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  • Question 1
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    Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n, respectively, are

  • Question 2
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    For complex numbers z1 = x1 + iy1 and z2 = x2 + iy2, (where i = √-1), we write z1 ∩ z2 for x1 ≤ x2 and y1 ≤ y2, then for all complex numbers z with 1 ∩ z, we have 

  • Question 3
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    In a plane, there are 37 straight lines, out of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through the same point, no line passes through both points A and B, and no two lines are parallel. The number of intersection points the lines have is equal to

  • Question 4
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    In a sequence of (4n + 1) terms, the first (2n + 1) terms are in AP, whose common difference is 2, and the last (2n + 1) terms are in GP, whose common ratio is 0.5. If the middle terms of the AP and GP are equal, then the middle term of the sequence is

  • Question 5
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     then the global maximum and local minimum values of f(x) for x ∈ [-2, 2], respectively, are

  • Question 6
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    The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola, is

  • Question 7
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  • Question 8
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    The lines  are coplanar, if the value of λ is

  • Question 9
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    The mean of n items is  If these n items are successively increased by 2, 22, 23, …, 2n, then the new mean is

  • Question 10
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