Explanation

The term "Facebook diplomacy" was coined in December 2008 in New York.

It refers to the use of social media platforms, particularly Facebook, by governments and diplomatic figures to engage with the public, influence international relations, and shape global perceptions.

This concept gained prominence as digital communication became more integral to diplomacy.

Explanation

To find the annual premium for Ali's life insurance policy, we need to calculate both the premium amount and the policy fee, then add them together.

Calculate the premium amount:

The premium is 4.5% of the total policy amount.

Premium = 4.5/100 × 500,000 = 0.045 × 500,000 Rs.

Calculate the policy fee:

The policy fee is 0.25% of the total policy amount.

Policy Fee = 0.25/100 × 500,000 = 0.0025 × 500,000 =1,250 Rs.

Add the premium amount and the policy fee to get the total annual premium:

Total Annual Premium = 22,500 + 1,250 = 23,750 Rs.

So, the annual premium for Ali's life insurance policy is Rs. 23,750.

Explanation

Let smallest angle = x

Then largest angle = 2 x − 24°

But x + 2 x − 24° = 180°

⇒3 x − 24° = 180°

⇒3 x = 180° + 24 = 204°

⇒x = 204/3 = 68°

∴ largest angle = 180 − 68° = 112°

Explanation

The only pattern in which they can sit according to the given situation is,

BGBGBGB

Now boys can be arranged among themselves in 4! ways, and girls among themselves in 3! ways,

So total no. of ways 

= 4 ! × 3 ! = 144

Explanation

The pattern follows the format n² + 1:

• 2² + 1 = 5
• 3² + 1 = 10
• 4² + 1 = 17
• 5² + 1 = 26

Given these, the correct 8th line should follow the same formula:

9² + 1 = 82

Explanation

Let's analyze the given inequality: k ≤ x ≤ 3k + 12

We can derive the following conclusions:

I. x - 12 ≤ 3k: Subtracting 12 from all parts of the inequality gives x - 12 ≤ 3k - 12 + 12, which simplifies to x - 12 ≤ 3k. (True)

II. k ≥ -6: Since k ≤ x and x ≤ 3k + 12, we can substitute x for k in the second part of the inequality, getting k ≤ 3k + 12. Subtracting 3k from both sides gives -2k ≤ 12, and dividing by -2 (which flips the inequality sign) gives k ≥ -6. (True)

III. x - k ≥ 0: Since k ≤ x, we can subtract k from both sides to get x - k ≥ 0. (True)

Since all three statements are true, the correct answer is: I, II, and III

Explanation

To solve this problem, we can follow these steps:

1. Calculate the total number of letters inserted by all clerks in 2 hours:

•     Clerk A: 1100 letters/hour × 2 hours = 2200 letters
•     Clerk B: 1450 letters/hour × 2 hours = 2900 letters
•     Clerk C: 1200 letters/hour × 2 hours = 2400 letters
•     Clerk D: 1300 letters/hour × 2 hours = 2600 letters
•     Clerk E: 1250 letters/hour × 2 hours = 2500 letters

   Total letters inserted in 2 hours:  

   2200 + 2900 + 2400 + 2600 + 2500 = 12600 letters

2. Determine the remaining letters to be inserted:

•     Total letters to be inserted: 24,000
•     Letters already inserted: 12,600

   Remaining letters: 24,000 - 12,600 = 11,400 letters

3. Calculate the rate of the remaining clerks (A, B, and E) per hour:

•     Clerk A: 1100 letters/hour
•     Clerk B: 1450 letters/hour
•     Clerk E: 1250 letters/hour

   Total rate of A, B, and E:  

   1100 + 1450 + 1250 = 3800 letters/hour

4. Calculate the time required to insert the remaining letters:

•     Time required = Remaining letters / Rate of A, B, and E
•     Time required = 11,400 letters / 3800 letters/hour = 3 hours

Answer: More than 2 hr, but less than 4 hr.

Explanation

To find the number of pieces that can be cut, divide the length of the rod (330 cm) by the length of each piece (13.2 cm):

330 cm ÷ 13.2 cm = 25

So, 25 pieces of 13.2 cm can be cut from the 330 cm long rod.

Explanation

The correct inequality that represents the relationship between Jerry's estimate and the actual number of marbles in the jar is m - 10 ≤ n ≤ m + 10.

This inequality states that Jerry's estimate, m, is within 10 marbles (inclusive) of the actual number, n. By subtracting 10 from Jerry's estimate and adding 10 to his estimate, you create a range within which the actual number must fall.

For example, if Jerry estimates there are 50 marbles (m = 50), the actual number of marbles (n) must be between 40 (50 - 10) and 60 (50 + 10), inclusive.

Explanation

A trackball is a pointing device where the ball is held in place by a socket, allowing users to rotate the ball to move the cursor on the screen.

Unlike a traditional mouse, which moves over a surface, a trackball stays stationary, and the ball's rotation controls the cursor's movement in different directions.