21.

For any two independent events E₁ and E₂ in a space S, $\mathrm{P}\left[\left({\mathrm{E}}_1 \cup {\mathrm{E}}_2\right) \cap \left({\mathrm{E}}_1 \cap {\mathrm{E}}_2\right)\right]$ is equal to

• $\le \frac{1}{4}$

• $> \frac{1}{4}$

• $\ge \frac{1}{2}$

• $> \frac{1}{2}$

The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. Then, P² : Q² : R² gven by

• 2 2 3

• 3 2 2

• 2 3 2

• 2 3 1

Forces ofmagnitudes 3, P, 5, 10 and Q are respectively acting along the sides AB, BC, CD, AD and the diagonal CA of a rectangle ABCD, where AB = 4m and BC = 3m. Ifthe resultant is a single force along the other diagonal BD, then P, Q and the resultant are

• $4, 10\frac{5}{12}, 12\frac{11}{12}$

• 5, 6, 7

• $3\frac{1}{2}, 8, 9\frac{1}{2}$

• None of the above

A gun projects a ball at the angle of 45° with the horizontal. If the horizontal range is 39.2 m, then the ball will rise to

• 9.8 m

• 4.9 m

• 2.45 m

• 19.6 m