# NCERT Class 12-Mathematics: Exemplar Chapter – 4 Determinants Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 then

**Answer: True**