Correct Answer: Rukmini Devi Arundale

Solution : The correct answer is Rukmini Devi Arundale.

Kalakshetra Foundation, formerly known as Kalakshetra, is an esteemed arts and cultural academy situated in Chennai, India. Established in January 1936 by Rukmini Devi Arundale and George Arundale, the foundation is devoted to preserving traditional values in Indian art and crafts, particularly in Bharatanatyam dance and Gandharva Veda music. Recognising its significance, an Act of the Parliament of India in January 1994 designated the Kalakshetra Foundation as an "Institute of National Importance".

Correct Answer: Industrial sector

Solution : The correct answer is the Industrial sector.

There are three sectors: primary (the agriculture sector), secondary (the industrial sector) and tertiary (the transport sector). The industrial sector falls under the secondary sector. It is called so because this sector contributes the most to the tax payment structure. The film industry, information technology, etc. come under this category. This sector plays a major role in the development of India's GDP growth.

Correct Answer: Calm

Solution : Given:
Worried : Anxious :: At ease : ?

Like, Worried and Anxious are synonyms of each other.
Similarly, At ease means free from worry, or relaxed. So, from the options, Calm is the synonym for At ease.

Hence, the second option is correct.

Correct Answer: (25, 8, 41)

Solution : Given:
(23, 6, 35) (13, 5, 23)

In the given set of numbers, multiply 2 by the second number and then add the first number to get the third number.
(23, 6, 35)→6 × 2 = 12 + 23 = 35
(13, 5, 23)→5 × 2 = 10 + 13 = 23
Let's check each option –
First option: (24, 5, 33)→5 × 2 = 10; 10 + 24 = 34 ≠ 33
Second option: (16, 4, 20)→4 × 2 = 8; 8 + 16 = 24 ≠ 20
Third option: (25, 8, 41)→8 × 2 = 16; 16 + 25 = 41
Fourth option: (13, 7, 28)→7 × 2 = 14; 14 + 13 = 27 ≠ 28

So, (25, 8, 41) follows the same pattern. Hence, the third option is correct.

Correct Answer: Cenozoic

Solution : The correct answer is Cenozoic.

The Cenozoic era is also known as the "age of mammals". The Cenozoic era began approximately 66 million years ago and continues to the present day. It is characterised by the dominance and diversification of mammalian life forms, including the evolution of various orders and families of mammals that exist today.

Correct Answer: $1$

Solution : The given equation is $k\left(\tan 45^{\circ} \sin 60^{\circ}\right)=\cos 60^{\circ} \cot 30^{\circ}$.
$⇒k\left(1 \times \frac{\sqrt{3}}{2}\right) = \frac{1}{2} \times \sqrt{3}$
$⇒k = \frac{\frac{1}{2} \times \sqrt{3}}{\frac{\sqrt{3}}{2}} = \frac{1}{2} \times \frac{2}{\sqrt{3}} \times \sqrt{3} = 1$
Hence, the correct answer is $1$.

Correct Answer: The sun is shining while it rains

Solution : The third option is the correct answer.

This idiom is a regional expression used to describe a weather phenomenon where it is raining while the sun is shining. The phrase, the devil is beating his wife is a colloquial way of referring to this specific weather condition. It's a folk saying that doesn't have a literal meaning but is used to describe the simultaneous occurrence of rain and sunshine.

Therefore, the correct answer is: The sun is shining while it rains.

Correct Answer: 6 km

Solution : Let $x$ be the required distance.
Time taken in the first case = $\frac{x}{3}$ hours
Time taken in the second case = $\frac{x}{4}$ hours
Time difference = $\frac{x}{3} - \frac{x}{4}$ hours
So, $\frac{x}{3} - \frac{x}{4}$ = $\frac{(20+10)}{60}$
⇒ $\frac{x}{12}$ = $\frac{1}{2}$
⇒ $x$ = 6 km
Hence, the correct answer is 6 km.

Correct Answer: very intimate terms

Solution : The correct choice will be the first option.

The idiom hand in glove means to be in a very close or friendly association or partnership with someone. It suggests a relationship where individuals work closely together, cooperate seamlessly or share a strong connection.

For example, if two colleagues are said to be hand in glove, it implies that they work closely together, coordinating their efforts seamlessly.

Therefore, the answer will be very intimate terms.

Correct Answer: Sachin Tendulkar

Solution : The correct option is Sachin Tendulkar

"Playing It My Way" is the autobiography of the former Indian cricketer Sachin Tendulkar. The book, co-authored with Boria Majumdar, was published in 2014 and provides insights into Tendulkar's life, cricket career, and personal experiences. Tendulkar shares anecdotes and behind-the-scenes stories from his cricketing career in the autobiography.