Correct Answer: RAPID

Solution : Given:
RAPPROCHEMENT

Now, let's compare all the option words with the word RAPPROCHEMENT –
First option: MACHETE; All the letters of MACHETE are present in the word RAPPROCHEMENT.
Second option: POACH; All the letters of POACH are present in the word RAPPROCHEMENT.
Third option: RAPID; I and D are not present in the word RAPPROCHEMENT. Therefore, all the letters of RAPID are not present in the word RAPPROCHEMENT.
Fourth option: TEAM; All the letters of TEAM are present in the word RAPPROCHEMENT.

So, from the above, only RAPID cannot be formed from the word RAPPROCHEMENT. Hence, the third option is correct.

Correct Answer: NCYAMAI

Solution : Given:
TRAILER is written as RPYGJCP –

Subtract 2 from each letter of TRAILER to obtain the required code –
T – 2 = R; R – 2 = P; A – 2 = Y; I – 2 = G; L – 2 = J; E – 2 = C; R – 2 = P
Thus, TRAILER is coded as RPYGJCP.
Similarly, follow the same pattern for PEACOCK –
P – 2 = N; E – 2 = C; A – 2 = Y; C – 2 = A; O – 2 = M; C – 2 = A; K – 2 = I

So, PEACOCK is coded as NCYAMAI. Hence, the third option is correct. 

Correct Answer: $\frac{9}{4}$

Solution : $16 y^2-k=\left(4 y+\frac{3}{2}\right)\left(4 y-\frac{3}{2}\right)$
$⇒(4y)^2-k=(4y)^2-(\frac{3}{2})^2$
$⇒k=(\frac{3}{2})^2$
$\therefore k = \frac{9}{4}$
Hence, the correct answer is $\frac{9}{4}$.

Correct Answer: Nebular hypothesis

Solution : The correct answer is the Nebular hypothesis.

The prevailing model for planetary formation is the nebular hypothesis, suggesting that approximately 4.6 billion years ago, the Solar System originated from the gravitational collapse of a vast molecular cloud. This cloud, spanning several light-years, underwent a collapse, giving rise to numerous stars, including our sun.

Correct Answer: 32, 38

Solution : Given:
4, 6, 8, 12, 14, 18, 20, 24, 30, ?, ?

Add 1 to the consecutive prime numbers to get the terms of the given series.
3 + 1 = 4; 5 + 1 = 6; 7 + 1 = 8; 11 + 1 = 12; 13 + 1 = 14; 17 + 1 = 18; 19 + 1 = 20; 23 + 1 = 24; 29 + 1 = 30
The next prime numbers are 31, 37. Thus, the next terms→31 + 1 = 32; 37 + 1 = 38

So, 32 and 38 are the missing terms of the given series. Hence, the third option is correct.

Correct Answer: 246

Solution : Given:
46, 66, 94, 132, 182, ?

Follow the pattern to obtain the required missing number –

So, 246 is the required missing number in the series. Hence, the first option is correct.

Correct Answer: the moon comes between the Earth and the Sun

Solution : The correct option is the moon comes between the Earth and the Sun.

When the Moon comes in front of the Sun, it blocks some or all of the Sun's light from reaching the Earth, and a solar eclipse takes place. When a total solar eclipse occurs, the Sun is entirely obscured by the moon as seen from the Earth. The solar corona, or outer atmosphere of the Sun, comes into view.

Correct Answer:

Solution : According to the given figures –
1. The figure inside the box is rotating by 90° in a clockwise direction.
2. The triangle at the corner of the box is shifting its position corner by corner in a clockwise direction.
Therefore, the required figure is as follows –

Hence, the third option is correct.

Correct Answer: 286 cm^2,

Solution : The total surface area $A$ of a cuboid, where $l$ is the length, $b$ is the breadth, and $h$ is the height of the cuboid.
$A = 2(lb + bh + hl)$
Substituting $l$ = 7 cm, $b$ = 5 cm, and $h$ = 9 cm into the formula,
$A = 2(7 \times 5 + 5 \times 9 + 7 \times 9) = 2(35 + 45 + 63) = 2 \times 143 = 286 \, \text{cm}^2$
Hence, the correct answer is 286 cm².

Correct Answer: gullible

Solution : The correct choice is the fourth option.

Explanation: Gullible refers to someone who is easily tricked or manipulated, often due to being too trusting or naive.

The meanings of the other options are as follows:

• Plausible means seemingly reasonable or credible, but not necessarily true.
• Agreeable means willing to agree or please others.
• Credible means someone who is able to be believed or trusted.

Therefore, the correct answer is gullible.