# NCERT Class 12-Mathematics: Exemplar Chapter –4 Determinants Part 8

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**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.