# NCERT Class 12-Mathematics: Exemplar Chapter – 4 Determinants Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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

**Question 12**:

Find the value of θ satisfying

**Answer**:

We have,

Expanding along , we get

Now, we know that

But is not possible

**Question 13**:

If then find values of .

**Answer**:

Given,

**Question 14**:

If are in G. P. , then prove that the determinant is independent of r.

**Answer**:

We know that,

Where term of a First term of a GP and Common ratio of GP

We have

**Question 15**:

Show that the points , and do not lie on a straight line for any value of a.

**Answer**:

Given, the point are

Hence, given points form a triangle i.e.. points do not lie in a straight line.