Explanation

Let's check each pair in the equation:

2x + 3y = 24

{6, 4} → 2(6) + 3(4) = 12 + 12 = 24 ✓

{12, 0} → 2(12) + 3(0) = 24 + 0 = 24 ✓

{0, 8} → 2(0) + 3(8) = 0 + 24 = 24 ✓

{9, -2} → 2(9) + 3(-2) = 18 - 6 = 12 ✗

Explanation

The correct phrase is "by his will", which means according to his desire or choice.

"By" is used to show the agent or means through which something happens — here, his own will.

Explanation

The Objective Resolution of 1949 defines the role of the people in the constitution of Pakistan, outlining the principles of democracy, justice, and equality.

It emphasizes the sovereignty of the people while recognizing the importance of Islamic principles.

Explanation

A set with no elements is commonly referred to as a null set, empty set, or void set.

All these terms mean the same: a set with zero elements, usually denoted by Ø or { }.

Explanation

The correct phrase is: "There is no substitute for hard work."

"Substitute" means a replacement, and the sentence implies hard work cannot be replaced.

Explanation

Astola and Manora are coastal islands of Pakistan, both located in the Arabian Sea.

Astola is Pakistan’s largest offshore island, while Manora is near Karachi.

Explanation

The Hunter Commission (1882) was appointed to evaluate the outcomes of Wood’s Despatch (1854) on education in India.

It recommended the promotion of primary and secondary education, especially through Indian languages.

Explanation

Raw materials are essential as they provide the basic inputs needed for industries to manufacture goods.

Availability of raw materials reduces production costs and supports sustained industrial growth.

Explanation

Homework helps in developing discipline and study habits in students.

It encourages self-learning and independent practice, which are crucial for academic growth.

Explanation

Given 2x - 6 = 0:

2x = 6

x = 6/2 = 3