Correct Answer: 21

Solution : Given: The numbers are 8, 12, and 14.
Let the fourth proportion be $x$.
So, $8:12::14:x$
⇒ $\frac{8}{12} = \frac{14}{x}$
⇒ $x = \frac{14 \times 12}{8}=21$
Hence, the correct answer is 21.

Correct Answer: Monotonous

Solution : The correct choice is the fourth option.

Monotonous means lacking in variety and interest, being repetitive and dull, which precisely describes the concept of never changing and being boring.

The meanings of other options are as follows:

• Outdated: This term refers to something that is no longer current or fashionable.

• Impractical: This word describes something that is not useful or effective in practice.

• Idealistic: It refers to having high moral or ethical principles.

Therefore, the correct one-word substitute is monotonous.

Correct Answer: (2)

Solution : The correct choice is the second option.

Explanation:

"Both of which are" is the most appropriate choice for the context, providing a clear and idiomatic way to express the idea that both Apple and IBM are in the computer business.

So, the correct sentence would be: "Two of the biggest corporate firms in the world are Apple and IBM, both of which are in the computer business."

Correct Answer: 18 sec

Solution : Distance = length of train = 180 m
Speed of train = 20 m/s
Speed of main = 10 m/s
The direction of both the train and the man is the same.
So, relative speed = 20 - 10 = 10 m/s
Required time = $\frac{180}{10}$ = 18 sec.
Hence, the correct answer is 18 sec.

Correct Answer: 16 cm

Solution : If two triangles are similar, then their perimeters are directly proportional to the length of their corresponding sides.
So, $\frac{\text{Perimeter of $\triangle$ABC}}{\text{Perimeter of $\triangle$ABC}}= \frac{AB}{DE} = \frac{32}{12}$
⇒ $AB = \frac{32}{12}\times 6$
⇒ $AB = 16\ \mathrm{cm}$
Hence, the correct answer is 16 cm.

Correct Answer: 2

Solution : Given: $a+\frac{1}{a-2}=4$
Subtracting 2 from both sides,
⇒ $a-2+\frac{1}{a-2}=2$
Squaring both sides,
⇒ $( a-2)^2+\frac{1}{( a-2)^2} + 2=2^2$
⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2^2-2$
⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2$
Hence, the correct answer is 2.

Correct Answer: Odisha

Solution : The correct option is Odisha.

One of India's biggest steel production sites is the Rourkela Steel Plant. It is located in the city of Rourkela in the Sundargarh district of Odisha. One of India's earliest integrated steel factories, the Rourkela Steel Plant was founded in 1959. It was a significant step toward India's industrialisation and self-sufficiency in steel production. Steel Authority of India Limited (SAIL), is the owner and operator of the plant.

Correct Answer: 217.50 m

Solution : In 1500 m race, Anil beats Bakul by 150 m.
When Anil completes the race, Bakul covers 1500 – 150 = 1350 m
Bakul beats Charles by 75 m in 1500 m race.
So in a 1350 m race, Bakul is ahead of Charles by $\frac{75}{1500}\times 1350=67.50$ m
So, Anil beats Charles by (150 + 67.5) = 217.50 m
Hence, the correct answer is 217.50 m.

Correct Answer: May success be achieved by you in all your endeavours.

Solution : The correct choice is the third option.

Explanation:
In a passive voice construction, the subject of the sentence receives the action, and the focus is on the action rather than the doer.
The verb "achieve" becomes "be achieved" (to be + past participle).
The subject "you" becomes the agent in the passive voice construction and is placed at the end of the sentence with "by you."
The passive construction shifts the focus from the doer (you) to the action (success being achieved).

Therefore, the passive voice would be: May success be achieved by you in all your endeavours.

Correct Answer: 9

Solution : Given: $4x^2-12x+k$ is a perfect square.
$4x^2-12x+k=(2x)^2-2×2x×3+k$
Since this a perfect,
So, $(2x)^2-2×2x×3+k=(2x)^2-2×2x×3+3^2=(2x–3)^2$
Value of $k$ is 3² = 9
Hence, the correct answer is 9.