PGDBA 2018 Question Paper

Instructions

Answer the question based on the following information.

Table 1 gives the men's and women's world record times for various outdoor running distances, recognized by the International Association of Athletics Federations (IAAF) as of 17 November 2017.

PGDBA 2018 - Question 21


The average speeds (rounded to 2 places of decimal) for the men's and women's fastest 1500 metersrace have been, respectively.

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PGDBA 2018 - Question 22


For which of the following categories, is the women's world record timeless than 110%of the men's world record time?

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PGDBA 2018 - Question 23


For which of the following categories is the ratio of the women's and men's record times, thatis, W/M, the largest?

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PGDBA 2018 - Question 24


The category in which the average speed is second highest is

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PGDBA 2018 - Question 25


If $$\alpha$$ is the factor by which the women's world record average speedreduces with doubling of the running distance, the smallest value of $$\alpha$$ occurs for the pair of categories

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Instructions

For the following questions answer them individually

PGDBA 2018 - Question 26


Each student in a class of 40 plays at least one indoor game-chess, carom and scrabble. 18 play chess, 20 play scrabble and 27 play carom. 7 play both chess and scrabble, 12 play both scrabble and carom and 4 play all 3 games. The number of players who play chess and carom but not scrabble is

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PGDBA 2018 - Question 27


The value of $$20_{C_1} + 2 \times 20_{C_2} + 3 \times 20_{C_3} + ..... + 20 \times 20_{C_{20}}$$ is

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PGDBA 2018 - Question 28


The circle $$x^2 + y^2 = 8$$ intersects the parabola $$y^2 = 2x$$ at a point P in the first quadrant. The acute angle between the tangents to the circle and the parabola at the point P is

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PGDBA 2018 - Question 29


In an isosceles right triangle $$PQR, \angle PRQ = 90^\circ$$. The points S and T are two trisection points of QR. The value of $$\tan(\angle SPT)$$ is

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PGDBA 2018 - Question 30


Let $$f: (0, \infty) \rightarrow (0, \infty)$$ be a strictly decreasing function. Consider $$h(x) = \frac{f\left(\frac{x}{1 + x}\right)}{1 + f\left(\frac{x}{1 + x}\right)}$$ Which one of the following is always true?

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