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# NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

## JEE : NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

The document NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Determinants

Exercise 4.1
Question 1: Evaluate the determinants in Exercises 1 and 2.

= 2(âˆ’1) âˆ’ 4(âˆ’5) = âˆ’ 2 + 20 = 18

Question 2: Evaluate the determinants in Exercises 1 and 2.

(i) = (cos Î¸)(cos Î¸) âˆ’ (âˆ’sin Î¸)(sin Î¸) = cos2 Î¸+ sin2 Î¸ = 1

(ii) = (x2 âˆ’ x + 1)(x + 1) âˆ’ (x âˆ’ 1)(x + 1)
= x3 âˆ’ x2 + x + x2 âˆ’ x + 1 âˆ’ (x2 âˆ’ 1)
= x+ 1 âˆ’ x2 + 1
= xâˆ’ x2 + 2

Question 3:

.

Question 4:

The given matrix is  .

Question 5: Evaluate the determinants

(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.

Question 6:
If

Question 7: Find values of x, if

Question 8:
If  , then x is equal to

(A) 6

(B) Â±6

(C) âˆ’6

(D) 0

Hence, the correct answer is B.

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## Mathematics (Maths) Class 12

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