Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 12 Mathematics I 4. Determinants to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 12 Mathematics I 4. Determinants to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 4.2. Whether you are studying for board exams or mid-term exams, 12 Mathematics I Chapter 4. Determinants solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise - 4.2
Using the properties of determinants and without expanding in Exercise 1 to 5, prove that:
Ques.1. 
Ans. Given:
Operating 
0 = 0 [
C1 and C2 are identical]
L.H.S. = R.H.S.
hance proved.
Ques.2. 
Ans. On 
Operating 
= 
= 
= 0 = R.H.S.
[ All entries of one column here first are zero]
hance proved.
Ques.3. 
Ans. On 
operating 
= 
= 
= 9 x 0 = 0 [ two columns are identical]
hance Proved.
Ques.4. 
Ans. Given: 
= 
Operating 
= 
= 
= 0 [ two columns are identical]
hance Proved.
Ques.5. 
Ans. L.H.S. = 
operating 
= 
= 
= 
= 
[operating 
]
= 
[operating 
]
= 
[operating 
]
= 
[Interchanging 
and 
]
= 
[Interchanging and ]
= 
= R.H.S.
hance proved.
Using the properties of determinants and with expanding in Exercise 6 to 14, prove that:
Ques.6. 
Ans. Let 
= 
[Taking 
common from each row]
Interchanging rows and columns.,
hance Proved.
Ques.7. 
Ans. L.H.S. = 
Taking common 
from 
respectively,
= 
= 
[operating 
]
= 
= 
= 
= 
= R.H.S.
hance proved.
Ques.8. (i) 
(ii) 
Ans. (i) L.H.S. = 
operating 
and ,
= 
= 
[Expanding along 1st column]
= 
= 
= 
= 
= R.H.S.
hance Proved.
(ii) L.H.S. = 
operating 
and
= 
= 
= 
= 
= 
= 
= 
= 
= 
= 
= R.H.S.
hance proved.
Ques.9. 
Ans.
L.H.S. = 
= 
[Multiplying 
by 
respectively]
= 
= 
= 
[operating 
]
= 
= 
= 
= 
= 
= 
= 
= 
= 
= 
= 
= R.H.S.
hance proved.
Ques.10. (i) 
(ii) 
Ans. (i) L.H.S. = 
= 
= 
= 
[operating and ]
= 
= 
= R.H.S.
hance proved.
(ii) L.H.S. = 
= 
= 
= 
[operating and ]
= 
= 
= 
= R.H.S.
hance Proved.
Ques.11. (i) 
(ii) 
Ans. (i) L.H.S. = 
= 
= 
= 
= 
= 
= 
= R.H.S.
hance Proved.
(ii) L.H.S. = 
= 
= 
= 
= 
= 
= 
= R.H.S.
hance Proved.
Ques.12. 
Ans. L.H.S. = 
= 
= 
= 
= 
= 
= 
= 
= 
= 
= 
= 
= R.H.S.
hance Proved.
Ques.13. 
Ans. L.H.S. = 
= 
= 
= 
= 
= 
= 
= R.H.S.
Ques.14. 
Ans. L.H.S. = 
Multiplying 
by respectively and then dividing the determinant by 
= 
= 
= 
= 
= 
= 
= 
= R.H.S.
hance, proved.
Choose the correct answer in Exercises 15 and 16.
Ques.15. Let A be a square matrix of order 3 x 3, then 
is equal to:
(A) 
(B) 
(C) 
(D) 
Ans. Let A = 
be a square matrix of order 3 x 3. ……….(i)
= [From eq. (i)]
hance, option (C) is correct.
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Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 4.2 include complete solutions for 12 Mathematics I Chapter 4. Determinants exercises. With step-by-step answers, you gain clarity and confidence to attempt similar exam questions.
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Our Exercise 4.2 are useful for both board exams and mid-term exams. For 12 Mathematics I, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 4.2 for 12 Mathematics I Chapter 4. Determinants are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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