Correct Answer: 462 cm²

Solution : Diameter = 14 cm
Radius, $r = \frac{14}{2} = 7$ cm
The total surface area of a hemisphere = $3\pi r^2= 3 \times \frac{22}{7} \times 7^2 = 462$ cm² 
Hence, the correct answer is 462 cm²​​​​​.

Correct Answer: Akbar

Solution : The correct option is Akbar.

The Mansabdari system, introduced by Akbar, was unique to the Mughal Empire's civil and military administrative systems. Under this system, each officer was awarded a rank. The lower rank was ten, and the highest was 5000 for the nobles; near the conclusion of his reign, it was raised to 7000.

Reigning from 1556 to 1605, Akbar is regarded as one of the most distinguished rulers in Indian history. Many people saw his rule as a time of significant intellectual and cultural advancement.

Correct Answer: demand for a commodity and its price

Solution : The correct option is demand for a commodity and its price.

The Law of Demand asserts a negative relationship between the price of a commodity and the quantity demanded. As the price rises, demand tends to decrease, and vice versa. This inverse correlation reflects consumers' inclination to buy more at lower prices and less at higher prices, influencing market dynamics.

Correct Answer: 1, 2, 4, 3, 5

Solution : Given:
1. Thighs 2. Stomach 3. Nose 4. Lips 5. Skull

Starting from the top of the human body, we have the skull, which houses and protects the brain. Just below that, we have the nose, which is responsible for our sense of smell and plays a crucial role in our respiratory system. Moving down, we have the lips, which not only help us speak and express emotions but also aid in eating and drinking. The stomach, located below the lips, is a vital organ that helps break down food and extract nutrients. Finally, at the bottom of the body, we have the thighs, which support us in standing and walking and play a crucial role in our movement.

On arranging the body parts from bottom to top, the sequence is as follows – Thighs→Stomach→Lips→Nose→Skull

So, the order is 1, 2, 4, 3, 5. Hence, the third option is correct.

Correct Answer: Methyl alcohol and H₂O.

Solution : The correct option is Methyl alcohol and H₂O.

Methyl alcohol (CH₃OH), usually known as methanol, is a kind of alcohol that may be used as an antifreeze in automotive radiators. It works as a coolant and antifreeze solution for the vehicle's engine when combined with water (H₂O) in the suitable ratio. In areas where extreme freezing temperatures can cause standard water-based coolants to freeze, possibly harming the engine, methanol-water combinations are widely employed. The combination reduces the freezing point of the coolant, keeping it from hardening in cold weather, and it also aids in the regulation of engine temperatures while in operation.
 

Correct Answer: accused of beating up on the

Solution : The correct choice is the third option.

The preposition "before" should be replaced with "on," as it helps correct the phrase "beat up on," which means "to assault and injure someone".

Therefore, the correct sentence is: "Mr. Arvind was accused of beating up on the students in the class."

Correct Answer: Chapter and verse.

Solution : The correct choice is the third option.

The idiom, chapter and verse means giving precise details or citing specific evidence about something. It means providing detailed information or being able to refer to specific sources accurately, which makes it the appropriate choice.

The meanings of the other options are as follows:

• Buying the pig in a poke means purchasing something without examining it beforehand.
• Cast pearls before swine signifies giving something valuable to someone who doesn't appreciate or understand its worth. It suggests offering something of high value to those who cannot or do not appreciate it.
• Beating about the bush means avoiding getting to the main point or being indirect about something. It suggests not addressing a topic directly and instead talking about it.

Correct Answer: 14 cm

Solution :
Given: Area of the circle = 154 $cm^2$
We know that,
Area of the circle = $\pi r^2$
According to the question, 
154 = $\pi r^2$
⇒ 154 = $\frac{22}{7}×r^2$
⇒ $\frac{154×7}{22}$ = $r^2$
⇒ $r$ = 7
Thus, length of PQ = 7 × 2 = 14
Hence, the correct answer is 14 cm.

Correct Answer: 17

Solution : The given figure can be labelled as shown below –

Now, in the above figure, there are a total of 17 triangles. They are ABK, BCG, DGN, DEF, HIF, IJK, LUT, STM, QRS, OQP, jPZ, igh, gbf, abY, Yec, cXW, WVd.

Therefore, there are 17 triangles. Hence, the second option is correct.

Correct Answer: 80°

Solution : $\triangle ABC \sim \triangle PQR$
⇒ $\angle C=\angle R$
In $\triangle ABC,$
$\angle A + \angle B + \angle C = 180°$
⇒ $35°+65°+\angle C = 180°$
⇒ $\angle C = 180° - 100°$
⇒ $\angle C = 80°$
⇒ $\angle R = 80°$
Hence, the correct answer is 80°.