Correct Answer: $9\frac{1}{2}$ km/h

Solution : Given: Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously, another train leaves Q for P. They meet at the end of six hours and the former train travels 8 km/h faster than the other.
Let the speed of the train from Q be x km/h.
Then the speed of the train from P is (x + 8) km/h.
Now in 6 hours the train from Q to P travels 6x km and 6(x + 8) km respectively.
Here, 6x + 6(x + 8) = 162
⇒ 12x = 162 – 48
⇒ x = $\frac{114}{12} = 9\frac{1}{2}$
Hence, the correct answer is $9\frac{1}{2}$ km/h.

Correct Answer: 761

Solution : Here, the given equations follows a pattern in which the first number, the middle number and the last number in LHS becomes the units place digit, the hundreds place digit and the tens place digit in the answer part in RHS respectively.

⇒ 5 x 4 x 0 = 405

⇒ 3 x 2 x 8 = 283

Following the same pattern in the unsolved equation, we get –

⇒ 1 x 7 x 6 = 761

Hence, option fourth is correct.

Correct Answer: 200 km

Solution : Let the speed of the boat in still water be $x$ km/hr and the speed of the current be $y$ km/hr.
Speed downstream = $x + y$
Speed upstream = $x - y$
Now, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
$\frac{120}{x + y} + \frac{120}{x - y} = 30$....(1)
and$\frac{40}{x + y} + \frac{25}{x – y} = 7$ ....(2)
Multiplying equation (2) by 3, we get,
$\frac{120}{x + y} + \frac{75}{x – y} = 21$ ......(3)
Subtracting equation (3) from (1), we get,
$\frac{45}{x – y} = 9$
$⇒x - y = 5$.......(4)
Putting the value of $x - y$ in equation (2), we get,
$x + y = 20$ .......(5)
Solving these two equations, we get the values of $x$ and $y$.
$x = 12.5$ and $y = 7.5$
Distance covered by the boat in 16 hours in still water = 16 × 12.5 = 200 km
Hence, the correct answer is 200 km.

Correct Answer: Gandhara

Solution : The correct answer is Gandhara.

Greco-Buddhist art or Gandhara art is the artistic manifestation of Greco-Buddhism, a cultural syncretism between Ancient Greek art and Buddhism. It had mainly evolved in the ancient region of Gandhara, located in the northwestern fringe of the Indian subcontinent.

Correct Answer: toe

Solution : The correct choice is the second option.

In the given sentence, the context of an athlete being injured due to a fall on the track suggests a physical injury, and toe refers to a part of the foot, making it the correct choice.

The meanings of other options are as follows:

• A toad is an amphibian similar to a frog.

• Tow refers to the act of pulling something, often with a rope or chain.

• To is a preposition, often indicating direction or action.

Therefore, the complete sentence is: The athlete’s toe was badly injured due to a fall on the track.

Correct Answer: Tidy

Solution : The most appropriate antonym is the first option.

• Dishevelled describes the boy's unkempt or messy appearance.
• Tidy means neat and well-organised, the opposite of messy or dishevelled.

The meanings of the other options are as follows:

• Clumsy means awkward or lacking skill or coordination.
• Infuriated means extremely angry or enraged.
• Excited means feeling enthusiastic, eager, or elated.

Correct Answer: QOMK

Solution : Given:
ZXVT : YWUS :: RPNL : ?

Like, ZXVT→Z – 1 = Y; X – 1 = W; V – 1 = U; T – 1 = S
Thus, ZXVT is related to YWUS.
Similarly, follow the same pattern for RPNL –
R – 1 = Q; P – 1 = O; N – 1 = M; L – 1 = K

Thus, RPNL is related to QOMK. Hence, the fourth option is correct.

Correct Answer: 15

Solution : Given: 

In the first column, 8 – 6 = 2 → 2 + 2 = 4

In the second column, 12 – 5 = 7 → 7 + 8 = 15

In the third column, 13 – 10 = 3 → 18 – 3 = 15

So, the missing number is 15.

Hence, first option is correct.

Correct Answer: $\frac{14}{3}$

Solution :
As we know,
PT² = PA × PB
⇒ 8² = 6($x$ + 6)
⇒ 64 = 6$x$ + 36
⇒ $x$ = $\frac{28}{6} = \frac{14}{3}$
Hence, the correct answer is $\frac{14}{3}$.

Correct Answer: Advantage out

Solution : The correct option is Advantage Out.

When the score is tied, the next point won by a player is referred to as an "advantage." If the receiver wins the next point after a deuce, the score becomes "advantage [receiver's name]". If the receiver wins the next point, they win the game.