NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise: Get inside detail NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise prepared by academic team of Physics Wallah all questions are solved in detail.
Krati Saraswat15 Jan, 2024
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NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise Determinants is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 4. Given below are step-by-step solutions to all questions given in NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise Determinants.NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1
NCERT Solution for Class 12 Maths Chapter 4 Miscellaneous Exercise Overview
NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Excercise addresses these significant subjects. In order to fully comprehend the concepts presented in the chapter and make effective use of the provided solutions, it is recommended that students go over each topic in great detail. The instructors at Physics Wallah have put a lot of effort into helping students better understand the ideas presented in this chapter, as evidenced by these solutions. The intention is for students to effortlessly achieve excellent exam scores after reviewing and practicing these responses.CBSE Class 12th Toppers List 2024
NCERT Solution for Class 12 Maths Chapter 4 Miscellaneous Exercise PDF
Educators at Physics Wallah has created NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Excercise comprehensive solutions for in order to assist students in comprehending and applying chapter themes. These questions are meant to help students understand explanations more easily. To download the NCERT Solutions for Class 12 Maths Chapter 4 PDF, click the following link:NCERT Solutions Class 12 Maths Chapter 4 PDF Download Link
NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise
Solve The Following Questions NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise Determinants:
Question 1. Prove that the determinant
is independent of
θ
.
Solution :
Hence, Δ is independent of
θ
.
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.2
Question 2. Without expanding the determinants, prove that:
Solution :
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3
Question 3. Evaluate:
Solution :
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4
Question 4. If a,b and c are real numbers and
Show that either a + b + c = 0 or a = b = c .
Solution :
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5
Question 5. Solve the equation:
Solution :
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6
Question 6. Prove that:
Solution :
Solution :
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | |
Solution :
Solution :
Question
10. Evaluate:
Solution :
Using properties of determinants in Exercises 11 to 15, prove that:
Question
11.
Solution :
Question
12.
Solution :
Question
13.
Solution :
Question
14.
Solution :
Question
15.
Solution :
Question
16. Solve the system of the following equations: (Using matrices):
Solution :
Choose the correct answer in Exercise 17 to 19.
Question
17. If a,b,c are in A.P., then the determinant
is:
(A) 0
(B) 1
(C) x
(D) 2x
Solution :
Here, all the elements of the first row (R
1
) are zero.
Hence, we have Δ = 0.
The correct answer is A.
Question
18. If x,y,z are non-zero real numbers, then the inverse of matrix A =
is:
(A)
(B)
(C)
(D)
Solution :
Therefore, option (A) is correct.
Question
19. Let
where 0 ≤
θ
≤ 2π, Then:
(A) Det (A) = 0
B. Det (A) ∈ (2, ∞)
C. Det (A) ∈ (2, 4)
D. Det (A)∈ [2, 4]
Solution :
Therefore, option (D) is correct.
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