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Mathematics Test - 7

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Mathematics Test - 7
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  • Question 2
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    The equation of the common tangent touching the circle (x-3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis, is

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  • Question 4
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    If for a variable line  the condition a–2 + b–2 = c–2 (c is a constant), is satisfied, then the locus of foot of the perpendicular drawn from origin to this is:

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  • Question 5
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    If A and B are two square matrices such that B = –A–1 BA, then (A+B)2 is equal to-

    Solution

    B = –A–1 BA 

    AB = A (–A–1BA) 

    AB = (AA–1)(BA)

    AB = –BA 

    AB + BA = 0 

    Now, (A + B)2 = A2 + B2 + AB + BA 

    (A + B)2 = A2 + B2, (∵AB + BA = 0)

  • Question 6
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    a, b, c are positive numbers and abc2 has the greatest value 1/64 Then

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  • Question 7
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    The altitude of a cone is 20cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of-

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  • Question 9
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    The value of K, for which the equation (K–2)x2 + 8x + K + 4 = 0 has both the roots real distinct and negative is:

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  • Question 10
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    The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-

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