PGDBA 2018

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.

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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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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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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Question 24

The category in which the average speed is second highest is

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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

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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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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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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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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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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