Correct Answer: uncontrolled fusion reaction

Solution : The correct answer is uncontrolled fusion reaction.

The theory of uncontrolled nuclear fusion underpins a hydrogen bomb. The process by which the nuclei of two light atoms join to generate a new nucleus is known as nuclear fusion.

Correct Answer: Rs. 10,500

Solution : Given, Sum= Rs. 15500
Rate of interest (r) = 30% per annum
Time (t) = 7 years
Let the principal be P.
⇒ [P + (simple interest)] = sum
⇒ [P + $\frac{\text{Prt}}{100}$] = sum
⇒ [P + $\frac{\text{P} × 30 × 7}{100}$] = 15500
⇒ [P + $\frac{\text{P} × 210}{100}$] = 15500
⇒ [P + $\frac{\text{21P}}{10}$] = 15500
⇒ $\frac{31\text{P}}{10}$ = 15500
⇒ P = $15500 × \frac{10}{31}$
⇒ P = 5000
Simple interest = 15500 – 5000 = Rs. 10500
Hence, the correct answer is Rs. 10500.

Correct Answer: INR 28,335

Solution : Let the cost price of the dishwater and vacuum cleaner be INR $y$ and INR $x$, respectively.
Total cost price of a dishwasher and a vacuum cleaner = INR 78,750
$x$ + $y$ = $78750$-------------------(i)
Profit of vacuum cleaner = 37% of $x$ = $0.37x$
Selling price of vacuum cleaner = $x$ + $0.37x$ = $1.37x$
Also, the loss of dishwasher = 23% of $y$ = $0.23y$
So, selling price of dishwasher = $y$ – $0.23y$ = $0.77y$
Since both have the same selling price,
⇒ $1.37x = 0.77y$
From equation (i),
⇒ $1.37(78750-y) = 0.77y$
⇒ $2.14y =107887.5$
⇒ $y$ = INR $50414.7 $
So, $x=78750-y= 78750-50414.7=28335.3$ = INR 28,335 approx
⇒ Since the vacuum cleaner is less expensive than the dishwasher.
Hence, the correct answer is INR 28,335.

Correct Answer: $9\frac{3}{5}$ days

Solution : Time taken by $x$ to complete $\frac{1}{4}$ of a job = 6 days
Time taken by $x$ to complete whole work = 6 × 4 = 24 days
Part of work done by $x$ in a day = $\frac{1}{24}$
Time taken by $y$ to complete $\frac{3}{4}$ of a job = 12 days
Time taken by $y$ to complete whole work = $\frac{12 × 4}{3}$ = 16 days
Part of work done by $y$ in a day = $\frac{1}{16}$
Part of work done by $x$ and $y$ in a day = $\frac{1}{24}$ + $\frac{1}{16}$ = $\frac{4 + 6}{96}$ = $\frac{10}{96}$
Time taken by $x$ and $y$ together to complete whole work = $\frac{96}{10}$ = $9\frac{3}{5}$ days
Hence, the correct answer is $9\frac{3}{5}$ days.

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.