Matrices: Class 12 Previous Year Questions

Matrices questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. (a) If A =             0 1 1 2 1 2 , find A–1 and use it to solve the following system of equations : –2y + z = 7, 2x – y – z = 8, x – 2y = 10 5 OR (b) If              2 7 11 2 cos 4 7 3 sin 1 3 x x is a singular matrix, then find all …
   Board 20265 markslong answerRepeated: 2023,2026
2. (a) If 1 2 0 0 3 1 A and 2 2 5 5 6 15 B 1 , find (AB) 1. OR (b) Solve the following system of equations by matrix method : x + 2y + 3z = 6 2x y + z = 2 3x + 2y 2z =
   Board 20235 markslong answerRepeated: 2023,2026
3. { } 2. Which of the following cannot be the order of a row-matrix ? 1 (A) 2  1 (B) 1  2 (C) 1  1 (D) 1  n 4 { } 3.            /   / ? 1 (i) (A + B) = A + B (ii) (A – B) = B – A (iii) (AB) =…
   Board 20261 markMCQ
4. If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric ? 1 (A) AB (B) AB + BA (C) (A + B)2 (D) A – B
   Board 20261 markMCQ
5. { } 2. If A and B are square matrices of same order, then which of the following statements is/are always true ? 1 (i) (A + B) (A – B) = A2 – B2 (ii) AB = BA (iii) (A + B)2 = A2 + AB + BA + B2 (iv) AB = 0  A = 0 or B = 0 (A) Only (i) and (iii) (B) Only (ii) a…
   Board 20261 markMCQ
6. Which of the following properties is/are true for two matrices of suitable orders ? 1 (i) (A + B) = A + B (ii) (A – B) = B – A (iii) (AB) = AB (iv) (kAB) = kBA (k is a scalar) (A) (i) only (B) (i), (ii) and (iii) (C) (i) and (ii) (D) (i) and (iv) 0…
   Board 20261 markMCQ
7. If A is a square matrix of order 2 such that det (A) = 4, then det (4 adj A) is equal to : 16 (A) (B) 64 (C) 256 (D) 512
   Board 20251 markMCQ
8. If A= 6x 4. 2x is a symmetric matrix, then (2x + y) is 8x (A) -8 (B) (C) (D) Page 5 of 24 5.y= sin-lx, -1 0, y: (A) (B) (C) (D) 3·· , - : 6. 4'3 ·· (A) (B) (C) (D) ()(F)() P(E) (A) (B)1 - P(E/F) P(F) 1-P(EUF) (C) 1 - P(E/F) (D) P(F) 8. 3 (A) (B)ff 3 ·C· (D) 9.…
   Board 20251 markMCQ
9. Which of the following can be both a symmetric and skew-symmetric matrix ? Unit Matrix (A) (B) Diagonal Matrix Null Matrix (C) (D)Row Matrix
   Board 20251 markMCQ
10. If A and B are square matrices of order m such that A2- B2 = (A- B) (A + B) then which of the following is always correct ? (A) A=B (B) AB=BA (C) A= O or B= 0 (D) A=Ior B= I
    Board 20251 markMCQ
11. If A and B are invertible matrices, then which of the following is not correct ? (A)(A + B)-1 = B-1 + A-1 (B) (AB)-1 = B-1A-1 (C) adj (A) = I A I A-1 (D)I A I-1 = A-1 I
    Board 20251 markMCQ
12. A school wants to allocate students into three clubs : Sports, Music and Drama, under following conditions : The number of students in Sports club should be equal to the sum of the number of students in Music and Drama club. The number of students in Music clu…
    Board 20255 markslong answer
13. Assertion (A) : A = diag [3 5 2] is a scalar matrix of order 3 × 3. Reason (R) : If a diagonal matrix has all non-zero elements equal, it is known as a scalar matrix.
    Board 20251 markAssertion-Reason
14. Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB + 3(AB +BA)-4 BA, where A and B are both matrices of order 2 × 2. It is known that A±B I and A-l ± B. Their answers are given as : Abhay : 6 AB Bina : 7AB-BA Chhaya: 8 AB Devesh : 7 BA - A…
    Board 20251 markMCQ
15. Page 3 of 23 1. If the sum of all the elements of a 3 ´ 3 scalar matrix is 9, then the product of all its elements is : (A) 0 (B) 9 (C) 27 (D) 729 666
    Board 20241 markMCQ
16. Page 10 of 23 20. A{^H$WZ (A) : Xmo eyÝ`oVa g{Xem| ® a Am¡a ® b Ho$ {bE, ® a . ® b = ® b . ® a . VH©$ (R) : Xmo eyÝ`oVa g{Xem| ® a Am¡a ® b Ho$ {bE, ® a ´ ® b = ® b ´ ® a . 666 Page 11 of 23 17. If F(x) = ú ú ú û ù ê ê ê ë é 1 0 0 0 x cos x sin 0 x sin – x cos…
    Board 20241 markAssertion-Reason
17. Page 3 of 23 2. If a matrix has 36 elements, the number of possible orders it can have, is : (A) 13 (B) 3 (C) 5 (D) 9 666 2 3 0 ìï
    Board 20241 markMCQ
18. : P + Q, where P is a symmetric and Q is a skew symmetric matrix, then Q is equal to 5/2 -5/2 7 (A) (B) 5/2 5/2 5/2 -5/2 (C) (D) -5/2 5/2
    Board 20231 markMCQ
19. If IAl = IkAl, where A is a square matrix of order 2, then sum of all possible values of k is (A) (B) -1 (C) (D)
    Board 20231 markMCQ
20. If A and B are symmetric matrices of same order, then   2BA T T AB  is a (a) Skew symmetric matrix (b)Symmetric matrix (c) Neither Symmetric matrix nor Skew symmetric matrix (d) Null matrix
    CBSE practice 2023-241 markMCQ

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