CBSE Class 12 Mathematics 2025 Sample Paper Set 07 Solved

1. If A is any square matrix of order 3 × 3 such that |𝐴| = 3 , Then the value of |𝑎𝑑𝑗𝐴| is
a) 3
b) 1/3
c) 9
d) 27

Answer : c

2. In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both.
One student is chosen at random. The probability that she fails in physics if she fails in mathematics is
a) 1/10
b) 2/5
c) 9/20
d) 1/3

Answer : b

3. Solution of the differential equation tan 𝑦 sec² 𝑥 𝑑𝑥 + tan 𝑥 sec² 𝑦 𝑑𝑦 = 0 is
a) tan 𝑥 + tan 𝑦 = 𝑘
b) tan 𝑥 − tan 𝑦 = 𝑘
c) 𝑡𝑎𝑛𝑥/𝑡𝑎𝑛𝑦 = 𝑘
d) tan 𝑥 tan 𝑦 = 𝑘

 Answer : d

4. The coordinate of the foot of the perpendicular drawn from point P (2, 3, 6) on 𝑥𝑦-plane are
a) (-2, 3, 0)
b) (0, 3, 6)
c) (-2, 0, 6)
d) (2, 3, 0)

Answer : d

5. If A is a matrix of order m x n and B is a matrix such that 𝐴𝐵𝑇 𝑎𝑛𝑑 𝐵𝑇𝐴 both are defined, then the order of matrix B is
a) m x m
b) n x n
c) m x n
d) n x m

Answer : c

6. If A is a square matrix such that 𝐴² – 𝐴 + 𝐼 = 𝑂 then the inverse of A is
a) 𝐼 – 𝐴
b) 𝐴 − 𝐼
c) 𝐴
d) 𝐼 + 𝐴

Answer : a

7. The function 𝑓(𝑥) = |𝑥| + |𝑥 − 1| is
a) continuous at 𝑥 = 0 as well as at 𝑥 = 1
b) continuous at 𝑥 = 1 but not at 𝑥 = 0
c) discontinuous at 𝑥 = 0 as well as at 𝑥 = 1
d) continuous at 𝑥 = 0 but not at 𝑥 = 1

Answer : a

8. If a line make angle a ,b , and γ with the coordinate axis respectively, then sin² a + sin2 b + sin² γ =
a) 1
b) 2
c) -1
d) -2

Answer : b

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