JEE Advanced: Previous year paper of 2013 (PAPER-2)

Physics:
Qu. A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)
(A) In the region 0 < r < R, the magnetic field is non-zero
(B) In the region R < r < 2R, the magnetic field is along the common axis.
(C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
(D) In the region r > 2R, the magnetic field is non-zero.
Ans: A, D

Qu. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is (are):
(A) If the wind blows from the observer to the source, f2 > f1.
(B) If the wind blows from the source to the observer, f2 > f1.
(C) If the wind blows from observer to the source, f2 < f1.
(D) If the wind blows from the source to the observer f2 < f1.
Ans: A, B

Mathematics:
Qu. In a triangle PQR, P is the largest angle and cos P = 1/3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are):
(A) 16         (B) 18
(C) 24         (D) 22
Ans: B, D

Paragraph for Questions
A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black balls.

Qu. If 1 ball is drawn from each of the boxes B1, B2 and B3, the probability that all 3 drawn
balls are of the same colour is
(A) 82/648    (B) 90/648
(C) 558/648    (D) 566/648
Ans: A

Qu. If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 is:
(A) 116/181     (B) 126/181
(C) 65/181     (D) 55/181
Ans: D

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