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  • Question 1
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    Let P and Q be 3 × 3 matrices with P ≠ Q. If P^3 = Q^3 and P^2 Q = Q^2 P, then determinant of (P^2 + Q^2 ) is equal to

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    An ellipse is drawn by taking a diameter of the circle (x – 1)^2 + y^2 = 1 as its semiminor axis and a diameter of the circle x^2 + (y – 2)^2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

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  • Question 6
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    At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100 - 12√x . If the firm employs 25 more workers, then the new level of production of items is

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  • Question 8
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    If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150 th term of this AP is

  • Question 9
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    A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

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