Correct Answer: displaced

Solution : The right option is the first option.

Established implies being settled, well-founded, or having achieved success, while displaced means being removed, unsettled, or forced to leave a place, which is its antonym in this context.

So, the meanings of the other given words are:

• Fail means to be unsuccessful or to not achieve the desired objective.
• Gratified means to be pleased or satisfied as a result of achieving or fulfilling something.
• Pupil refers to a student or a learner, especially in a school or educational setting.

So, the most appropriate antonym of established is displaced.

Correct Answer: 3

Solution : Given: $\sqrt{11-3 \sqrt{8}}=a+b \sqrt{2}$
⇒ $\sqrt{11-3 \sqrt{2\times2\times2}}=a+b \sqrt{2}$
⇒ $\sqrt{9+2-2×3\sqrt{2}}=a+b \sqrt{2}$
⇒ $\sqrt{(3)^2+(\sqrt2)^2-2\times3\sqrt{2}}=a+b \sqrt{2}$
⇒ $\sqrt{(3-\sqrt{2})^2}=a+b \sqrt{2}$
⇒ $3-\sqrt{2}=a+b \sqrt{2}$
Comparing both sides, we get, $a=3,b=-1$
Now, $(2a+3b)$
= $(2\times3+3\times(-1))$
= $3$
Hence, the correct answer is 3.

Correct Answer: looking for his book

Solution : The correct choice is the third option.

In this context, looking for is the correct phrase to convey the idea of searching for his book. The preposition for is used with the verb looking to indicate the purpose or direction of the action whereas "looking into" means to investigate.

Therefore, the correct sentence is: He was looking for his book for the last two hours but couldn't find it.

Correct Answer: $\frac{5}{9}$th of the marked price

Solution : Let the marked price = $p$ and the cost price = $q$
According to the question,
∴ 50% of $p$ = 90% of $q$
⇒ $\frac{p×50}{100}=\frac{q×90}{100}$
∴ $q=\frac{5}{9}p$
So, the cost price is $\frac{5}{9}$th of the marked price.
Hence, the correct answer is $\frac{5}{9}$th of the marked price.

Correct Answer: diverted

Solution : The correct word to fill in the blank is the second option.

It means to change the direction or route of something. In the context of the sentence, "diverted" is the most suitable choice because it accurately conveys the idea that the flight's route was changed from its original destination (Jaipur) to Agra airport.

The meanings of the other options are as follows:

Shifted: It means moving or transferring something from one place to another.

Reverted: It means returning to a previous state or condition.

Deflected: It means changing the direction of something by turning it aside.

Therefore, the correct sentence is, "Our flight was diverted from Jaipur to Agra airport."

Correct Answer: 27

Solution : When 8961 is divided by 84, the quotient is 106, and the remainder is 57.
The required number which should be added = Divisor $-$ remainder
= 84 $-$ 57 = 27
Hence, the correct answer is 27.

Correct Answer: 27

Solution : $X\propto Y^2⇒ X = kY^2$
⇒ $\frac{\mathrm{X{_1}}}{\mathrm{Y^2{_1}}} = \frac{\mathrm{X{_2}}}{\mathrm{Y^2{_2}}} $
⇒ $\frac{12}{2^2} = \frac{\mathrm{X{_2}}}{3^2}$
⇒ $\mathrm{X{_2}} = \frac{12}{4}\times 9$
⇒ $\mathrm{X{_2}} = 27$
Hence, the correct answer is 27.

Correct Answer: 1800

Solution : 120 = 2 × 2 × 2 × 3 × 5
450 = 2 × 3 × 3 × 5 × 5
LCM of 120 and 450 is (2 × 2 × 2 × 3 × 3 × 5 × 5) = 1800
i.e. 1800 is the least common multiple of 120 and 450.
Hence, the correct answer is 1800.

Correct Answer: 1930

Solution : The correct option is - 1930

The Civil Disobedience Movement was launched by Mahatma Gandhi on April 6, 1930. This movement was a nonviolent protest against the British colonial government's salt monopoly and other oppressive policies. As part of the movement, Gandhi and his followers defied the Salt Laws by marching to the Arabian Sea to make their own salt. The movement aimed to exert economic and political pressure on the British authorities and played a significant role in India's struggle for independence.

Correct Answer: A Primary key is also a candidate key.

Solution : The correct answer is A Primary key is also a candidate key.

In a relational database, a candidate key is a set of one or more columns that can uniquely identify a row in a table. A primary key is a specific candidate key that is chosen to uniquely identify rows within a table.