt=∫2t2t2+1 dt

    ⇒2∫t2+1−1t2+1 dt

    ⇒2∫t2+1t2+1 dt−2∫dtt2+1

    ⇒2∫dt−2∫dtt2+1

    ⇒2t−2tan−1⁡t+C

    Putting t=ex−1,

    ⇒2ex−1−2tan−1⁡(ex−1)+C

    We can write this equation as,

    =2fog(x)−2tan−1⁡(fog(x))+C

    Comparing this equation with equation (1), we get A=2 and B=−2

    Therefore, A+B=2+(−2)=0

  • Question 9/10
    3 / -1

    Solutions

  • Question 10/10
    3 / -1

    Solutions

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