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

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## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Example 10 and 11

**Question 10:**

Let

(A)

(B)

(C)

(D) None of these

**Answer:**

(C) Is the correct answer

Since

**Question 11:**

If , then the determinant lies in the interval.

(A)

(B)

(C)

(D)

**Answer:**

The correct choice is A. Indeed applying , we get

Expanding along , we have

Hence

### Fill in the Blanks in Each of the Examples 12 to 14

**Question 12:**

If A, B, C are the angles of a triangle, then

**Answer:**

Answer is 0. Apply .

**Question 13:**

The determinant is equal to ……….

**Answer:**

Answer is .Taking common from and and applying , we get the desired result.

**Question 14:**

The value of the determinant …..

**Answer:**

. Apply.

### State Whether the Statements in the Examples 15 to 18 is True or False

**Question 15:**

The determinant is independent of only.

**Answer:**

True. Apply , and expand

**Question 16:**

The value of

**Answer: True**

**Question 17:**

If then

**Answer: False.**

**Question 18:**

If

**Answer: True**