# NCERT Class 12-Mathematics: Exemplar Chapter –4 Determinants Part 5

Doorsteptutor material for UGC is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

## 4.3 EXERCISE

### Short Answer (S.A)

**Using the properties of determinants in Exercises 1 to 6, evaluate:**

**Question 1:**

**Answer:**

We have,

**Question 2:**

**Answer:**

We have,

**Question 3:**

**Answer:**

We have,

**Question 4:**

**Answer:**

We have,

Appling,

Now, expanding along first column, we get

**Question 5:**

**Answer:**

We have,

[Here, given determinant is expressed in sum of two determinants]

[Taking common from first row of first determinant and 4 from first row of second determinants]

Applying and in first and applying in second we get

Expanding both the along first column, we get