Correct Answer: $64:25:49$

Solution : Given: $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}$
Let $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}=k$
$⇒A=3k,B=2k,C=5k$
Putting these values, we get,
$(C+A)^{2}:(A+B)^{2}:(B+C)^{2}$
$=(5k+3k)^{2}:(3k+2k)^{2}:(2k+5k)^{2}$
$=64k^{2}:25k^{2}:49k^{2}$
$=64:25:49$
Hence, the correct answer is $64:25:49$.

Correct Answer: Gautama

Solution : The correct answer is Gautama.

Gautama, who is also known as the author of the Nyaya Sutra, is said to have developed this school of thought. According to the Nyaya Sutra, there are four ways to gain valid knowledge: perception, inference, comparison, and verbal testimony.

Correct Answer: Atal Tunnel

Solution : The correct answer is Atal Tunnel.

The Atal Tunnel is built using ultra-modern techniques in the Pir Panjal range of the Himalayas at an elevation of 3000 metres above mean sea level. At an elevation of more than 10,000 feet, it is the world's

Correct Answer: shoulder

Solution : The right choice is the third option.

The most appropriate collocation word to fill in the blank is shoulder.

Shoulder in this context means to bear or take on responsibilities. It's a commonly used collocation when referring to assuming or handling duties or

Correct Answer: be scattered

Solution : The correct option is be scattered.

A strong beam of light is dispersed when it passes through a colloidal solution. The Tyndall effect was named after the 19th-century scientist John Tyndall, who first observed it. The Tyndall effect happens when light collides with colloidal

Correct Answer: Evocative

Solution : The correct choice is the second option.

Evocative is the synonym here because it means something that brings strong images, memories, or feelings to mind, which aligns well with the idea of painting a vivid picture through words.

The meanings of the other options are

Correct Answer: i-b, ii-a, iii-d, iv-c

Solution : The correct option is i-b, ii-a, iii-d, iv-c.

Chlorophyceae (Green Algae): Contains chlorophyll a and b, can be unicellular or multicellular, and is found in freshwater and marine environments.

Phaeophyceae (Brown Algae): large, multicellular seaweeds with brown colour due to fucoxanthin

Correct Answer: Silk

Solution : The correct option is Silk.

Silk is the strongest natural fibre. It is well-known for its high strength-to-weight ratio and flexibility.  Mulberry silk, which is generated from silkworms, is renowned for its strength and has been used for a variety of uses for ages.  Silkworm

Correct Answer: Union

Solution : The correct option is Union

The federal government retains the authority to form and supervise investigative bodies such as the Federal Bureau of Investigation despite the Seventh Schedule not particularly addressing these matters. Agencies like the CBI are regarded as being on the Union List

Correct Answer: $\frac{1-\sqrt{3}}{2}$

Solution : $\theta=135^{\circ}$
$y=15^{\circ}$
$2 \cos (\theta) \sin (y)$
= $2 \cos (135^{\circ}) \sin (15^{\circ})$
= $2 \cos (180^{\circ}-45^{\circ}) \sin (45^{\circ}-30^{\circ})$
= $2$ × $[-\cos45^{\circ}]$ × $[ \sin (45^{\circ})\cos(30^{\circ})-\cos (45^{\circ})\sin(30^{\circ})]$
= $2$ × $[ -\frac{1}{\sqrt2}]$ × $[ \frac{1}{\sqrt2}×\frac{\sqrt3}{2}-\frac{1}{\sqrt2}×\frac{1}{2}]$
= $2$ × $[-\frac{1}{\sqrt2}]$ × $[\frac{\sqrt3-1}{2\sqrt2}]$
= $\frac{1-\sqrt3}{2}$
Hence,