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  • Question 1
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    \(\int_{0}^{\pi / 2} \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x=\)

  • Question 2
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    The area of an expanding rectangle is increasing at the rate of 48 cm2/sec. The length of the rectangle is always equal to the square of the breadth. At the instant when the breadth is 4.5 cm, The length is increasing at the rate of

  • Question 3
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    The following age group are included in the proportion indicated

    Age Group Relative Proportion in Population
    12 - 17 0.17
    18 - 23 0.31
    24 - 29 0.27
    30 - 35 0.21
    36 + 0.04
    Then number of people respectively in each age group should be included in a sample of 3000 people to make the sample representative is

  • Question 4
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    If ln(x + y) = 2xy, theny′ (0) is equal to

  • Question 5
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    ABCD is a square whose vertices A, B, C and D are (0, 0), (2, 0), (2, 2) and (0, 2) respectively. This square is rotated in the X - Y plane with an angle of 30° in anticlockwise direction about the vertex A. Now points B, C, D are converted as B', C' and D' respectively. Then equation of diagonal B' D' and equation of circumcircle AB'E is (E is centre of new square)

  • Question 6
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    The probability that at least one of the events \(A\) and \(B\) occurs is \(0.6 .\) If \(A\) and \(B\) occur simultaneously with probability \(0.2,\) then \(P(\bar{A})+P(\bar{B})\) is: (where \(\bar{A}\) and \(\bar{B}\) are complements of \(A\) and \(B\) respectively)

  • Question 7
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    Consider the straight line ax + by = c, where a, b, c ∈ R+this line meets the coordinate axes at A and B respectively. If the area of the ΔOAB, O being origin, is always a constant equal to half, then

  • Question 8
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    The tangent at \(P\) on the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) meets one of the asymptote at \(Q\). Then the locus of the mid point of \(\mathrm{PQ}\) is \(4\left(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}\right)=\mathrm{k},\) where \(\mathrm{k}\) is

  • Question 9
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    If y=7x − x3and x increases at the rate of 4 units per second, then the rate of change in slope of the curve when x = 3, is

  • Question 10
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    The equation of the common tangent to the equal parabolas y2 = 4ax and x2 = 4ay is

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