Explanation

Light signals, such as semaphore flags or lantern flashes, were commonly used by sailors to communicate over distances.

These signals conveyed messages visually before the invention of modern communication tools.

Explanation

A transitive verb needs a direct object to complete its meaning.

In this sentence, "brought" is the transitive verb and "a gift" is its direct object.

Explanation

"To catch the bus" starts with "to" + verb, which is an infinitive form.

It functions as a phrase explaining the purpose or reason related to "time."

Explanation

Carbon has a valency of 4, and Oxygen has a valency of 2.

By crossing the valencies, we get CO₂ (i.e., one carbon and two oxygen atoms), and the ratio simplifies to the empirical and molecular formula: CO₂.

Explanation

Given cos θ = 4/5 and θ lies in the 4th quadrant.

In the 4th quadrant, cosine is positive, and sine is negative.

We know that sin² θ + cos² θ = 1

sin² θ = 1 - cos² θ

= 1 - (4/5)²

= 1 - 16/25

= 9/25

sin θ = ±√(9/25)

= ±3/5

Since θ lies in the 4th quadrant, sin θ is negative:

sin θ = -3/5

Explanation

Given:

a² + b² + c² = 12

a + b + c = 5

We know that:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Expanding the equation:

5² = 12 + 2(ab + bc + ca)

25 = 12 + 2(ab + bc + ca)

Subtract 12 from both sides:

13 = 2(ab + bc + ca)

Divide by 2:

ab + bc + ca = 13/2

Explanation

The LCM of 8 and 24 is 24 (since 24 is a multiple of 8).

The common multiples are: 24, 48, 72, 96 (4th common multiple).

Explanation

Sympathetic imitation involves emotional response imitation, like crying when others cry.

It is often instinctive and driven by empathy rather than conscious effort.

Explanation

In soap-making (saponification), steam helps melt fats or oils, allowing them to react efficiently with caustic soda (NaOH).

This ensures the chemical reaction proceeds smoothly to form soap and glycerol.

Explanation

سبق اسلام میں گداگری کی مذمت معروف ادیب اور مصلح الطاف حسین حالی کی تحریر ہے۔

اس میں حالی نے اسلام کے نقطۂ نظر سے گداگری (بھیک مانگنے) کی مخالفت کی ہے اور محنت و خودداری کی تلقین کی ہے۔