It's a Question of your Career!

Correct Answer: 1 km/h

Solution : Suppose he moves 4 km downstream in $x$ hours.
⇒ Speed downstream =$\frac{4}{x}$ km/hr
And, speed upstream =$\frac{3}{x}$ km/hr
According to the question,
$\frac{48}{\frac{4}{x}}+\frac{48}{\frac{3}{x}}=14$
⇒ $\frac{48x}{4}+\frac{48x}{3}=14$
⇒ $\frac{144x+192x}{12}=14$
⇒ $336x=168$
⇒ $x=\frac{168}{336}=\frac{1}{2}$
⇒ Speed downstream = 8 km/hr
And, speed upstream = 6 km/hr.

Correct Answer: 0

Solution : Given:
$x= {\frac{1}{\sqrt{2}+1}}$
Rationalising the denominator, we get,
⇒ $x ={\frac{{\sqrt{2}-1}}{(\sqrt{2}+1)×{(\sqrt{2}-1)}}}=\frac{\sqrt{2}-1}{2-1} = {\sqrt{2}-1}$
Putting this value in the expression $(x^{2}+2x-1)$, we get,
$=[(\sqrt{2}-1)^{2}+2(\sqrt{2}-1)-1]$
$=2-2\sqrt{2}+1+2\sqrt{2}-2-1 $
$= 0$
Hence, the correct answer is 0.

Correct Answer: $1 : 2$

Solution :
Given:
$\angle$ABC = 90°, AB = BC
In $\triangle$ABC, AC² = AB² + BC² = AB² + AB² = 2AB²
Since, $\triangle$ACD $\sim$ $\triangle$ABE,
$\frac{\text{area of} \triangle ABE}{\text{area of} \triangle ACD}=\frac{AB^2}{AC^2}$
⇒ $\frac{\text{area of} \triangle ABE}{\text{area of}

Correct Answer: Rush

Solution : The first option is the correct choice.

Bustle refers to a lot of energetic and noisy activity, often associated with movement and hurry. Rush has a similar meaning, conveying the idea of moving hurriedly and with great activity.

The meanings of the other options are

Correct Answer: ÷, +, ÷, +, =

Solution : Given:
12 * 4 * 15 * 3 * 16 * 24

Replace * with the mathematical signs and solve the equations one by one using BODMAS.
Let's check the given options –
First option: +, –, ÷, ×, =
⇒

Correct Answer: 6

Solution : $6 \cot \theta = 5$
⇒ $\cot \theta = \frac{5}{6}$
Now, $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos \theta-4\sin \theta)}$
Dividing numerator and denominator by $\sin \theta$ in the above expression
⇒ $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos \theta-4\sin \theta)}=\frac{(6\cot \theta + 1)}{(6\cot \theta-4)}$
$=\frac{6 \times \frac{5}{6} +

Correct Answer: $\sqrt{2}+1$

Solution : Given: The expression is $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}$.
Take $\sqrt2$ common in the term $\frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}$, we get,
$\frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}=\frac{\sqrt2}{\sqrt2}\times\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}}=\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}}$
The expression can be written as $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \div\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} +\frac{\sqrt{10}}{\sqrt{5}}$
= $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \times\frac{\sqrt{7}–\sqrt{5}}{\sqrt{7}+\sqrt{5}} +\frac{\sqrt{10}}{\sqrt{5}}$
= $1+\sqrt2$
= ${\sqrt{2}}+1$
Hence, the correct answer is ${\sqrt{2}}+1$.

Correct Answer: The Littoral Zone

Solution : The correct option is The Littoral Zone.

The Littoral Zone is a region of the sea that is characterised by an abundance of dissolved oxygen, sunlight, nutrients, high wave energies and water motion. The intertidal subzone of the Littoral Zone experiences tidal

Correct Answer: 144

Solution : Given:
16 : 45 :: 36 : 105 :: 49 : ?

Like, 16 : 45→(16 × 3) – 3 = 48 – 3 = 45
36 : 105→(36 × 3) – 3 = 108 – 3 = 105
Similarly, for 49 : ?→(49 ×

Correct Answer: Eratosthenese

Solution : The correct answer is Erastothenese.

Erastothenese was a Greek astronomer, mathematician and philosopher. He was the first to used the word geography which meant Earth writing in Greek. He is also known as father of geography. He invented the system of latitudes and longitudes and