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 4.3. 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_solutionsQues.1. Find the area of the triangle with vertices at the points given in each of the following:
(i) (1, 0), (6, 0), (4, 3)
(ii) (2, 7), (1, 1), (10, 8)
(iii) (-2,-3), (3,2), (-1,-8)
Ans. (i) Area of triangle = Modulus of 
= 
= 
= 
= 
= 
sq. units
(ii) Area of triangle = Modulus of = 
= 
= 
= 
= 
= 
= 
sq.units
(iii) Area of triangle = Modulus of = 
= 
= 
= 
= 
= 
= 15 sq. units
B
C
are collinear.Ans. Area of triangle ABC = Modulus of = 
= 
= 
= 
= 
= 0
hance, points A, B and C are collinear.
if area of triangle is 4 sq. units and vertices are:(i) 
(ii) 
Ans. (i) Given: Area of triangle = Modulus of = 4
Modulus of 
= 4
Taking positive sign, 
Taking negative sign, 
(ii) Given: Area of triangle = Modulus of = 4
= 4
Taking positive sign,
Taking negative sign,
(ii) Find the equation of the line joining (3, 1) and (9, 3) using determinants.
Ans. (i) Let P
is any point on the line joining the points (1, 2) and (3, 6).
so, Area of triangle formed by these points is zero.
Area of triangle = Modulus of = 0
Modulus of 
= 0
is required line.
(ii) Let P is any point on the line joining the points (3, 1) and (9, 3).
Then, Area of triangle formed by these points is zero.
Area of triangle = Modulus of = 0
Modulus of 
= 0
is required line.
and 
Then is:(A) 12
(B) 
(C) 
(D) 
Ans. Given: Area of triangle = Modulus of = 35
Modulus of 
= 35
Taking positive sign, 
Taking negative sign, 
hance, option (D) is correct.
Exercise 4.3 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 12 Mathematics I Chapter 4. Determinants solutions help you understand the core concepts and practice effectively.
Revision is the key to exam success. Our notes for 12 Mathematics I highlight important formulas, key definitions, and exam-ready points from Chapter 4. Determinants. These quick revision notes make last-minute preparation easy.
Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 4.3 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.
To boost your preparation, we also provide additional important questions with answers. These are prepared from previous year board papers, sample papers, and important concepts of Chapter 4. Determinants. Practicing these ensures you are well-prepared for both board and mid-term exams.
Our Exercise 4.3 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 4.3 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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