NCERT Solutions for Class 12 Maths Chapter 4 – Determinants Ex 4.1
Page No 108:
Question 1:
Evaluate the determinants in Exercises 1 and 2.

Answer:

Question 2:
Evaluate the determinants in Exercises 1 and 2.
(i)
(ii) 


Answer:
(i)
= (cos θ)(cos θ) − (−sin θ)(sin θ) = cos2 θ+ sin2 θ = 1

(ii) 

= (x2 − x + 1)(x + 1) − (x − 1)(x + 1)
= x3 − x2 + x + x2 − x + 1 − (x2 − 1)
= x3 + 1 − x2 + 1
= x3 − x2 + 2
Question 3:
If
, then show that


Answer:
The given matrix is
.


Question 4:
If
, then show that


Answer:
The given matrix is
.

It can be observed that in the first column, two entries are zero. Thus, we expand along the first column (C1) for easier calculation.


From equations (i) and (ii), we have:

Hence, the given result is proved.
Question 5:
Evaluate the determinants
(i)
(iii) 


(ii)
(iv) 


Answer:
(i) Let
.

It can be observed that in the second row, two entries are zero. Thus, we expand along the second row for easier calculation.

(ii) Let
.

By expanding along the first row, we have:

(iii) Let

By expanding along the first row, we have:

(iv) Let

By expanding along the first column, we have:

Page No 109:
Question 6:
If
, find
.


Answer:
Let

By expanding along the first row, we have:

Question 7:
Find values of x, if
(i)
2451=2x46x(ii)
2345=x32x5
Answer:
(i) 


(ii) 


Question 8:
If
, then x is equal to

(A) 6 (B) ±6 (C) −6 (D) 0
Answer:
Answer: B


Hence, the correct answer is B.