Explanation

Given a ≠ 0, b ≠ 0, and ab = 0:

In this case, a and b are called Zero divisors.

Explanation

The function y = x + 100 is in the slope-intercept form y = mx + c, where:

m = 1 (slope)

c = 100 (y-intercept)

This confirms that the graph of the function is a straight line.

Explanation

A spectrometer is an instrument used to measure the properties of light over a specific portion of the electromagnetic spectrum, especially to analyze line spectra produced by atoms or molecules.

It helps identify elements or compounds by detecting their unique emission or absorption lines in the spectrum.

Explanation

The argument of the product of two complex numbers is the sum of their arguments.

This property comes from the multiplication of complex numbers in polar form.

Explanation

Realist Curriculum is grounded in the belief that reality exists independently of human perception.

It emphasizes teaching factual knowledge and objective truths derived from the external world.

Explanation

Geometric Mean = ∛(2 × 4 × 8)

= ∛64

= 4

Explanation

Given lim x → 1⁺ (2 + √x - 1)

As x approaches 1 from the right:

√x approaches √1 = 1

So, √x - 1 approaches 1 - 1 = 0

2 + 0 = 2

The limit is 2.

Explanation

Passage

Hazrat Muhammad (PBUH) knew that goodwill and all the actions of people were necessary for an Islamic state. Hazrat Muhammad (PBUH) knew tolerance was necessary to bring different communities together. With all these objectives in mind, Hazrat Muhammad (PBUH) drafted a charter which is generally known as the Medina Charter.

1. The first sentence of the paragraph is in _____?

Past Tense

2. Communities is a/n ____?

Noun

3. Necessary is a/n _____?

Adjective 

Explanation

The Axiom of Choice is a fundamental principle in set theory that states you can select an element from each set in a collection of nonempty sets, even without a specific rule.

It is essential for many proofs in mathematics but is independent of other axioms of set theory.

Explanation

Step 1: Calculate the mean of the marks.

Mean = (6 + 8 + 10 + 12 + 4 + 20) / 6

= 60 / 6

= 10

Step 2: Calculate the mean deviation.

Mean Deviation = (|6-10| + |8-10| + |10-10| + |12-10| + |4-10| + |20-10|) / 6

= (4 + 2 + 0 + 2 + 6 + 10) / 6

= 24 / 6

= 4

Step 3: Calculate the coefficient of dispersion.

Coefficient of Dispersion = Mean Deviation / Mean

= 4 / 10

= 0.4