NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

Mathematics (Maths) Class 12

Created by: Tarun Kaushik

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.

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Answer
NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev = 2(−1) − 4(−5) = − 2 + 20 = 18

Question 2: Evaluate the determinants in Exercises 1 and 2.
NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Answer

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

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

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

(ii) = (x2 − x + 1)(x + 1) − (x − 1)(x + 1)
= x3 − x2 + x + x2 − x + 1 − (x2 − 1)
= x+ 1 − x2 + 1
= x− x2 + 2

Question 3:
NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Answer

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


Question 4:
NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Answer
The given matrix is NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev .
NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Question 5: Evaluate the determinants
NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Answer
(i) Let NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

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


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

 


Question 6:
 If NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Answer

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

 


Question 7: Find values of x, if

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev

Answer

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev


Question 8:
If NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev , then x is equal to 

(A) 6 

(B) ±6 

(C) −6 

(D) 0


Answer
Answer: B

NCERT Solutions - Determinants, Exercise 4.1 JEE Notes | EduRev
Hence, the correct answer is B.

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