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Questions

### Physics

Multiple Choice Question Based on Passage
Relative Velocity
If two objects A and B are moving in a straight line with velocities VA and VB respectively, the relative velocity of object A with respect to object B is given by VAB = VA - VB
It follows that the relative velocity of object B with respect to A will be VBA = VB - VA
If objects A and B are moving along different directions in a plane, the relative velocity of one object with respect to the other is found by using the parallelogram law of vector addition. To find VAB, we find the resultant of vectors VA and - VB. To find VBA, we find resultant of vectors VB and - VA.
Rain is falling vertically with a speed of 4 ms-1. A man riding a bicycle is travelling at a speed of 3 ms-1 in the north to south direction. With what speed does the rain strike his umbrella ?
 (a) 1 ms-1 (b) 7 ms-1 (c) 5 ms-1 (d) 3.5 ms-1

### Chemistry

A mixture of ethane (C2H6) and ethane (C2H4) occupies 40 litres at 1.00 atm and 400 K. The mixture reacts completely with 130 g of O2 to produce CO2 and H2O. Assuming ideal gas behaviour, calculate the mole fractions of C2H4 and C2H6 in the mixture.

### Mathematics

Passage Based Question
Passage I
Suppose E1, E2, E3 be three mutually exclusive events such that P(Ei) = pi for i = 1, 2, 3.
If p1 = (1 + 3p), p2 = (1 - p) and p3 = (1 - 2p), then p belongs to
 (a) (-1/3, 1) (b) (-1/9, 1/4) (c) (-2/3, 2/3) (d) (-1, 0)
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