Correct Answer: at the station, it take

Solution : The segment that contains a grammatical error is the second option.

Explanation: The error lies in the tense consistency as per zero conditional. The correct form should be "it took" instead of "it take". In this context, took is the correct verb form to indicate that the action took place in the past as the subordinate clause is also in the past tense to maintain tense consistency.

So, the correct sentence would be: "When the train pulled in at the station, it takes Joseph some time to get off."

Correct Answer: $4\sqrt{3}\ \text{cm}$

Solution : Given: Side of the equilateral triangle = 12 cm
We know that,
The radius of a circle circumscribing in an equilateral triangle
= $\frac{\text{side}}{\sqrt3}$
= $\frac{12}{\sqrt3}$
= $4\sqrt3\ \text{cm}$
Hence, the correct answer is $4\sqrt3\ \text{cm}$.

Correct Answer:

Solution : In a 3D view of dice,
1. Each face out of the three faces in the 3D view should be from all the pairs.
2. Two opposite faces cannot appear adjacently in the 3D view of a folded cube figure. So, the opposite pairs of faces are as follows –

Based on the above diagram and rules, the following image can be formed –

Hence, the first option is correct.

Correct Answer: To be forced to use one's last and weakest resource

Solution : The correct choice is the fourth option.

The idiom, scrape the barrel is used when you've exhausted all other options and have to resort to your last and often less favourable choice or resource. It's not about trying to find something, hiding something, or using all possible ways; it's specifically about using your last and weakest resource.

Correct Answer: a-b-c-d

Solution : The correct option is a-b-c-d.

In 2021–22, neighbouring countries of India are arranged according to their Human Development Index (HDI) ranking:

a) Sri Lanka holds the highest HDI rank (73) with a value of 0.782, reflecting high development status.

b) The Maldives ranked second (90) with an HDI value of 0.747, also categorised under high development.

c) Bhutan follows (127) with an HDI value of 0.666, categorised under medium human development.

d) Bangladesh ranked lowest (129) with an HDI value of 0.661, also categorised under medium human development.

Correct Answer: Aggravate

Solution : The right option is the third option.

Pacify means to calm or soothe, while aggravate means to worsen or intensify a situation, making it the antonym in this context.

The meanings of other words are:

• Placate: This means to make someone less angry or hostile by making concessions or soothing gestures; to appease or calm.
• Assuage: This means to ease or alleviate a problem, discomfort, or pain; to make something less intense or severe.
• Quell: This means to suppress, pacify, or put an end to something, especially by using force or authority

Correct Answer: Justice Ashok Bhushan

Solution : The correct option is Justice Ashok Bhushan.

Justice Ashok Bhushan, a former Supreme Court judge, was appointed as the new Chairperson of the National Company Law Appellate Tribunal (NCLAT) on November 8, 2021. His tenure is set for four years or until he reaches the age of 70, whichever comes first.

Correct Answer: $\sec 3 \theta - \tan 3 \theta$

Solution : $\sqrt{\frac{1 – \sin 3 \theta}{1 + \sin 3 \theta}}$
= $\sqrt{\frac{(1 – \sin 3 \theta)(1 – \sin 3\theta)}{(1 + \sin 3\theta)(1 – \sin 3\theta)}}$
= $\sqrt{\frac{(1 – \sin 3\theta)^{2}}{1 – \sin^{2}3\theta}}$
= $\sqrt{\frac{(1 – \sin 3\theta)^{2}}{\cos^{2}3\theta}}$
= $\frac{1 - \sin 3\theta}{\cos 3\theta}$
= $\sec 3\theta  - \tan 3\theta$
Hence, the correct answer is $\sec 3\theta  - \tan 3\theta$.

Correct Answer: 1

Solution : Given: $\left (x+\frac{1}{x} \right)=5$
⇒ $\frac{x^2+1}{x}=5$
⇒ $x^2+1=5x$
Adding $x$ on both sides,
⇒ $x^2+1+x=5x+x$
⇒ $x^2+x+1=6x$
Now, put the value of $x^2+x+1=6x$ in the expression $\frac{6x}{x^{2}+x+1}$
So, $\frac{6x}{x^{2}+x+1}=\frac{6x}{6x}=1$
Hence, the correct answer is 1.

Correct Answer: $\frac{92}{11}\ \text{hours}$

Solution : Let the capacity of the tank be 120 units (LCM of 15, 20, and 40)
Pipe A fills = $\frac{120}{15}$ = 8 units per hour
Pipe B fills = $\frac{120}{15}$ = 6 units per hour
Pipe C empties = $\frac{120}{40}$ = 3 units per hour
A and B in 2 hours fill (8 + 6) × 2 units of the tank = 28 units of the tank
Remaining units of the tank to be filled = 120 – 28 = 92 units/hour
After 2 hours, C joins.
So, units of the tank filled by A, B, and C = (8 + 6 – 3) = 11 units/hour
So, the time needed to fill the remaining tank = $\frac{92}{11}$ hours
Hence, the correct answer is $\frac{92}{11}\ \text{hours}$.