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

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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.