Explanation

• A formal letter follows a proper and respectful writing format.
• It includes a polite greeting and a formal closing.
• Closing lines show respect and professionalism.
• Common formal closings include “Yours faithfully” and “Yours obediently.”
• “Yours obediently” is used when the sender’s name is unknown.

Last verified on 04-05-2026

Explanation

• Idioms and phrases have figurative meanings different from literal words.
• “A bag (or back) of bones” is used in descriptive language.
• It refers to a person who is extremely thin.
• Such a person looks weak and underweight.

Last verified on 04-05-2026

Explanation

• Numbers in English grammar are mainly divided into cardinal and ordinal numbers.
• Cardinal numbers show quantity (one, two, three).
• Ordinal numbers show position or order (first, second, third).
• The word “second” indicates position in a sequence.
• Therefore, it is an ordinal number.

Last verified on 04-05-2026

Explanation

• Gender shows whether a noun is male, female, or both.
• The word “Teacher” does not specify male or female.
• Therefore, it is classified as common gender.

Additional information:

• Common gender: Teacher, doctor, student, parent
• Masculine gender: Boy, man, king, father
• Feminine gender: Girl, woman, queen, mother
• Neuter gender: Table, chair, book, pen

Last verified on 04-05-2026

Explanation

• A proper noun is the name of a specific place, person, or thing.
• “Karachi” refers to a particular city.
• Proper nouns always start with a capital letter.

• Common noun: city, boy, river (general names)
• Abstract noun: happiness, beauty, honesty (feelings/ideas)

Last verified on 04-05-2026

Explanation

Make b the same in both ratios  

a:b = 3:4  

b:c = 2:5 → multiply by 2 → b:c = 4:10  

Now a:b:c = 3:4:10  

So a:c = 3:10

Last verified on 04-05-2026

Explanation

• In geometry, a tangent is a line that touches a circle at only one point.
• At the point of contact, it forms a right angle (90°).
• The tangent is always perpendicular to the radius of the circle.

Last verified on 04-05-2026

Explanation

Identity: 1 + tan²θ = sec²θ

Last verified on 04-05-2026

Explanation

For similar triangles: area ratio = (side ratio)²  

(side ratio)² = 9/16  

side ratio = √9/16

side ratio = 3/4

Last verified on 04-05-2026

Explanation

Right triangle: a² + b² = c²  

5² + b² = 13²  

25 + b² = 169  

b² = 169 - 25  

b² = 144  

b = 12  

Last verified on 04-05-2026