1
IIT-JEE 2007 Paper 2 Offline
+3
-1

Two trains $$A$$ and $$B$$ are moving with speeds $$20 \mathrm{~m} / \mathrm{s}$$ and $$30 \mathrm{~m} / \mathrm{s}$$ respectively in the same direction on the same straight track, with $$B$$ ahead of $$A$$. The engines are at the front ends. The engines of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from $$f_{1}=800 \mathrm{~Hz}$$ to $$f_{2}=1120 \mathrm{~Hz}$$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $$320 \mathrm{~Hz}$$. The speed of sound in still air is $$340 \mathrm{~m} / \mathrm{s}$$.

The spread of frequency as observed by the passengers in train B is

A
310 Hz
B
330 Hz
C
350 Hz
D
290 Hz
2
IIT-JEE 2007 Paper 2 Offline
+4
-0

Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situation in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Column I Column II
(A) The object moves on the x-axis under a conservative force in such a way that its "speed" and "position" satisfy $$v = {c_1}\sqrt {{c_2} - {x^2}}$$, where $$c_1$$ and $$c_2$$ are positive constants. (P) The object executes a simple harmonic motion.
(B) The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy $$v=-kx$$, where $$k$$ is a positive constant. (Q) The object does not change its direction.
(C) The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. (R) The kinetic energy of the object keeps on decreasing
(D) The object is projected from the earth's surface vertically upwards with a speed $$2\sqrt {GMe/{\mathop{\rm Re}\nolimits} }$$, where, M$$_e$$ is the mass of the earth and R$$_e$$ is the radius of the earth. Neglect forces from objects other than the earth. (S) The object can change its direction only once.

A
$$[\mathrm{A} \rightarrow(\mathrm{P}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{Q}, \mathrm{R})]$$
B
$$[\mathrm{A} \rightarrow(\mathrm{Q, R}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{S}, \mathrm{R})]$$
C
$$[\mathrm{A} \rightarrow(\mathrm{P, S}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]$$
D
$$[\mathrm{A} \rightarrow(\mathrm{P, R}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{S})]$$
EXAM MAP
Medical
NEET