Given:

Speed of car A = 75 km/h

Speed of car B = 90 km/h

Time taken by A  = Time taken by B + 0.5 hours

Formula used:

Speed = Distance/Time

Calculation:

Let the distance between points P and Q be D km

Then, Time taken by A (TA) = D/75     -----(1)

And, Time taken by B (TB) = D/90      -----(2)

According to the question

⇒ T_A = T_B + 0.5

Put the values from equation(1) and equation(2)

⇒ D/75 = D/90 + 0.5

⇒ D/75 - D/90 = 0.5

⇒ (6D - 5D)/450 = 0.5

⇒ D = 0.5 × 450 = 225

Hence, the distance between P and Q is 225 km.

According to the given information,

1) S, at a corner, is sitting fourth to the right of E.

2) G is at the immediate right of S.

3) R, at a corner, is between G and P.

4) H is at the immediate left of F and is second to the right of P.

5) Thus, the final arrangement is:

Here, we can see that Q is sitting between F and S.

Hence, the correct answer is "Q".

The correct answer is Three.

Key Points

• The president has three veto powers, i.e. absolute, suspension & pocket.
• The president can send the bill back to parliament for changes, which constitutes a limited veto that can be overridden by a simple majority.
• But the Bill reconsidered by the parliament becomes law with or without the assents of the President after 14 days.
• The president can also take no action indefinitely on a bill, sometimes referred to as a pocket veto.
• The president can refuse to assent, which constitutes an absolute veto.

Important Points

The three types of Vetoes are:

1. Absolute Veto
2. Suspensive Veto
3. Pocket Veto

The correct answer is Pulakesin II.

Key Points

• Pulakesin II defeated Harshavardhana when he invaded the Chalukya kingdom in the Deccan.
• Pulakeshin II, the King of the Chalukya dynasty defeated Harshavardhana when he sought to enlarge his Empire into the southern peninsula of India.
• He defeated Harshavardhana on the banks of the Narmada river in 618-619 AD.
• The Aihole inscription was written by the Ravikirti, court poet of Chalukya King, Pulakesin II who reigned from 610 to 642 CE.

Additional Information

• Chalukya dynasty:  
  • It lasted from 543 A.D. to 755 A.D.
  • Pulakesin I was the founder of the Chalukya dynasty. He established a small kingdom with Vatapi or Badami as its capital.
  • The Western Chalukyas ruled over an extensive area in the Deccan for about two centuries after which the Rashtrakutas became powerful.
  • The family of Western Chalukyas had its offshoots like the Eastern Chalukyas of Vengi and the Chalukyas of Kalyani.
  • Kirtivarman II was the last of the rulers of the Chalukyas.
  • He was defeated by Dantidurga, the founder of the Rashtrakuta dynasty.

Given:

ABCD is a quadrilateral in which

Also {w, x} < 90 and {y, z} > 90

Formula used:

Sum of angle of a quadrilateral is 360°

Calculations:

Let, k = 1

⇒ z = y, w = x,  y = x

⇒ w, x = 90° (not possible)

Let k = 2,

⇒ x = 2w

⇒ y = 2x = 4w and z = 2y = 8w

⇒ x + y + z + w = 360°

⇒ 2w + 4w + 8w + w = 360°

⇒ w = 24°

⇒ z = 8w = 8 × 24 = 192°

∴ The value of (z - w) is 168°.

Additional Information

Let k = 3

⇒ z = 3y,

But according to question,

y > 90° ⇒  z > 270°  (not possible)

The mirror image of the given figure is:

Hence, the correct answer is "Option (4)".

The correct answer is Nagabhata-I.

Key Points

• Nagabhatta I was the founder of the Gurjara-Pratiharas Dynasty.
• The Pratiharas Dynasty(8th-11th Century A.D): 
  • The Pratiharas were also renamed as Gurjara.
  • Between the 8th and 11th century A.D, they ruled over northern and western India.
  • Pratiharas: A fortification- Against the hostility of the Muslims from the days of Junaid of Sind, the Pratiharas stood as a fortification of India’s defense to Mahmud of Ghazni.

Additional Information

• Basic Information about other Kings given in Option:
  • Narasimhadeva I: Narasingha Deva I was a powerful monarch and warrior of the Eastern Ganga Dynasty or suryabansha of early medieval Odisha who reigned from 1238 to 1264.
  • Harshvardhan: He was an Indian emperor who ruled majorly in North India from 606 to 647 CE. He was a member of the Vardhana dynasty. 
  • Ramachandra: He was a ruler of the Sauna (Yadava) dynasty of Deccan region in India. He established his capital in Devagiri which is presently located in Maharashtra.

Solution:

To divide 455 in the ratio of 4:3, we need to find the two parts that add up to 455 and are in the ratio of 4:3.

Let the two parts be 4x and 3x. Then, the sum of the two parts is 4x + 3x = 7x, which should be equal to 455.

⇒ 7x = 455

⇒ x = 65

Therefore, the two parts are 4x = 4 × 65 = 260 and 3x = 3 × 65 = 195.

Hence, the two parts are 260 and 195.

The logic followed here is:

Logic: (1st number)³ - 1 = 2nd number,

1st number × 3 - 1 = 3rd number.

Now,

For, 3 : 26 : 8

⇒ (3)³ - 1 = 27 - 1 = 26.

⇒ 3 × 3 - 1 = 9 - 1 = 8.

For, 7: 342 : 20

⇒ (7)3 - 1 = 343 - 1 = 342.

⇒ 7 × 3 - 1 = 21 - 1 = 20.

Similarly, Option 4) 4 : 63 : 11

⇒ (4)³ - 1 = 64 - 1 = 63.

⇒ 4 × 3 - 1 = 12 - 1 = 11.

Hence, the correct answer is "Option 4".

Gross domestic product (GDP) is a monetary measure of the value of all final goods and services produced in a period. Nominal GDP estimates are commonly used to determine the economic performance of a whole country or region, and to make international comparisons.