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Preparing the family tree using the following symbols

From the family tree diagram it is clear that Soma is the sister of Chandra. Since Soma is the mother of Dwip, Dwip could be the niece or Nephew of Chandra. In the given options since nephew is present. Dwip is the nephew of Chandra.

The correct answer is Narsimhavarman.

Key Points

• The best or most significant emperor of the Pallava dynasty is often considered to be Narasimhavarman I (reigned c. 630–668 AD).
• Narasimhavarman I, also known as Mamalla, is particularly known for his military exploits and patronage of art and architecture.
• He is considered one of the greatest warriors of his time and is also credited with successfully defending his kingdom against the Chalukya ruler Pulakeshin II, thereby bringing about a shift in the regional power dynamics.
• One of his most renowned achievements is the defeat of Pulakeshin II of the Chalukya dynasty in the Battle of Manimangalam.
• After this, he took on the title "Vatapikonda", translating to "the conqueror of Vatapi" – the capital of the Chalukyas.
• Narasimhavarman I is also celebrated for his contribution towards the expansion of the rock-cut and structural temples in Mamallapuram, a UNESCO World Heritage Site. The city of Mamallapuram, earlier known as Mahabalipuram, also gets its modern name from the title Mamalla.

Additional Information

• Pulakeshin II was a notable ruler of the Chalukya dynasty.
• Rajaraja I was a prominent emperor of the Chola dynasty.
• Govinda III was a reputable ruler from the Rashtrakuta dynasty.

In conclusion, Narasimhavarman I is often considered the best emperor of the Pallava dynasty due to his military triumphs and significant contributions to art and architecture.

According to given information,

The distance between home and the last place = 20 km - 7 km

                                                                            = 13 km

Solution:

\(\frac{1}{4} - \frac{1}{8} = \frac{1}{8}\)

\(2\frac{1}{2} = 2.5\)

\(2.5 \times \frac{1}{8} = \frac{5}{16}\)

\(\frac{3}{8} - \frac{5}{16} = \frac{1}{16}\)

\(2\frac{2}{3} = 2.\overline{6}\)

\(2.\overline{6} \times \frac{1}{16} = \frac{1}{6}\)

\(\frac{3}{4} + \frac{1}{6} = \frac{11}{12}\)

\(1\frac{2}{9} = \frac{11}{9}\)

\(\frac{11}{9} \div \frac{11}{12} =\frac{11}{9} \times \frac{12}{11}\)

⇒ 4/3 = \(1\frac{1}{3}\)

∴ The Correct answer is option (4).

Solution:

Let's assume the breadth of the rectangular field as "x" meters.

According to the given information, the length of the field is twice the breadth, so the length is "2x" meters.

The area of a rectangle is given by the formula:

Area = Length × Breadth

Given that the area of the field is 338 square meters, we can write the equation as:

338 = 2x × x

338 = 2x^2

Dividing both sides of the equation by 2:

169 = x^2

Taking the square root of both sides:

x = √169

x = 13

So, the breadth of the field is 13 meters, and the length is 2x = 2 × 13 = 26 meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (Length + Breadth)

Substituting the values:

Perimeter = 2 × (26 + 13)

Perimeter = 2 × 39

Perimeter = 78 meters

Therefore, the perimeter of the rectangular field is 78 meters.

Given:

Side of the square = 45 m

Speed of the person = 9 km/h

To find the distance traveled for two rounds around the square, we can calculate the perimeter of the square and multiply it by 2:

Perimeter of the square = 4 * Side

                       = 4 * 45

                       = 180 m

The total distance traveled for two rounds around the square is 180 m * 2 = 360 m.

To convert the speed from km/h to m/s, we divide it by 3.6:

Speed in m/s = 9 km/h / 3.6

             = 2.5 m/s (approx)

Now, we can use the formula: Time = Distance / Speed

Time = 360 m / 2.5 m/s

      = 144 seconds

Therefore, it will take a person 144 seconds to go around twice around a square of side 45 m at a speed of 9 km/h.

The logic followed here is :-

We take the opposite letter of the former alphabet.

The correct answer is Kelvin.

 Key Points

• Kelvin is the base unit of temperature in the International System of Units (SI).
• It is one of the seven SI base units.
• It is named after the Scottish physicist William Thomson, 1^st Baron Kelvin.

 Additional Information

• Celsius, while commonly used for everyday temperature measurements, is not the SI base unit. The Celsius scale is based on the temperatures at which water freezes and boils.
• Fahrenheit is a temperature scale used primarily in the United States and its territories. It's not an SI unit.
• 'Degree' is a common unit used to measure temperature, but it's not specific to any scale. Both Celsius and Fahrenheit scales use the term 'degree.'

Solution:

⇒ Total Distance = 200 + 150 = 350 metres

⇒ Speed = 70 km/h = 70 × (5/18) = (35 x 5/9) m/sec

Distance = Speed × Time

⇒ 350 = (35 x 5/9) × Time

⇒ Time = (90)/5

⇒ Time = 18 seconds

∴ Time taken by train to cross the bridge is 18 seconds

9×7×4 + 10 = 262

6×5×3 + 9 = 99

10×8×7 + 13 = 573

Hence the correct answer is Option 2: 573