Explanation

The correct preposition is "on" because the spider is attached to the surface of the ceiling.

"On the ceiling" means something is resting or moving along its surface.

Explanation

The Laplace equation is a 2nd order partial differential equation, given by:

∇²u = 0 or ∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z² = 0

Explanation

The preposition "at" is used to indicate a specific time.

So, "I will come at 2 o'clock" is grammatically correct.

Explanation

The use of "will" here shows willingness to help someone.

It expresses a voluntary action or offer.

Explanation

Hazrat Ismael (AS) is called Abu-ul-Arab (Father of the Arabs) because Arab tribes trace their lineage through him.

He settled in Makkah and married into the Jurhum tribe, giving rise to Arab ancestry.

Explanation

Variance measures the spread of data around the mean.

For a constant number, all values are the same, so there is no variation, making variance 0.

Explanation

A sequence is a function whose domain is the set of natural numbers (1, 2, 3, ...).

Each natural number input gives a specific term in the sequence.

Explanation

To find the range, subtract the smallest value from the largest value:

Maximum value = 28

Minimum value = 20

Range = Maximum value - Minimum value

= 28 - 20

= 8

Explanation

Certain and Unsure are opposites.

Hard and Soft are also opposites, so this analogy fits the pattern.

Explanation

The phrase "Allahumma fiqqih-hu fid Deen" is a du'a (supplication) meaning "O Allah, give him deep understanding of the religion."

It is often made for students or children to excel in religious knowledge.

This du'a (supplication) was made by the Prophet Muhammad ﷺ for Ibn Abbas (RA).