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: ÷, +, ÷, +, =

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: $\sqrt{2}+1$

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: 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

Correct Answer: 182

Solution : Given:
382, 322, 272, 232, 202, ?

Subtract the multiples of 10 (in decreasing order), starting from 60 from the previous number to obtain the following number of the series.
382 – 60 = 322; 322 – 50 = 272; 272 – 40 = 232;

Correct Answer: Chandragupta II

Solution : The correct answer is Chandragupta II.

Chandragupta II, who was famously called Chandragupta Vikramaditya, served as a Gupta emperor. His royal assembly boasted the esteemed presence of both Aryabhata and Kalidasa. Among the nine pearls of Chandragupta's court was the celebrated Sanskrit writer Kalidasa.

Correct Answer: Dr. Kanak Rele

Solution : The correct answer is Dr. Kanak Rele.

Kanak Rele was a prominent Indian dancer, choreographer, and academic renowned for her expertise in Mohiniyattam. She gained recognition not only for her contributions as a performer but also for her role as an advisor on

Correct Answer: violations

Solution : The correct choice is the fourth option.

Explanation:

In the context of the sentence, the blank describes the range of activities or issues that NGOs address. The word that best fits in this context is violations. This term can encompass a broad spectrum of

Correct Answer: 2

Solution : The sentence can be improved using the second option.

The phrase "how to think out of the box" is the correct and idiomatic expression. "Out of the box" is an established idiom that means thinking in an innovative, creative, or unconventional way. The correct form