12th Math chapter 3 Bihar board with NCERTDetails & 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) skewsymmetric matri
 (a) unit matrix
Answer: (d) skewsymmetric 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
 (a) 2, 2, 3, 4
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
 (a) 2, 7, 1, 3, 5, 2
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
 (a) 2 × 3
Answer: (d) 3 × 3
Question 6. A=[12−1−1],B=[xy1−1] and (A + B)^{2} = A^{2} + B^{2}, then x + y =

 (a) 2
(b) 3
(c) 4
(d) 5
 (a) 2
Answer: (d) 5
Question 7. If A = ⎡⎣⎢211232112⎤⎦⎥, then A^{4} – 2^{4 }(A – I) =

 (a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I
 (a) 5I + A
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
 (a) m × n matrix
Answer: (b) n × m matrix
Question 9. If [1324], then A^{2} – 5A is equal to

 (a) 2I
(b) 3I
(c) 2I
(d) null matrix
 (a) 2I
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
 (a) A + B = B + A and A + (B + C) = (A + B) + C
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 = a^{2} + b^{2}, β = ab
(b) α = a^{2} + b^{2}, β = 2ab
(c) α = a^{2} + b^{2}, β = a^{2} – b^{2}
(d) α = 2ab, β = a^{2} + b^{2}
 (a) α = a^{2} + b^{2}, β = ab
Answer: (b) α = a^{2} + b^{2}, β = 2ab
Question 12. If A = ⎡⎣⎢100210x01⎤⎦⎥ and B = ⎡⎣⎢100−210y01⎤⎦⎥ and AB = I_{3}, then x + y equals

 (a) 0
(b) 1
(c) 2
(d) None of these
 (a) 0
Answer: (a) 0
Question 13. If A = [1334] and A^{2} – KA – 5I = 0, then K =

 (a) 5
(b) 3
(c) 7
(d) None of these
 (a) 5
Answer: (a) 5
Question 14. If matrix A = ⎡⎣⎢abcbcacab⎤⎦⎥ where a, b, c are real positivenumbers, abc = 1 and A^{T}A = I, then the value of a^{3} + b^{3} + c^{3} is

 (a) 1
(b) 2
(c) 3
(d) 4
 (a) 1
Answer: (d) 4
Question 15. Find the values of x, y, z respectively if the matrix A=⎡⎣⎢0xx2yy−yz−zz⎤⎦⎥ satisfy the equation A^{T}A = I_{3}.

 (a) 12√⋅16√,13√
(b) −12√,−16√,−13√
(c) Both (a) and (b)
(d) None of these
 (a) 12√⋅16√,13√
Answer: (c) Both (a) and (b)
Question 16. If A=[cosxsinx−sinxcosx], find AAT.

 (a) Zero Matrix
(b) I_{2}
(c) [1111]
(d) None of these
 (a) Zero Matrix
Answer: (b) I_{2}
Question 17. If A=⎡⎣⎢01−2−10−3230⎤⎦⎥, then A + 2A^{T} equals

 (a) A
(b) A^{T}
(c) A^{T}
(d) 2A^{2}
 (a) A
Answer: (c) A^{T}
Question 18. For any square matrix A, AA^{T} is a

 (a) unit matrix
(b) symmetric matrix
(c) skewsymmetric matrix
(d) diagonal matrix
 (a) unit 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 askewsymmetric matrix
(c) AB + BA is a symmetric matrix
(d) AB – BA is a symmetric matrix
 (a) AB 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
 (a) 4
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) skewsymmetric matrix
(c) symmetric matrix
(d) none of these
 (a) diagonal matrix
Answer: (b) skewsymmetric matrix
Question 22. If A is any square matrix, then which of the following is skewsymmetric?

 (a) A + A^{T}
(b) A – A^{T}
(c) AA^{T}
(d) A^{T}A
 (a) A + A^{T}
Answer: (b) A – A^{T}
Question 23. If A = ⎡⎣⎢649827531⎤⎦⎥ is the sum of a symmetric matrix B and skewsymmetric 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
 (a) 4, 2, 3
Answer: (b) 4, 2, 3
Question 25. If a matrix A is both symmetric and skewsymmetric, 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
 (a) A is a diagonal matrix
Answer: (b) A is a zero matrix
Question 26. The matrix ⎡⎣⎢0−5750−11−7110⎤⎦⎥ is

 (a) a skewsymmetric matrix
(b) a symmetric matrix
(c) a diagonal matrix
(d) an upper triangular matrix
 (a) a skewsymmetric matrix
Answer: (a) a skewsymmetric matrix
Question 27. If A^{2} – A + I = O, then the inverse of A is

 (a) I – A
(b) A – I
(c) A
(d) A + I
 (a) I – A
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
 (a) 9
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
 (a) diagonal 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
 (a) m × m
Answer: (d) m × n
Question 31. If A and B are matrices of the same order, then (AB’ – BA’) is a

 (a) skewsymmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix
 (a) skewsymmetric matrix
Answer: (a) skewsymmetric matrix
Question 32. If A is a square matrix such that A^{2} = I, then (A – I)^{3} + (A + I)^{3} – 7A is equal to

 (a) A
(b) I – A
(c) I + A
(d) 3A
 (a) A
Answer: (a) A
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