Marking Scheme link is given at every page.
CBSE EXAM 2025 20 Sets
Class : 12th
Sub : Maths
How to see answers or marking scheme ?
Click above on Every page
If you are unable to click, please open this file using a PDF viewer in Google Drive.
Disclaimer: These papers are based on the SQP released by CBSE and
published by a private organization just for the practice of the students.
CBSE has not released these papers and CBSE is not related to these papers
in any manner. Publisher of these papers clearly state that these paeprs
are only for practice of students and questions may not be come in main
exam.
,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
, NODIA APP Sample Paper 01 Page 3
1−x y−2 z−3 x−1 6−z
14. If the lines 3 = 2α = 2 and 3α = y−1 = 5 are perpendicular, then the value of α is
(a) - 10 (b) 10
7 7
(c) - 10 (d) 10
11 11
15. A bag A contains 4 green and 3 red balls and bog B contains 4 red and 3 green balls. One bag is taken at
random and a ball is drawn and noted to be green. The probability that it comes from bag B is
(a) 2 (b) 2
7 3
(c) 3 (d) 1
7 3
16. Find the area of a curve xy = 4 , bounded by the lines x = 1 and x = 3 and X -axis.
(a) log 12 (b) log 64
(c) log 81 (d) log 27
17. If P ^Ah = 4 , and Q ^A k B h = 7 , then P c B m is equal to
5 10 A
(a) 1 (b) 1
10 8
(c) 7 (d) 17
8 20
18. The point on the curve x2 = 2y which is nearest to the point (0, 5) is
(a) `2 2 , 4 j (b) `2 2 , 0j
(c) ^0, 0h (d) ^2, 2h
19. Assertion : # ex + dx
e−x + 2
= 1 +C
ex + 1
d {f (x)}
Reason : # =− 1 + C
{f (x)} 2 f (x)
(a) Assertion is true, reason is true, reason is a correct explanation for assertion.
(b) Assertion is true,reason is true, reason is not a correct explanation for assertion.
(c) Assertion is true, reason is false.
(d) Assertion is false, reason is true.
20. Assertion : # xex dx = ex + C
(x + 1) 2 x+1
Reason : # ex {f (x) + f ' (x)} dx = ex f (x) + C
(a) Assertion is true, reason is true, reason is a correct explanation for assertion.
(b) Assertion is true,reason is true, reason is not a correct explanation for assertion.
(c) Assertion is true, reason is false.
(d) Assertion is false, reason is true.
CBSE EXAM 2025 20 Sets
Class : 12th
Sub : Maths
How to see answers or marking scheme ?
Click above on Every page
If you are unable to click, please open this file using a PDF viewer in Google Drive.
Disclaimer: These papers are based on the SQP released by CBSE and
published by a private organization just for the practice of the students.
CBSE has not released these papers and CBSE is not related to these papers
in any manner. Publisher of these papers clearly state that these paeprs
are only for practice of students and questions may not be come in main
exam.
,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
, NODIA APP Sample Paper 01 Page 3
1−x y−2 z−3 x−1 6−z
14. If the lines 3 = 2α = 2 and 3α = y−1 = 5 are perpendicular, then the value of α is
(a) - 10 (b) 10
7 7
(c) - 10 (d) 10
11 11
15. A bag A contains 4 green and 3 red balls and bog B contains 4 red and 3 green balls. One bag is taken at
random and a ball is drawn and noted to be green. The probability that it comes from bag B is
(a) 2 (b) 2
7 3
(c) 3 (d) 1
7 3
16. Find the area of a curve xy = 4 , bounded by the lines x = 1 and x = 3 and X -axis.
(a) log 12 (b) log 64
(c) log 81 (d) log 27
17. If P ^Ah = 4 , and Q ^A k B h = 7 , then P c B m is equal to
5 10 A
(a) 1 (b) 1
10 8
(c) 7 (d) 17
8 20
18. The point on the curve x2 = 2y which is nearest to the point (0, 5) is
(a) `2 2 , 4 j (b) `2 2 , 0j
(c) ^0, 0h (d) ^2, 2h
19. Assertion : # ex + dx
e−x + 2
= 1 +C
ex + 1
d {f (x)}
Reason : # =− 1 + C
{f (x)} 2 f (x)
(a) Assertion is true, reason is true, reason is a correct explanation for assertion.
(b) Assertion is true,reason is true, reason is not a correct explanation for assertion.
(c) Assertion is true, reason is false.
(d) Assertion is false, reason is true.
20. Assertion : # xex dx = ex + C
(x + 1) 2 x+1
Reason : # ex {f (x) + f ' (x)} dx = ex f (x) + C
(a) Assertion is true, reason is true, reason is a correct explanation for assertion.
(b) Assertion is true,reason is true, reason is not a correct explanation for assertion.
(c) Assertion is true, reason is false.
(d) Assertion is false, reason is true.
