12th Math chapter 3: full solution, notes, MCQ, & free PDF | Bihar board

12th Math chapter 3: cover all important question with new latest pattern. you can download Math chapter 3 notes & full solution as PDF format in English. below we are goin to cover chapter 3 Math class 12 Bihar board

Bihar board Math chapter 3 class 12: specially we focused on Bihar board latest pattern of Math, and on this post covered class 12th Math chapter 3 based on Bihar board. check out below to get full solutions of Math chapter 3 class 12 bihar board.

12th Math chapter 3 Bihar board with NCERT-Details & Highlights

name of content	12th Math chapter 3 full solution
content	Math objective type MCQ question with answer
name of subjects	class 12 Math
important for exam	Bihar board & other state board
pattern & Level	NCERT & State level question

12th Math chapter 3 all objective solutions – download PDF

Question 1.

Answer: (b)

Question 2. The matrix A = [0110] is a

• • (a) unit matrix
    (c) symmetric matrix
    (b) diagonal matrix
    (d) skew-symmetric matri

Answer: (d) skew-symmetric matrix

Question 3. If [x+yx−y2x+z2z+w]=[40710], then the values of x, y, z and w respectively are

• • (a) 2, 2, 3, 4
    (b) 2, 3, 1, 2
    (c) 3, 3, 0, 1
    (d) None of these

Answer: (a) 2, 2, 3, 4

Question 4.
 then find the values of a, b, c, x, y and z respectively

• • (a) -2, -7, -1, -3, -5, 2
    (b) 2, 7, 1, 3, 5, -2
    (c) 1, 3, 4, 2, 8, 9
    (d) -1, 3, -2, -7, 4, 5

Answer: (a) -2, -7, -1, -3, -5, 2

Question 5. The order of the single matrix obtained from

• • (a) 2 × 3
    (b) 2 × 2
    (c) 3 × 2
    (d) 3 × 3

Answer: (d) 3 × 3

Question 6. A=[12−1−1],B=[xy1−1] and (A + B)² = A² + B², then x + y =

• • (a) 2
    (b) 3
    (c) 4
    (d) 5

Answer: (d) 5

Question 7. If A = ⎡⎣⎢211232112⎤⎦⎥, then A⁴ – 2⁴ (A – I) =

• • (a) 5I + A
    (b) 5I – A
    (c) 5I
    (d) 6I

Answer: (b) 5I – A

Question 8. If A is an m × n matrix such that AB and BA are both defined, then B is a

• • (a) m × n matrix
    (b) n × m matrix
    (c) n × n matrix
    (d) m × n matrix

Answer: (b) n × m matrix

Question 9. If [1324], then A² – 5A is equal to

• • (a) 2I
    (b) 3I
    (c) -2I
    (d) null matrix

Answer: (a) 2I

Question 10.

• • (a) A + B = B + A and A + (B + C) = (A + B) + C
    (b) A + B = B + A and AC = BC
    (c) A + B = B + A and AB = BC
    (d) AC = BC and A = BC

Answer: (a) A + B = B + A and A + (B + C) = (A + B) + C

BSEB 12th math chapter 3 most mcq notes

Question 11.

• • (a) α = a² + b², β = ab
    (b) α = a² + b², β = 2ab
    (c) α = a² + b², β = a² – b²
    (d) α = 2ab, β = a² + b²

Answer: (b) α = a² + b², β = 2ab

Question 12. If A = ⎡⎣⎢100210x01⎤⎦⎥ and B = ⎡⎣⎢100−210y01⎤⎦⎥ and AB = I₃, then x + y equals

• • (a) 0
    (b) -1
    (c) 2
    (d) None of these

Answer: (a) 0

Question 13. If A = [1334] and A² – KA – 5I = 0, then K =

• • (a) 5
    (b) 3
    (c) 7
    (d) None of these

Answer: (a) 5

Question 14. If matrix A = ⎡⎣⎢abcbcacab⎤⎦⎥ where a, b, c are real positivenumbers, abc = 1 and A^TA = I, then the value of a³ + b³ + c³ is

• • (a) 1
    (b) 2
    (c) 3
    (d) 4

Answer: (d) 4

Question 15. Find the values of x, y, z respectively if the matrix A=⎡⎣⎢0xx2yy−yz−zz⎤⎦⎥ satisfy the equation A^TA = I₃.

• • (a) 12√⋅16√,13√
    (b) −12√,−16√,−13√
    (c) Both (a) and (b)
    (d) None of these

Answer: (c) Both (a) and (b)

Question 16. If A=[cosxsinx−sinxcosx], find AAT.

• • (a) Zero Matrix
    (b) I₂
    (c) [1111]
    (d) None of these

Answer: (b) I₂

Question 17. If A=⎡⎣⎢01−2−10−3230⎤⎦⎥, then A + 2A^T equals

• • (a) A
    (b) -A^T
    (c) A^T
    (d) 2A²

Answer: (c) A^T

Question 18. For any square matrix A, AA^T is a

• • (a) unit matrix
    (b) symmetric matrix
    (c) skew-symmetric matrix
    (d) diagonal matrix

Answer: (b) symmetric matrix

Question 19. If A and B are symmetric matrices of the same order, then

• • (a) AB is a symmetric matrix
    (b) A – Bis askew-symmetric matrix
    (c) AB + BA is a symmetric matrix
    (d) AB – BA is a symmetric matrix

Answer: (c) AB + BA is a symmetric matrix

Question 20. If A=[32x+3x−1x+2] is a symmetric matrix, then x =

• • (a) 4
    (b) 3
    (c) -4
    (d) -3

Answer: (c) -4

Bihar Board 12th math chapter 3 most mcq solution

Question 21. If A is a square matrix, then A – A’ is a

• • (a) diagonal matrix
    (b) skew-symmetric matrix
    (c) symmetric matrix
    (d) none of these

Answer: (b) skew-symmetric matrix

Question 22. If A is any square matrix, then which of the following is skew-symmetric?

• • (a) A + A^T
    (b) A – A^T
    (c) AA^T
    (d) A^TA

Answer: (b) A – A^T

Question 23. If A = ⎡⎣⎢649827531⎤⎦⎥ is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is

Answer: (a) A=⎡⎣⎢667625751⎤⎦⎥

Question 24. If the matrix A = ⎡⎣⎢5y422tx−3−7⎤⎦⎥ is a symmetric matrix, then find the value of x, y and t respectively.

• • (a) 4, 2, 3
    (b) 4, 2, -3
    (c) 4, 2, -7
    (d) 2, 4, -7

Answer: (b) 4, 2, -3

Question 25. If a matrix A is both symmetric and skew-symmetric, then

• • (a) A is a diagonal matrix
    (b) A is a zero matrix
    (c) A is a scalar matrix
    (d) A is a square matrix

Answer: (b) A is a zero matrix

Question 26. The matrix ⎡⎣⎢0−5750−11−7110⎤⎦⎥ is

• • (a) a skew-symmetric matrix
    (b) a symmetric matrix
    (c) a diagonal matrix
    (d) an upper triangular matrix

Answer: (a) a skew-symmetric matrix

Question 27. If A² – A + I = O, then the inverse of A is

• • (a) I – A
    (b) A – I
    (c) A
    (d) A + I

Answer:  (a) I – A

Question 28. Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is

• • (a) 9
    (b) 27
    (c) 81
    (d) 512

Answer: (d) 512

Question 29. The matrix ⎡⎣⎢05−8−50−128120⎤⎦⎥ is a

• • (a) diagonal matrix
    (b) symmetric matrix
    (c) skew symmetric matrix
    (d) scalar matrix

Answer: (c) skew symmetric matrix

Question 30. If A is a matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is

• • (a) m × m
    (b) n × n
    (c) n × m
    (d) m × n

Answer: (d) m × n

Question 31. If A and B are matrices of the same order, then (AB’ – BA’) is a

• • (a) skew-symmetric matrix
    (b) null matrix
    (c) symmetric matrix
    (d) unit matrix

Answer: (a) skew-symmetric matrix

Question 32. If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ – 7A is equal to

• • (a) A
    (b) I – A
    (c) I + A
    (d) 3A

Answer: (a) A

---

Next Subject

Next Chapter

---

Bihar board 12th Math chapter 3 complete objective

12th Math objective: we have covered all mcq type objective question of 12th Math chapter 3 on this post, and I hope it will be helpful your board exam. now its time to share it with your friends, and also suggest me what you need.

---

chapter 3 Math objective question

12th Math chapter 3, class 12 Math chapter 3 objective questions in hindi, class 12 Math chapter 3 mcq questions pdf download, Math mcq for class 12 with answers chapter 3 electric charges and fields, 12th class Math chapter 3 objective, class 12 Math chapter 3, Bihar board Math chapter 3 class 12.

Math multiple choice questions with answers for class 12 pdf,  mcq questions for class 12 Math chapter wise pdf, Math objective questions for 12th pdf, Math objective questions for 12th pdf in hindi, Math objective questions for 12th bihar board pdf,

---

Bihar board 12th science stream subjects wise solution

click here to check out Bihar board science stream all subjects solutions

SL.N.	Subject name with solutions
01	Physics
02	Chemistry
03	Biology
04	Math
05	Hindi
06	English