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Multiple Choice Question Based on Passage
Relative Velocity
If two objects A and B are moving in a straight line with velocities V_A and V_Brespectively, the relative velocity of object A with respect to object B is given by V_AB = V_A - V_B
It follows that the relative velocity of object B with respect to A will be V_BA = V_B- V_A
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 V_AB, we find the resultant of vectors V_A and - V_B. To find V_BA, we find resultant of vectors V_B and - V_A.
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. In order to protect himself from rain, the man should hold his umbrella at an angle

given by
(a) tan^-1

in the north-west direction
(b) tan^-1

in the south-west direction
(c) tan^-1

in the north-east direction
(d) tan^-1

in the south-east direction

Chemistry

Increasing/Decreasing Characteristics

Increasing bond strength

HCl, HBr, HF, HI

Mathematics

Passage Based Question
Passage I
Suppose E₁, E₂, E₃ be three mutually exclusive events such that P(E_i) = p_i for i = 1, 2, 3.
If p₁, p₂, p₃ are the roots of 27x³ - 27x² + ax - 1 = 0 then value of a is

(a)	9	(b)	6
(c)	3	(d)	[0, 1/5]

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