NODIA APP Sample Paper 01 Page 1
Sample Paper 01
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. If f (x) = log e (log e x), then f' (e) is equal to
(a) e-1 (b) e
(c) 1 (d) 0
dy dy 2 1 dy 3
The degree of the differential equation x = 1 + b
dx l 2! b dx l 3! b dx l
2. +1 + + ..., is
(a) 3 (b) 2
(c) 1 (d) not defined
R1 2 4V
S W
3. The symmetric part of the matrix A = S6 8 2W is equal to
SS2 − 2 7WW
R 0 - 2 - 1V T X R1 4 3VW
S W S
(a) S- 2 0 - 2W (b) S2 8 0W
SS- 1 - 2 0 WW SS3 0 7WW
TR X TR X
S 0 - 2 1W
V
S1 4 3VW
(c) S 2 0 2W (d) S4 8 0W
SS- 1 2 0WW SS3 0 7WW
T X T X
x - 1 m dx is
2
4. The value of #c
x
2 2
(a) x + log x − 2x + C (b) x + log x + 2x + C
2 2
(c) x2 − log x − 2x + C (d) None of these
2
, Page 2 Sample Paper 01 CBSE Mathematics Class 12
dy ax + g
5. The solution of = represents a circle, when
dx by + f
(a) a = b (b) a = − b
(c) a =− 2b (d) a = 2b
6. If y = tan−1 1 − sin x , then the value of dy at x = π is
1 + sin x dx 6
(a) - 1 (b) 1
2 2
(c) 1 (d) - 1
7. The area of enclosed by y = 3x − 5 , y = 0 , x = 3 and x = 5 is
(a) 12 sq units (b) 13 sq units
(c) 13 1 sq units (d) 14 sq units
2
dy
8. The general solution of the differential equation = ey (ex + e−x + 2x) is
dx
(a) e−y = ex − e−x + x2 + C (b) e−y = e−x − ex − x2 + C
(c) e−y =− e−x − ex − x2 + C (d) ey = e−x + ex + x2 + C
9. If λ (3it + 2tj − 6kt) is a unit vector, then the value of λ is
(a) ! 1 (b) ! 7
7
(c) ! 43 (d) ! 1
43
2
10. If av = it − 2tj + 3kt and bv is a vector such that av $ bv = bv and av − bv = 7 , then bv is equal to
(a) 7 (b) 3
(c) 7 (d) 3
11. The area of the region bounded by the lines y = mx, x = 1, x = 2 and X -axis is 6 sq units, then m is
equal to
(a) 3 (b) 1
(c) 2 (d) 4
12. The direction cosines of the line joining the points (4, 3, - 5) and (- 2, 1, - 8) are
(a) b 6 , 2 , 3 l (b) b 2 , 3 , - 6 l
7 7 7 7 7 7
(c) b 6 , 3 , 2 l (d) None of these
7 7 7
13. The least, value of the function f (x) = ax + b/x , a 2 0 , b 2 0 , x 2 0 is
(a) ab (b) 2 a
b
(c) 2 b (d) 2 ab
a
Sample Paper 01
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. If f (x) = log e (log e x), then f' (e) is equal to
(a) e-1 (b) e
(c) 1 (d) 0
dy dy 2 1 dy 3
The degree of the differential equation x = 1 + b
dx l 2! b dx l 3! b dx l
2. +1 + + ..., is
(a) 3 (b) 2
(c) 1 (d) not defined
R1 2 4V
S W
3. The symmetric part of the matrix A = S6 8 2W is equal to
SS2 − 2 7WW
R 0 - 2 - 1V T X R1 4 3VW
S W S
(a) S- 2 0 - 2W (b) S2 8 0W
SS- 1 - 2 0 WW SS3 0 7WW
TR X TR X
S 0 - 2 1W
V
S1 4 3VW
(c) S 2 0 2W (d) S4 8 0W
SS- 1 2 0WW SS3 0 7WW
T X T X
x - 1 m dx is
2
4. The value of #c
x
2 2
(a) x + log x − 2x + C (b) x + log x + 2x + C
2 2
(c) x2 − log x − 2x + C (d) None of these
2
, Page 2 Sample Paper 01 CBSE Mathematics Class 12
dy ax + g
5. The solution of = represents a circle, when
dx by + f
(a) a = b (b) a = − b
(c) a =− 2b (d) a = 2b
6. If y = tan−1 1 − sin x , then the value of dy at x = π is
1 + sin x dx 6
(a) - 1 (b) 1
2 2
(c) 1 (d) - 1
7. The area of enclosed by y = 3x − 5 , y = 0 , x = 3 and x = 5 is
(a) 12 sq units (b) 13 sq units
(c) 13 1 sq units (d) 14 sq units
2
dy
8. The general solution of the differential equation = ey (ex + e−x + 2x) is
dx
(a) e−y = ex − e−x + x2 + C (b) e−y = e−x − ex − x2 + C
(c) e−y =− e−x − ex − x2 + C (d) ey = e−x + ex + x2 + C
9. If λ (3it + 2tj − 6kt) is a unit vector, then the value of λ is
(a) ! 1 (b) ! 7
7
(c) ! 43 (d) ! 1
43
2
10. If av = it − 2tj + 3kt and bv is a vector such that av $ bv = bv and av − bv = 7 , then bv is equal to
(a) 7 (b) 3
(c) 7 (d) 3
11. The area of the region bounded by the lines y = mx, x = 1, x = 2 and X -axis is 6 sq units, then m is
equal to
(a) 3 (b) 1
(c) 2 (d) 4
12. The direction cosines of the line joining the points (4, 3, - 5) and (- 2, 1, - 8) are
(a) b 6 , 2 , 3 l (b) b 2 , 3 , - 6 l
7 7 7 7 7 7
(c) b 6 , 3 , 2 l (d) None of these
7 7 7
13. The least, value of the function f (x) = ax + b/x , a 2 0 , b 2 0 , x 2 0 is
(a) ab (b) 2 a
b
(c) 2 b (d) 2 ab
a
