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The correct answer is Emiliano Martínez

Key Points

• Emiliano Martinez, the acclaimed goalkeeper who played a crucial role in Argentina's World Cup triumph in Qatar, arrived at Kolkata's Netaji Subhas Chandra Bose International Airport to an exuberant reception from passionate supporters.

Given:

We need to find the largest number that divides 303 and 207 and leaves remainders of 3 in both cases.

Concept:

To find the largest number that divides two numbers and leaves the same remainder, we first subtract the remainder from each number and then find the greatest common divisor (GCD) of the resulting numbers.

Calculation:

We have,

⇒ 303 - 3 = 300

⇒ 207 - 3 = 204

Now, we find the GCD of 300 and 204.

Prime factorization:

⇒ 300 = 2² × 3 × 5²

⇒ 204 = 2² × 3 × 17

The common factors are 2² × 3.

Hence, GCD = 2² × 3 = 4 × 3 = 12

∴ The largest number that divides 303 and 207 and leaves remainders of 3 in both cases is 12.

The correct answer is Amir Khusharu.

Key Points

• Amir Khusro, also known as Abul Hasan Yaminuddin Khusro, was an Indo-Persian Sufi singer, musician, poet, and scholar who flourished under the Delhi Sultanate.
• He is a legendary person in the Indian subcontinent's cultural history.
• He was a mystic and spiritual follower of Delhi"s Nizamuddin Auliya.
• He mostly wrote poetry in Persian, although he also wrote in Hindavi.
• Khusrau is known as the "Voice of India" or the "Parrot of India," and has been dubbed the "Father of Urdu Literature."

Additional Information The Navratnas of Akbar were as follows-

• Raja Birbal- Foreign Minister
• Miyan Tansen- Culture Minister
• Abul Fazal- Prime Minister
• Faizi- Education Minister
• Raja Man Singh- Chief of Staff of Mughal Army
• Raja Todar Mal- Finance Minister
• Mullah Do Piyaza- Home Minister
• Fakir Aziao-Din- Religious Minister
• Abdul Rahim Khan-I-Khana- Defence Minister

The correct answer is ​Bal Gangadhar Tilak

Key Points

• Kesari is a Marathi newspaper which was founded on 4 January 1881 by Lokmanya Bal Gangadhar Tilak, a prominent leader of the Indian Independence movement.
• The newspaper was used as a spokespiece for the Indian national freedom movement, and continues to be published by the Kesari Maratha Trust and Tilak's descendants.
• Bal Gangadhar Tilak used to run his two newspapers, Kesari, in Marathi and Mahratta in English from Kesari Wada, Narayan Peth, Pune.

Additional Information 

• The editors of Kesari included a number of freedom fighters and social activists / reformers, including Agarkar (its first editor), Chiplunkar and Tilak.
• Agarkar left Kesari in 1887 to start his own news paper, Sudharak (The Reformer) after which Tilak continued to run the paper on his own.
• Narasimha Chintaman Kelkar, a close associate of Tilak, served as editor twice when Tilak was imprisoned in 1897 and 1908.

Given:

a + 2b = 5 and a2 + 4b2 = 13

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

We have,

a + 2b = 5

On squaring both sides,

(a + 2b)² = 5²

⇒ a2 + 4b2 + 2 × a × 2b = 25

⇒ a2 + 4b2 + 4ab = 25

⇒ 13 + 4ab = 25

⇒ 4ab = 25 - 13 = 12

⇒ ab = 12/4 = 3

Hence, ab = 3

The logic followed here is:

→√64 + √25 + √144 + √36 = 8 + 5 + 12 + 6 = 31

→√81 + √9 + √25 + √361 = 9 + 3 + 5 + 19 = 36

→ √49 + √169 + √36 + √81 = 7 + 13 + 6 + 9 = 35

Hence the correct answer is Option 2:35

The correct answer is 1556.

Key Points

• The Second Battle of Panipat took place on 5^th November 1556, between the emperor of north India, Hemu, and the forces of the Mughal emperor Akbar.
• On January 24, 1556, the Mughal ruler Humanyun died in Delhi and was succeeded by his son, Akbar at Kalanaur, who was only thirteen years old.
• Akbar and his guardian Bairam Khan did not participate in the battle and were stationed 8 miles away from the war zone.
• The 13 year old child King was not permitted to be present on the battlefield in person, instead he was provided with a special guard of 5000 well trained and most faithful troops and was stationed at a safe distance far behind the battle lines.
• The Mughal Vanguard consisted of 10,000 cavalry, out of which 5000 were experienced veteran soldiers and were ready to meet the advancing army of Hemu.
• Hemu led his army himself and his army consisted of 1500 war elephants and a vanguard of artillery.
• Hemu marched in excellent order with 30,000 practiced horsemen composed of Rajputs and Afghans.
• But Hemu died in this battle and his army was in disarray and defeated in the ensuing confusion.

Additional Information

• The First Battle of Panipat was fought on April 21, 1526, between the forces of Babur and Ibrahim Lodhi.
• The Third Battle of Panipat was fought on 14^th January 1761 between the Marathas and the Durrani Empire (Afghanistan).

The logic followed here is:

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Hence, the correct answer is "159".

Given:

The number is 6351.

We need to find the smallest number to be added to 6351 to make it a square number.

Concept Used:

To determine the smallest number to be added to make a perfect square, we can calculate the nearest square greater than 6351 and subtract 6351 from it.

Calculation:

We have,

⇒ 6351

Find the smallest integer greater than or equal to √6351:

⇒ √6351 ≈ 79.68

Next integer is 80:

⇒ 80² = 6400

Difference between 6400 and 6351:

⇒ 6400 - 6351 = 49

∴ The smallest number to be added to 6351 is 49.

The correct venn diagram representing the relationship between wife, mother and doctor is shown below:

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Hence, the correct answer is "C".