Class 12 PT I Question Paper 2024-25 Maths

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Question Paper for CBSE Board, KV Schools,
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Question Paper based on NCERT Syllabus
CBSE Board Question Paper / KV Schools Question Paper

Unit Test -01 (2024-25)
Class : XII
Mathematics (Code-041)

Time Allowed:90 minutes Maximum Marks :40
General Instructions:
1. This question paper contains five sections – A, B, C, D and E. Each part is compulsory.
2. Section A has 8 multiple choice type questions of 1 mark each and 1 assertion reasoning question of 1
mark.
3. Section- B has 4 questions of 2 marks each.
4. Section- C has 3 questions of 3 marks each.
5. Section- D has 2 questions of 5 marks each
6. Section- E has 1 case based question of 4 marks.
7.There is an internal choice in some of the questions.

Q.NO. SECTION – A ( Multiple Choice Questions) Marks
1. A and B are two sets with m and n elements respectively (m < n). How many onto 1
functions can be defined from set A to set B?
(a) 0 (b) n!
(c) m! (d) 𝑛𝑚
2. √3
The value of sin-1[ cos (sin-1 2 )] is 1

𝜋 𝜋
(a) 6 (b) - 6
𝜋 𝜋
(c) 4 (d) - 4

3. If A is an invertible matrix of order 2, then det(A-1) is equal to 1
1
(a) det (A) (b) det(𝐴)

(c) 1 (d) 0
4. Let A be square matrix of order 3 x 3, then |𝑘𝐴| is equal to 1
(a) k |𝐴| (b) k2 |𝐴|
(c) k3 |𝐴| (d) 3k |𝐴|
5. Derivative of sec(tan-1x) with respect to x is 1
𝑥 𝑥
(a) (b) 1+𝑥 2
√1+𝑥 2
1
(c) x√1 + 𝑥 2 (d)

√1+𝑥 2

6. 𝑑𝑦 1
If y = √sin 𝑥 + 𝑦 , then 𝑑𝑥 is equal to
cos 𝑥 cos 𝑥
(a) 2𝑦−1 (b) 1−2𝑦
sin 𝑥 sin 𝑥
(c) 1−2𝑦 (d) 2𝑦−1

7. 3 4 1
If 𝐴 = [ ] and B is the inverse of A. Which of the following is AB?
−5 2
0 0 0 1
(a) [ ] (b) [ ]
0 0 1 0

1 0 1 1
(c) [ ] (d) [ ]
0 1 1 1
8. 2 −1 1
If A and B are two matrices such that the transpose of (A+B) is [ ].
7 6
3 −2
If B=[ ], which of the following is A?
6 0
−1 1 −1 9
(a) [ ] (b) [ ]
1 6 −7 6

1 −9 −4 4
(c) [ ] (d) [ ]
7 −6 0 7
9 In the following question, a statement of assertion (A) is followed by a statement of 1
Reason (R). Choose the correct answer out of the following choices.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.

Assertion (A) : Let f :R →R defined as 𝑓 (𝑥) = [𝑥], where [ . ] represents the greatest
integer function. Then f is not one-one.
Reason (R) : A function is one-one if 𝑓 (𝑥) = 𝑓 (𝑦) implies 𝑥 = 𝑦
SECTION B
10 −1 −1 2 2
If 𝑎𝑑𝑗 (𝐵) = [ 1 4 3 ], find |𝐵|
0 1 −2
11 𝑑𝑓(𝑡) 2
If 𝑥 = 𝑎 log 𝑡 and 𝑓(𝑡) = 𝑎 sin−1 𝑡 where a is constant. Find 𝑑𝑥

12 −1 −1 2
Find the value of tan-1 1 + cos-1( 2 ) + sin-1 ( 2 ).

13 1 0 2 𝑥 2
Find x, if [𝑥 −5 −1] [0 2 1] [4] = 0
2 0 3 1
SECTION C
14 1 2 3 −7 −8 −9 3

Find the matrix X so that X [ ]=[ ]
4 5 6 2 4 6
OR
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
15 Differentiate : (sin x)x + sin - 1√𝑥 3

16 A ladder 5 m long is leaning against wall. The bottom of the ladder is pulled along the 3
ground away from the wall at the rate of 2 m/sec. How fast is its height on the wall
decreasing, when the foot of ladder is 4 m away from the wall.
SECTION D
17. −4 4 4 1 −1 1 5
Determine the product [−7 1 3 ] [1 −2 −2] and use it to solve the system of
5 −3 −1 2 1 3
equations:
𝑥– 𝑦 + 𝑧 = 4
𝑥 – 2𝑦 – 2𝑧 = 9
2𝑥 + 𝑦 + 3𝑧 = 1

OR
1 2 −3
Find A-1, where A = [2 3 2 ], Hence solve the system of equations:
3 −3 −4

𝑥 + 2𝑦 − 3𝑧 = − 4
2𝑥 + 3𝑦 + 2𝑧 = 2
3𝑥 − 3𝑦 − 4𝑧 = 11

18 Show that the relation S in the set A = {𝑥 ∈ 𝑍: 0 ≤ 𝑥 ≤ 12} given by 5
S = {(𝑎, 𝑏): 𝑎, 𝑏 ∈ 𝑍, |𝑎 − 𝑏| is divisible by 4} is an equivalence relation. Find the set of
all elements related to 1
SECTION E
( CASE BASED QUESTION)
19 4

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