It's a Question of your Career!

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: Tropical evergreen forests

Solution : The correct answer is Tropical evergreen forests

Tropical evergreen forests are prevalent in areas characterised by consistently high temperatures and abundant rainfall. These ecosystems, often referred to as rainforests, support a diverse array of plant and animal life. Among the notable flora found in tropical evergreen forests are commercially valuable trees such as ebony, mahogany, rosewood, rubber, and cinchona.

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: 4 hours

Solution : P can fill a tank in 5 hours.
Q can fill the same tank in 10 hours.
R can empty the same tank in 20 hours.
P's per hour efficiency = $\frac{1}{5}$
Q's per hour efficiency = $\frac{1}{10}$
R's per hour efficiency = $- \frac{1}{20}$ (negative because it is emptying the tank)
Total efficiency of P, Q, and R working together = $\frac{1}{5} + \frac{1}{10} − \frac{1}{20}$ = $\frac{5}{20}$ = $\frac{1}{4}$
$\therefore$ Together they will take 4 hours to fill the tank.
Hence, the correct answer is 4 hours.

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.

Correct Answer: To admit that one is wrong

Solution : The correct choice is the fourth option.

Explanation: To eat crow originated from a time when eating a crow (a scavenging bird) was considered a humiliating act. So, figuratively, it means admitting a mistake or being forced to accept a humiliating situation.

Correct Answer: Nil

Solution : Let the amount deposited in the bank and post office be Rs. $x$ and Rs. $(300000-x)$ respectively.
We know, interest = $\frac{PRT}{100}$, where $P$ is principal, and $R$ is the rate of interest per annum for $T$ years.
So, Interest gained from a 10% interest rate from Rs. $x$ in a year = Rs. $0.1x$
And Interest gained from a 6% interest rate from Rs. 3 Lacs in a year = Rs. $0.06(300000-x)$
Given, 1 month of interest income = 2000
So, 1 year interest income = 2000(12)= Rs. 24,000
Now, Total interest in a year = Interest from the bank + Interest from the post office
⇒ $24000 = 0.06(300000-x) + 0.1x$
⇒ $24000-18000 = 0.04x$
⇒ $x = 1,50,000$
⇒ $(300000 - x) = 1,50,000$
So, the Amount deposited = Rs. $1,50,000$ each
and difference = 0
Hence, the correct answer is 'Nil'.