Determinants: Class 12 Previous Year Questions

Determinants 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. -2 and B = 35. (a) Given A = find AB. Hence, solve -3 -1 the system of linear equations : x-y+z=4 x- 2y - 2z = 9 2x+y+ 3z= 1 OR If A= -2 -1 (b) -2, then find A-1. -1 Hence, solve the system of linear equations : x- 2y = 10 2x-y-z= 8 -2y + z = 7 Page 19 of 24 (…
   Board 20255 markslong answerRepeated: 2023,2025
2. { } 32. (a) If P =         2 1 0 4 3 2 and Q =         5 1 – 2 4 – 2 4 – , find (QP) and hence solve the following system of equations using matrices : x – y = 3, 2x + 3y + 4z = 17, y + 2z = 7 5 OR 18 { } (b)  = z 1 1 1 1 y 1 1 1 1 1   x …
   Board 20265 markslong answer
3. If A = 1. , then A-1 is [-1 (A) -1 (B) -1 -1 -1 [-1 07 [-1 (C) -1 (D) Page 3 of 24 (A) (B) (C) (D) 3. dx, x ± 0; ·· : -1 (A)-1 (B) (C) (D) 4. (A) y2 - xy (B) ·-3y (C) sin? + (D) tan x- sec y xx 5. ()· (A) = = f() (B) (C) (D) 6. A 2 det (A) = 4, det (4 adj A) (…
   Board 20251 markMCQ
4. JJJJ Page 3 3. Let A be a 3 3 matrix such that |adj A| = 64. Then |A| is equal to : (a) 8 only (b) 8 only (c) 64 (d) 8 or 8 JJJJ Page 4 4. `{X A = 2 5 4 3 h¡ VWm 2A + B EH$ eyÝ` Amì`yh h¡, Vmo B ~am~a h¡ : (a) 4 10 8 6 (b) 4 10 8 6 (c) 3 10 8 5 (d) 3 10 8 5 5.…
   Board 20231 markMCQ
5. If A be a 3  3 square matrix such that   5 0 0 0 5 0 0 0 5 A adj A           then the value of Adj A is (a) 5 (b) 25 (c) 125 (d) 625
   CBSE practice 2023-241 markMCQ
6. Under which of the following conditions will |A| be equal to 0? i) a - 2p = b - 2q = c - 2r = 0 ii) x = y = z = 0 iii) a : b : c = x : y : z A. only ii) B. only i) and ii) C. only i) and iii) D. all - i), ii) and iii)
   CBSE practice 2022-231 markMCQ
7. Sravan is a nutritionist. He wants to create a mixture of orange juice, beetroot juice and kiwi juice that can provide 1860 mg of vitamin C, 22 mg of iron and 760 mg of calcium. The quantity of each nutrient per litre of juice is shown below. Using the matrix …
   CBSE practice 2022-235 markslong answer
8. Abdul threw a basketball in the direction of the basketball hoop which traversed a parabolic path in a vertical plane as shown below. (Note: The image is for representation purpose only.) The equation of the path traversed by the ball is y = ax2 + bx + c with …
   CBSE practice 2023-245 markslong answer
9. To celebrate their child's birthday, a family decided to distribute fruits among children in three orphanages. The fruit vendor packed three different types of baskets, according to the quantity required at each orphanage, details are given as follows: Basket …
   Sample paper 2026-274 marksshort answer
10. If abc = 2, what is the value of the determinant below? A. -48 B. -24 C. 48 D. (cannot be found without the values of a, b and c) 1
    CBSE practice 2022-231 markMCQ

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