Preparing for the Mathematics section of the SSC CHSL exam requires practicing a variety of questions from different topics. Here are some sample questions along with solutions to help you get started:

### 1. **Arithmetic**

#### Percentage

**A number is increased by 20% and then decreased by 20%. What is the net percentage change?**- A) 4% decrease
- B) 4% increase
- C) No change
- D) 2% decrease

**Answer**: A) 4% decrease**Solution**: Let the original number be 100. Increased number = 100 + 20% of 100 = 100 + 20 = 120. Decreased number = 120 – 20% of 120 = 120 – 24 = 96. Net change = 96 – 100 = -4. Net percentage change = (4/100) * 100% = 4% decrease.

#### Ratio and Proportion

**The ratio of the ages of two friends is 4:5. Six years later, the ratio of their ages will be 5:6. What is the present age of the younger friend?**- A) 12 years
- B) 15 years
- C) 18 years
- D) 24 years

**Answer**: A) 12 years**Solution**: Let the present ages be 4x and 5x. Six years later: (4x + 6) / (5x + 6) = 5/6. Solving, 6(4x + 6) = 5(5x + 6) => 24x + 36 = 25x + 30. => x = 6. Present age of the younger friend = 4x = 4 * 6 = 24 years.

#### Simple Interest

**A sum of money amounts to ₹6900 in 3 years and to ₹7500 in 5 years at simple interest. What is the principal amount?**- A) ₹5000
- B) ₹5500
- C) ₹6000
- D) ₹6500

**Answer**: B) ₹6000**Solution**: Let the principal be ₹P. Interest for 3 years = 6900 – P. Interest for 5 years = 7500 – P. Therefore, interest for 2 years = 7500 – 6900 = 600. Interest per year = 600 / 2 = 300. Interest for 3 years = 3 * 300 = 900. Hence, P = 6900 – 900 = 6000.

### 2. **Algebra**

#### Linear Equations

**Solve for x: 3x – 7 = 2x + 5**- A) 7
- B) -7
- C) 12
- D) -12

**Answer**: A) 12**Solution**: 3x – 2x = 5 + 7 => x = 12.

### 3. **Geometry**

#### Triangles

**In a right-angled triangle, one angle is 30 degrees. What is the ratio of the lengths of the hypotenuse to the side opposite the 30-degree angle?**- A) 1:1
- B) 2:1
- C) √3:1
- D) 2:√3

**Answer**: B) 2:1**Solution**: In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. Therefore, the hypotenuse is twice the length of the side opposite the 30-degree angle.

### 4. **Trigonometry**

#### Trigonometric Ratios

**If sin θ = 3/5, find cos θ.**- A) 4/5
- B) 3/4
- C) 5/3
- D) 4/3

**Answer**: A) 4/5**Solution**: Using the Pythagorean identity: sin²θ + cos²θ = 1. (3/5)² + cos²θ = 1 => 9/25 + cos²θ = 1 => cos²θ = 1 – 9/25 => cos²θ = 16/25 => cos θ = 4/5.

### 5. **Statistics**

#### Mean and Median

**Find the mean of the following set of numbers: 2, 4, 6, 8, 10.**- A) 5
- B) 6
- C) 7
- D) 8

**Answer**: B) 6**Solution**: Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

### 6. **Mensuration**

#### Area and Perimeter

**What is the area of a circle with radius 7 cm?**- A) 154 cm²
- B) 144 cm²
- C) 164 cm²
- D) 134 cm²

**Answer**: A) 154 cm²**Solution**: Area = πr² = π * 7² = 22/7 * 49 = 154 cm².

Regular practice with a variety of questions from different topics is essential for performing well in the Mathematics section of the SSC CHSL exam.