NODIA APP Sample Paper 02 Page 1
Sample Paper 02
Class - 12th Exam - 2024 - 25
Mathematics (Code-041)
Time : 3 Hours Max. Marks : 80
General Instructions :
Read the following instructions very carefully and strictly follow them :
1. This Question paper contains 38 questions. All questions are compulsory.
2. This Question paper is divided into five Sections - A, B, C, D and E.
3. In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and Questions no. 19 and 20
are Assertion-Reason based questions of 1 mark each.
4. In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks
each.
5. In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each.
6. In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each.
7. In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks each.
8. There is no overall choice. However, an internal choice has been provided some questions.
9. Use of calculators is not allowed.
Section - A
Section A consists of 20 questions of 1 mark each.
1. Of all the points of the feasible region, for maximum or minimum of objective functions, the point lies:
(a) inside the feasible region
(b) at the boundary line of the feasible region
(c) vertex point of the boundary of the feasible region
(d) none of the above
2. The maximum value of y = 2x3 − 21x2 + 36x − 20 is
(a) - 128 (b) - 126
(c) - 120 (d) None of these
3. A ball thrown vertically upwards according to the formula s = 13.8t − 4.9t2 , where s is in metres and t is
in seconds. Then its velocity at t = 1 sec is
(a) 6m/ sec (b) 4 m/ sec
(c) 2 m/ sec (d) 8 m/ sec
p
4. #
- p2
2
sin9 x dx = ?
(a) -1 (b) 0
(c) 1 (d) π
2
5. What type of a relation is “Less than” in the set of real numbers?
(a) only symmetric (b) only transitive
(c) only reflexive (d) equivalence relation
, Page 2 Sample Paper 02 CBSE Mathematics Class 12
6. tan−1 x + cot−1 x = ?
(a) 0 (b) 1
(c) π (d) - π
2 2
7. Which of the following is the unit matrix of order 3 # 3 ?
R1 0 0VW R1 0 0V
S S W
(a) S1 0 0W (b) S0 1 0W
SS1 0 0WW SS0 0 1WW
TR XV TR VX
S0 0 1W S0 1 0W
(c) S0 0 1W (d) S0 1 0W
SS0 0 1 W
W SS0 1 0WW
T X T X
d2 y 2
The degree of the equation c 2 m − x b dx l = y is
dy 3 3
8.
dx
(a) 0 (b) 1
(c) 2 (d) 3
sin 20c - cos 20c
9. >sin 70c cos 70c H = ?
(a) 1 (b) -1
(c) 0 (d) 2
10. #x 2 3
$ ex dx =
(b) 1 ex + c
3 3
(a) ex + c
3
(c) ex + c
2
1
(d) ex + c
2
3
dx 6 @
11. d tan x = ?
(a) sec2 x (b) sec x
(c) cot x (d) - sec2 x
12. The radius of a circle is increasing at the rate of 0.4 cm/s. The rate of increase of its circumference is
(a) 0.4π cm/s (b) 0.8π cm/s
(c) 0.8 cm/s (d) None of these
13. Which of the following is a homogeneous differential equation?
(a) x2 ydx − ^x2 + y2h dy = 0 (b) ^xy h dx − ^x 4 + y 4h dy = 0
(c) ^2x + y − 3h dy − ^x + 2y − 3h dx = 0 (d) ^x − y h dy = ^x2 + y + 1h dx
14. # x dx = ..........
5
6 5
(a) x + k (b) x + k
6 5
(c) x7 + k 8
(d) x + k
7 8
Sample Paper 02
Class - 12th Exam - 2024 - 25
Mathematics (Code-041)
Time : 3 Hours Max. Marks : 80
General Instructions :
Read the following instructions very carefully and strictly follow them :
1. This Question paper contains 38 questions. All questions are compulsory.
2. This Question paper is divided into five Sections - A, B, C, D and E.
3. In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and Questions no. 19 and 20
are Assertion-Reason based questions of 1 mark each.
4. In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks
each.
5. In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each.
6. In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each.
7. In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks each.
8. There is no overall choice. However, an internal choice has been provided some questions.
9. Use of calculators is not allowed.
Section - A
Section A consists of 20 questions of 1 mark each.
1. Of all the points of the feasible region, for maximum or minimum of objective functions, the point lies:
(a) inside the feasible region
(b) at the boundary line of the feasible region
(c) vertex point of the boundary of the feasible region
(d) none of the above
2. The maximum value of y = 2x3 − 21x2 + 36x − 20 is
(a) - 128 (b) - 126
(c) - 120 (d) None of these
3. A ball thrown vertically upwards according to the formula s = 13.8t − 4.9t2 , where s is in metres and t is
in seconds. Then its velocity at t = 1 sec is
(a) 6m/ sec (b) 4 m/ sec
(c) 2 m/ sec (d) 8 m/ sec
p
4. #
- p2
2
sin9 x dx = ?
(a) -1 (b) 0
(c) 1 (d) π
2
5. What type of a relation is “Less than” in the set of real numbers?
(a) only symmetric (b) only transitive
(c) only reflexive (d) equivalence relation
, Page 2 Sample Paper 02 CBSE Mathematics Class 12
6. tan−1 x + cot−1 x = ?
(a) 0 (b) 1
(c) π (d) - π
2 2
7. Which of the following is the unit matrix of order 3 # 3 ?
R1 0 0VW R1 0 0V
S S W
(a) S1 0 0W (b) S0 1 0W
SS1 0 0WW SS0 0 1WW
TR XV TR VX
S0 0 1W S0 1 0W
(c) S0 0 1W (d) S0 1 0W
SS0 0 1 W
W SS0 1 0WW
T X T X
d2 y 2
The degree of the equation c 2 m − x b dx l = y is
dy 3 3
8.
dx
(a) 0 (b) 1
(c) 2 (d) 3
sin 20c - cos 20c
9. >sin 70c cos 70c H = ?
(a) 1 (b) -1
(c) 0 (d) 2
10. #x 2 3
$ ex dx =
(b) 1 ex + c
3 3
(a) ex + c
3
(c) ex + c
2
1
(d) ex + c
2
3
dx 6 @
11. d tan x = ?
(a) sec2 x (b) sec x
(c) cot x (d) - sec2 x
12. The radius of a circle is increasing at the rate of 0.4 cm/s. The rate of increase of its circumference is
(a) 0.4π cm/s (b) 0.8π cm/s
(c) 0.8 cm/s (d) None of these
13. Which of the following is a homogeneous differential equation?
(a) x2 ydx − ^x2 + y2h dy = 0 (b) ^xy h dx − ^x 4 + y 4h dy = 0
(c) ^2x + y − 3h dy − ^x + 2y − 3h dx = 0 (d) ^x − y h dy = ^x2 + y + 1h dx
14. # x dx = ..........
5
6 5
(a) x + k (b) x + k
6 5
(c) x7 + k 8
(d) x + k
7 8
