Algebra, Mensuration and Number Basics — Practice

Question 1

Solve for x: 2x + 5 = 15.
(a) 5 (b) 10 (c) 7.5 (d) 4

Accepted Answer

(a) 5.

Subtract 5 from both sides: 2x = 10. Divide by 2: x = 5.

Question 2

What is the HCF (highest common factor) of 12 and 18?
(a) 6 (b) 3 (c) 9 (d) 36

Accepted Answer

(a) 6.

12 = 2² × 3 and 18 = 2 × 3². The common factors give HCF = 2 × 3 = 6.

Question 3

A rectangle has length 8 cm and breadth 5 cm. What is its area?
(a) 40 cm² (b) 26 cm² (c) 13 cm² (d) 45 cm²

Accepted Answer

(a) 40 cm².

Area = length × breadth = 8 × 5 = 40 cm². (The perimeter, by contrast, would be 2(8 + 5) = 26 cm.)

Question 4

What is the LCM (least common multiple) of 4 and 6?
(a) 12 (b) 24 (c) 8 (d) 2

Accepted Answer

(a) 12.

Multiples of 6 are 6, 12, 18…; 12 is the smallest also divisible by 4. Check: HCF × LCM = 2 × 12 = 24 = 4 × 6.

Question 5

A father is three times as old as his son. In 12 years, he will be twice as old as his son. What is the son's present age?
(a) 12 years (b) 10 years (c) 15 years (d) 8 years

Accepted Answer

(a) 12 years.

Let the son be x, so the father is 3x. In 12 years: 3x + 12 = 2(x + 12) = 2x + 24, giving x = 12. The son is 12 and the father is 36.

Question 6

Find the area of a circle of radius 7 cm (take π = 22/7).
(a) 154 cm² (b) 44 cm² (c) 49 cm² (d) 22 cm²

Accepted Answer

(a) 154 cm².

Area = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm².

Question 7

The sum of three consecutive integers is 72. What is the largest of them?
(a) 25 (b) 24 (c) 23 (d) 26

Accepted Answer

(a) 25.

Let them be x, x + 1, x + 2. Then 3x + 3 = 72, so 3x = 69 and x = 23. The integers are 23, 24, 25; the largest is 25.

Question 8

A rectangular plot has length twice its breadth and a perimeter of 60 m. What is its area?
(a) 200 m² (b) 180 m² (c) 100 m² (d) 240 m²

Accepted Answer

(a) 200 m².

Let breadth = b, length = 2b. Perimeter = 2(2b + b) = 6b = 60, so b = 10 m and length = 20 m. Area = 20 × 10 = 200 m².

Practice — Algebra, Mensuration and Number Basics

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities