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  • Question 1
    4 / -1

    The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

  • Question 2
    4 / -1

    Suppose a, b, and c are distinct real numbers such that a, 2b, 3c are in AP and a, b, c are in GP. Then, which of the following can be the common ratio of the GP

  • Question 3
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    If In=0π/4tannθdθ, then lg+16 is equal to

  • Question 4
    4 / -1

    C1 and C2 are circles of unit radii with centres at (0, 0) and (1, 0), respectively. C3 is a circle of unit radius, which passes through the centres of the circles C1 and C2 and has its centre above the x-axis. The equation of the common tangent to C1 and C3, which does not pass through C2, is

  • Question 5
    4 / -1

    If nC4, nC5 and nC6 are in AP, then the value of n can be

  • Question 6
    4 / -1

    If cos1(x2y2x2+y2)=loga, then dydx is equal to

  • Question 7
    4 / -1

    Let S = (x – 1)10 + (x – 1)9 (x + 1) + (x – 1)8 (x + 1)2 + …….+ (x + 1)10

    Which of the following is a constant term in the expansion of S?

  • Question 8
    4 / -1

    If an denotes the term independent of x in the expansion of [x+sin(1/n)x2]3n, then limx(an)n!3npn equals

  • Question 9
    4 / -1

    The equation of a circle touching the coordinate axes and the line x cosα + y sinα = 2 is x2 + y2 – 2gx + 2gy + g2 = 0, where g is equal to

  • Question 10
    4 / -1

    The circles x2 + y2 – 10x + 16 = 0 and x2 + y2 = r2 intersect each other at two distinct points if

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