NODIA APP Sample Paper 06 Page 1
Sample Paper 06
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. The area bounded by the parabola y2 = 8x and its latus rectum is
(a) 16/3 sq units (b) 32/3 sq units
(c) 8/3 sq units (d) 64/3 sq units
2. If av $ bv = av bv , then av, bv are
(a) perpendicular (b) like parallel
(c) unlike parallel (d) coincident
3. Let f ^x h = x3 + 3 x2 + 3x + 3 , then f ^x h is
2
(a) am even function (b) an odd function
(c) an increasing function (d) a decreasing function
1 2 1
If P = >
1 3 1H
4. and Q = PPT , then the value of Q is
(a) 2 (b) - 2
(c) 1 (d) 0
5. # dx is equal to
x (x7 + 1)
7 7
(a) log c 7x m + C (b) 1 log c 7x m + C
x +1 7 x +1
7 7
(c) log c x +7 1 m + C (d) 1 log c x +7 1 m + C
x 7 x
, Page 2 Sample Paper 06 CBSE Mathematics Class 12
6. The value of #0
1 dx is
ex + e
(a) 1 log b 1 + e l (b) log b 1 + e l
e 2 2
(c) 1 log (1 + e) (d) log b 2 l
e 1+e
7. If A = {1, 3, 5, 7} and B = {1, 2, 3, 4, 5, 6, 7, 8} , then the number of one-one function from A into B is
(a) 1340 (b) 1860
(c) 1430 (d) 1680
The relation cosec−1 b x + 1 l = 2 cot−1 x is valid for
2
8.
2x
(a) x $ 1 (b) x $ 0
(c) x $1 (d) none of these
y + ey+... dy
9. If x = ey + e , then is equal to
dx
(a) 1 (b) 1 - x
x x
(c) x (d) None of these
1+x
10. The point of discontinuous of tan x are
(a) nπ , n d I (b) 2nπ , n d I
(c) (2n + 1) π , n d I (d) None of these
2
11. The length of the largest interval in which the function 3 sin x - 4 sin3 x is increasing, is
(a) π (b) π
3 2
(c) 3π (d) π
2
12. Two dice are thrown n times in succession. The probability of obtaining a doublet six atleast once is
(a) b 1 l (b) 1 - b 35 l
n n
36 36
(c) b 1 l
n
(d) None of these
12
d2 y 2 d2 y
The degree of the differential equation c 2 m + b dx l = x sin c m
dy 2
13.
dx dx2
(a) 1 (b) 3
(c) 2 (d) none of these
dy y
14. The solution of the differential equation x2 − xy = 1 + cos is
dx x
y y
(a) tan = c − 12 (b) tan = c+ 1
2x 2x x x
y y
(c) cos = 1+c (d) x2 = (c + x2) tan
x x x
Sample Paper 06
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. The area bounded by the parabola y2 = 8x and its latus rectum is
(a) 16/3 sq units (b) 32/3 sq units
(c) 8/3 sq units (d) 64/3 sq units
2. If av $ bv = av bv , then av, bv are
(a) perpendicular (b) like parallel
(c) unlike parallel (d) coincident
3. Let f ^x h = x3 + 3 x2 + 3x + 3 , then f ^x h is
2
(a) am even function (b) an odd function
(c) an increasing function (d) a decreasing function
1 2 1
If P = >
1 3 1H
4. and Q = PPT , then the value of Q is
(a) 2 (b) - 2
(c) 1 (d) 0
5. # dx is equal to
x (x7 + 1)
7 7
(a) log c 7x m + C (b) 1 log c 7x m + C
x +1 7 x +1
7 7
(c) log c x +7 1 m + C (d) 1 log c x +7 1 m + C
x 7 x
, Page 2 Sample Paper 06 CBSE Mathematics Class 12
6. The value of #0
1 dx is
ex + e
(a) 1 log b 1 + e l (b) log b 1 + e l
e 2 2
(c) 1 log (1 + e) (d) log b 2 l
e 1+e
7. If A = {1, 3, 5, 7} and B = {1, 2, 3, 4, 5, 6, 7, 8} , then the number of one-one function from A into B is
(a) 1340 (b) 1860
(c) 1430 (d) 1680
The relation cosec−1 b x + 1 l = 2 cot−1 x is valid for
2
8.
2x
(a) x $ 1 (b) x $ 0
(c) x $1 (d) none of these
y + ey+... dy
9. If x = ey + e , then is equal to
dx
(a) 1 (b) 1 - x
x x
(c) x (d) None of these
1+x
10. The point of discontinuous of tan x are
(a) nπ , n d I (b) 2nπ , n d I
(c) (2n + 1) π , n d I (d) None of these
2
11. The length of the largest interval in which the function 3 sin x - 4 sin3 x is increasing, is
(a) π (b) π
3 2
(c) 3π (d) π
2
12. Two dice are thrown n times in succession. The probability of obtaining a doublet six atleast once is
(a) b 1 l (b) 1 - b 35 l
n n
36 36
(c) b 1 l
n
(d) None of these
12
d2 y 2 d2 y
The degree of the differential equation c 2 m + b dx l = x sin c m
dy 2
13.
dx dx2
(a) 1 (b) 3
(c) 2 (d) none of these
dy y
14. The solution of the differential equation x2 − xy = 1 + cos is
dx x
y y
(a) tan = c − 12 (b) tan = c+ 1
2x 2x x x
y y
(c) cos = 1+c (d) x2 = (c + x2) tan
x x x
