Correct Answer: $\frac{135}{7}$

Solution : Let the upstream speed be $x$ km/hr and the downstream speed be $y$ km/hr.
A boat goes 2 km upstream and 3 km downstream in 20 minutes.
According to the question,
$\frac{2}{x} + \frac{3}{y} = \frac{20}{60}$
⇒ $\frac{120}{x} + \frac{180}{y} =20$
⇒ $\frac{240}{x} + \frac{360}{y} = 40$ ............................ (1) [Multiplying by 2 on both sides]
The boat goes 7 km upstream and 2 km downstream in 53 minutes.
According to the question,
$\frac{7}x + \frac{2}y = \frac{53}{60}$
⇒ $\frac{420}{x} + \frac{120}{y} = 53$
⇒ $\frac{1260}{x} + \frac{360}{y} = 159$ ........ (2) [Multiplying by 3 on both sides]
Applying (2) – (1) we get,
$\frac{1260}{x} – \frac{240}{x} = 159 – 40$
⇒ $\frac{1020}{x} = 119$
⇒ $x = \frac{1020}{119}$
$\therefore x = \frac{60}{7}$
Putting the value of $x$ in (1), we get,
$240 \times (\frac{7}{60}) + \frac{360}{y} = 40$
⇒ $\frac{360}{y} = 40 – 28$
⇒ $\frac{360}{y} = 12$
⇒ $y = \frac{360}{12}$
$\therefore y = 30$
$\therefore$ Upstream speed = $\frac{60}{7}$ km/h and downstream speed = 30 km/hr
$\therefore$ Speed of the boat in still water =$\frac{ [\frac{60}{7}+ 30]}{2}$ = $\frac{270}{14}$ km/h = $\frac{135}{7}$ km/hr
Hence, the correct answer is $\frac{135}{7}$ km/hr.

Correct Answer: Russia

Solution : The correct answer is Russia.

Russia is the leading producer and exporter of Diamonds in the world. It has the world's richest diamond reserves. Russia, Botswana, and Canada are the top 3 diamond-producing countries in the world. India is the 4th largest producer of Iron Ore in the world. The USA has the largest gold mines in the world, followed by Germany, and Italy. While Peru, China, and Poland have the highest silver reserves.

Correct Answer: zt

Solution : Given:
1. Live long⇒mu ae
2. Road is long⇒ae si du
3. Game is live⇒si mu zt

By comparing all the coded sentences, we find that –
In sentences 1 and 2, long is a common word and ae is a common code.
In sentences 2 and 3, is is a common word and si is a common code.
In sentences 1 and 3, live is a common word and mu is a common code.
The remaining words and codes in sentence 2 are Road and du, sentence 3 are Game and zt.
Finally, long ⇒ ae; is ⇒ si, live ⇒ mu, Road ⇒ du, Game ⇒ zt

So, Game will be coded as zt. Hence, the third option is correct.

Correct Answer: 2, 3, 1, 4

Solution : Given:
1. Centre 2. Center 3. Central 4. Centrum

Step 1: Compare the first letter of each word. Since all the words start with the same letter C, then move on to the next letter.
Step 2: The second, third, and fourth letters of each word are the same, i.e., e, n, and t. So, move on to the next letter. 
Step 3: The fifth letter of each word is either r or e. Based on the alphabetical order of these letters, we can arrange them – Center, Centre, Central, Centrum
Step 4: Compare the sixth letter of (Centre, Central, Centrum). Central will come before Centre and Centrum in the sequence as a comes before e, and u in the alphabetical system. Similarly, Centre will come before Centrum as e comes before u.

So, the sequence is Center, Central, Centre, Centrum, or 2, 3, 1, 4. Hence, the fourth option is correct.

Correct Answer: 60

Solution : Factors of 960 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5
Factors of 1020 = 2 × 2 × 3 × 5 × 17
$\therefore$ HCF of 960 and 1020 = 2 × 2 × 3 × 5 = 60
Hence, the correct answer is 60.

Correct Answer: Ernst Mayr

Solution : The correct option is Ernst Mayr.

German-American biologist, ornithologist, and science historian Ernst Mayr (1904–2005) made important contributions to the disciplines of evolutionary biology and biology philosophy. He was instrumental in the contemporary synthesis of evolutionary theory, which combined Mendelian genetics and Darwinian natural selection.

Correct Answer: Sarangi

Solution : The correct answer is Sarangi.

Ustad Khan was an Indian Sarangi player and also a classical vocalist from Sikar Gharana. He was also awarded the third highest civilian award, Padma Bhushan, by the government of India in 2010, and he died in 2011.

Correct Answer: 11

Solution : Given:
144 C 8 B 20 A 81 D 3 = ?

After replacing the letters with the mathematical signs, we get –
= 144 – 8 × 20 + 81 ÷ 3
= 144 – 8 × 20 + 27
= 144 – 160 + 27
= 11

So, 11 is the answer to the given equation. Hence, the second option is correct.

Correct Answer: –3

Solution : Given: $\left(5 \sqrt{5} x^3-3 \sqrt{3} y^3\right) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$
⇒ $\frac{(5 \sqrt{5} x^3-3 \sqrt{3} y^3)}{(\sqrt{5} x-\sqrt{3} y)}=\left(A x^2+B y^2+C x y\right)$
⇒ $\frac{(x\sqrt{5})^3-(y\sqrt{3})^3)}{(\sqrt{5} x-\sqrt{3} y)}=(A x^2+B y^2+C x y)$
⇒ $\frac{(\sqrt{5}x-\sqrt{3}y)(5x^2+\sqrt{15}xy+3y^2)}{(\sqrt{5} x-\sqrt{3} y)}=(A x^2+B y^2+C x y)$
⇒ $5x^2+\sqrt{15}xy+3y^2=A x^2+B y^2+C x y$
On comparing,
⇒ $A=5$
⇒ $B=3$
⇒ $C=\sqrt{15}$
Now, $(3 A-B-\sqrt{15} C)$
Putting the values, we get:
= $(3\times5-3-\sqrt{15}\times\sqrt{15})$
= $(15-3-15)$
= –3
Hence, the correct answer is –3.

Correct Answer: $8\sqrt{30}$ cm²

Solution : Let the sides of the triangle be $a$, $b$, and $c$.
Given Perimeter = 32 cm
⇒ $a+b+c=32$ ...... equation (1)
One side, let $a$ =11 cm
Also, the difference between the other two sides, $b−c=5$........ equation (2)
Performing equation (1) + equation (2)
$a+2b=37$
⇒ $11+2b=37$
⇒ $2b=26$
⇒ $b=13$ cm
Now, using equation (2),
$c=b−5$
⇒ $c=13−5=8$ cm
Area of the triangle according to Heron's formula = $\sqrt{s(s−a)(s−b)(s−c)}$ where $s$ is the semi-perimeter
$s=\frac{11+13+8}{2} = 16$ cm
Area $= \sqrt{16(16−11)(16−13)(16−8)}$
$= \sqrt{16(5)(3)(8)}$
$= 8\sqrt{30}$ cm²
Hence, the correct answer is $8\sqrt{30}$ cm².