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Mathematics Test 151
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Mathematics Test 151

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  • Question 1/10
    4 / -1

    For what values of 'a', f(x) = –x3 + 4ax2 + 2x – 5 is decreasing for all x :-

    Solutions

     

    f(x) = –x3 + 4ax2 + 2x – 5

    f '(x) = –3x2 + 8ax + 2

    since f(x) is decreasing for all x, therefore f '(x) < 0

    ⇒ –3x2 + 8ax + 2 < 0

    since a < 0, so D must be < 0, for the inequality, so

    64a2 – 4.(–3)(2) < 0

    from above it is clear that for no value of 'a' f(x) is decreasing.

     

  • Question 2/10
    4 / -1

    If one of the root of the equation x2 + xf(a) + a=0 is the cube of the other for all x ∈ R then f(x)

  • Question 3/10
    4 / -1

    Let ƒ : (–10, 10) → R be an even function. If n be the number of values of x for which  then value of n is

    Solutions

     

  • Question 4/10
    4 / -1

    Let f(x) = [2x3 – 5]; then number of points in (1, 2) where the function is discontinuous are (where [.] → G.I.F.)

  • Question 5/10
    4 / -1

    The angle of elevation of the top of a mobile tower from three points P, Q and R (on a straight line through the foot of the tower) are α, β and γ respectively. If all three points are lie on same side of foot of tower and α : β : γ = 1 : 2 : 3 and PQ = ℓ, then height of tower is -

    Solutions

     

  • Question 6/10
    4 / -1

    Write contrapositve of conditional statement "If x = 2 or y = 6 then x + 4y ≠ 22" is :-

  • Question 7/10
    4 / -1

    The integral is equal to

    (where c is a constant of integration)

    Solutions

     

  • Question 8/10
    4 / -1

    The differential equation satisfied by the system of parabolas y2 = 4a(x + a) is :

    Solutions

     

     

  • Question 9/10
    4 / -1

    Let f : [–3, 1] → R be given as

    If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to ______.

    Solutions

     

  • Question 10/10
    4 / -1

    Solutions

     

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