Test Codes: SIA (Multiple-choice Type) and SIB (Short Answer Type ...

(A) 4n − 2. (B) 4n. (C) 8n − 4. (D) 8n − 2.21. A lantern is placed on the ground 100 feet away from a wall. A mansix feet tall is walking at a speed of 10 feet/second from the lanternto the nearest point on the wall. When he is midway between thelantern and the wall, the rate of change (in ft./sec.) in the length ofhis shadow is(A) 2.4. (B) 3. (C) 3.6. (D) 12.22. An isosceles triangle with base 6 cms. and base angles 30 ◦ each isinscribed in a circle. A second circle touches the first circle and alsotouches the base of the triangle at its midpoint. If the second circleis situated outside the triangle, then its radius (in cms.) is(A) 3 √ 3/2. (B) √ 3/2. (C) √ 3. (D) 4/ √ 3.23. Let n be a positive integer. Definef(x) = min{|x − 1|, |x − 2|, . . . , |x − n|}.Then(A)∫ n+10f(x)dx equals(n + 4). (B)4(n + 3). (C)4(n + 2). (D)2(n + 2).424. Let S = {1, 2, . . . , n}. The number of possible pairs of the form (A, B)with A ⊆ B for subsets A and B of S isn∑( )( )n n(A) 2 n . (B) 3 n . (C). (D) n!.k n − k25. Consider three boxes, each containing 10 balls labelled 1, 2, . . . , 10.Suppose one ball is drawn from each of the boxes. Denote by n i , thelabel of the ball drawn from the i-th box, i = 1, 2, 3. Then the numberof ways in which the balls can be chosen such that n 1 < n 2 < n 3 is(A) 120. (B) 130. (C) 150. (D) 160.k=026. The maximum of the areas of the isosceles triangles with base on thepositive x-axis and which lie below the curve y = e −x is:(A) 1/e. (B) 1. (C) 1/2. (D) e.5