Correct Answer: C. did not give due regard to God

Correct Answer: D. Insufficient food

Correct Answer: D. \(400cm^3\)

Explanation

Molarity = 0.100 mol / 0.250 mol dm3

= 0.100 mol / 0.250 dm3 * 1000 cm3/dm3

= 400 cm3

Volume (V) = Amount (n) / Concentration (C)

Given that the amount of HCl is 0.100 mol and the concentration of the solution is 0.250 mol/dm³, you can calculate the volume:

Volume (V) = 0.100 mol / 0.250 mol/dm³ = 0.4 dm³

Since 1 dm³ is equal to 1000 cm³, you can convert the volume from dm³ to cm³:

Volume (V) = 0.4 dm³ × 1000 cm³/dm³ = 400 cm³

Therefore, the volume of 0.100 mol of HCl in a 0.250 mol/dm³ solution is 400 cm³.

Explanation

Let T and B be the top and base of the control tower respectively; P, the point of pilot's observation and PS, the line of observation.

(a) Shortest distance is |PB|.

\(\therefore \cos 33° = \frac{8.5}{PB}\)

\(PB = \frac{8.5}{\cos 33} = \frac{8.5}{0.8387}\)

\(|PB| = 10.135km \approxeq 10.1km\)

(b) Height of the control tower = |SB| - |ST|

\(\therefore \tan 33° = \frac{|SB|}{8.5 km} \implies |SB| = 8.5 \tan 33°\)

\(|SB| = 5.52 km\)

\(\tan 30° = \frac{|ST|}{8.5 km} \implies |ST| = 8.5 \tan 30°\)

\(|ST| = 4.907 km\)

\(\therefore\) The height of the tower = 5.52 km - 4.907 km = 0.613 km.

Correct Answer: B. obligatory and prohibited

Correct Answer: A. 10

Explanation

n(PuQ) = n(p) + n(q) - n(PnQ)

40 = 20 + 30 - n(PnQ)

n(PnQ) = 50 - 40 = 10

Correct Answer: D. increases during the dry season

Correct Answer: D. walk in his ways

Correct Answer: D. is an advantage because it is in the opposite direction of the motion of the car

Explanation

When the brakes in a car are applied, the car is moving forward, and the goal is to slow it down or stop it. To achieve this, a force must act in the direction opposite to the car's motion. This force is the frictional force between the tires and the road.

• Direction of friction: For the car to decelerate, the frictional force must act in the opposite direction of the car's motion. If it acted in the same direction, it would accelerate the car.

• Advantage or disadvantage: Slowing down or stopping the car is the intended purpose of applying brakes, and it's crucial for safety. Therefore, the frictional force that accomplishes this is an advantage.

Combining these two points: the frictional force is an advantage because it acts in the opposite direction of the car's motion, causing deceleration.

Therefore, the correct option is:

D. is an advantage because it is in the opposite direction of the motion of the car

Explanation

(a) \(T_{n} = a + (n - 1)d\) (terms of an A.P)

3rd term = -9 ; 8th term = 26

\(\implies T_{3} = a + 2d = -9 ... (1)\)

\(\implies T_{8} = a + 7d = 26 ..... (2)\)

(i) Solving (2) - (1), we have

\(7d - 2d = 26 - (-9)\)

\(5d = 35 \implies d = 7\)

(ii) Putting d = 7 in (1) above, we have

\(a + 2(7) = -9\)

\(a + 14 = -9\)

\(a = - 9 - 14 = -23\)

(b) \(\frac{XP}{XY} = \frac{2}{5}\) (similar triangles)

\(\frac{24}{\text{Area of \Delta XYZ} = \frac{2^{2}}{5^{2}}\)

\(\text{Area of } \Delta XYZ = \frac{24 \times 25}{4} = 150 cm^{2}\)

\(\therefore \text{Area of trapezium PQZY} = 150 - 24 = 126 cm^{2}\)