Set-II
DESIGN OF THE QUESTION
PAPER
MATHEMATICS – CLASS XII
Time : 3 Hours
Max. Marks : 100
The weightage of marks over different dimensions of the question paper shall
be as follows:
(A)Weightage to different topics/content units
S.No. Topic Marks
1. Relations and functions 10
2. Algebra 13
3. Calculus 44
4. Vectors and three-dimensional geometry 17
5. Linear programming 06
6. Probability 10
Total 100
(B) Weightage to different forms of questions:
S.No. Form of Questions Marks for Total No. of Total
each Question Questions Marks
1. MCQ/Objective type/VSA 01 10 10
2. Short Answer Questions 04 12 48
3. Long Answer Questions 06 07 42
Total 29 100
(C) Scheme of Option
There is no overall choice. However, an internal choice in four questions of
four marks each and two questions of six marks each has been provided.
Blue Print
Units/Type of Question MCQ/VSA S.A. L.A. Total
Relations and functions 2(2) 8 (2) – 10 (4)
Algebra 3 (3) 4 (1) 6 (1) 13 (5)
Calculus 2 (2) 24(6) 18(3) 44 (11)
Vectors and 3-dimensional
geometry 3 (3) 8 (2) 6 (1) 17 (6)
Linear programming – – 6 (1) 6 (1)
Probability – 4 (1) 6 (1) 10 (2)
Total 10 (10) 48 (12) 42 (7) 100 (29)
, DESIGN OF THE QUESTION PAPER SET-II 337
Section–A
Choose the correct answer from the given four options in each of the Questions 1 to 3.
1. If ∗ is a binary operation given by ∗: R × R → R, a ∗ b = a + b2, then –2∗5 is
(A) –52 (B) 23 (C) 64 (D) 13
π 3π 1
2. If sin–1 : [–1, 1] → , is a function, then value of sin–1 − is
2 2 2
−π −π 5π 7π
(A) 6 (B) 6 (C) 6 (D) 6
9 6 2 3 3 0
3. Given that = . Applying elementary row transformation
3 0 1 0 1 2
R1 → R1–2 R2 on both sides, we get
3 6 2 3 1 −4 3 6 0 3 3 0
(A) = (B) =
3 0 1 0 1 2 3 0 1 0 1 2
−3 6 2 3 3 0 −3 6 −4 3 3 0
(C) = (D) =
3 0 1 0 −3 2 3 0 1 0 1 2
4. If A is a square matrix of order 3 and |A| = 5, then what is the value of |Adj. A|?
5. If A and B are square matrices of order 3 such that |A| = –1 and |B| = 4, then
what is the value of |3(AB)|?
d y 3 d 2 y 2
6. The degree of the differential equation 1 + d x = 2 is_______.
d x
Fill in the blanks in each of the Questions 7 and 8:
dy
7. The integrating factor for solving the linear differential equation x d x – y = x2
is_______.
, 338 MATHEMATICS
2
8. The value of ˆi – ˆj is_______.
9. What is the distance between the planes 3x + 4y –7 = 0 and 6x + 8y + 6 = 0?
10. If a is a unit vector and (x – a) . (x + a) = 99, then what is the value of | x |?
Section–B
11. Let n be a fixed positive integer and R be the relation in Z defined as a R b if
and only if a – b is divisible by n, ∀ a, b ∈ Z. Show that R is an equivalence
relation.
12. Prove that cot–17 + cot–18 + cot–118 = cot–13.
OR
−1 −1 −1 2
Solve the equation tan (2 + x) + tan (2 − x) = tan ,− 3>x> 3.
3
x + 2 x + 6 x −1
13. Solve for x, x + 6 x − 1 x + 2 = 0
x −1 x + 2 x + 6
OR
1 2 1 −1 2
If A = and B = , verify that (AB)′ = B′ A′ .
3 4 3 2 –3
14. Determine the value of k so that the function:
k .cos 2 x
π − 4 x , π
if x ≠
f (x) = 4
5, π
if x =
4
π
is continuous at x = .
4
DESIGN OF THE QUESTION
PAPER
MATHEMATICS – CLASS XII
Time : 3 Hours
Max. Marks : 100
The weightage of marks over different dimensions of the question paper shall
be as follows:
(A)Weightage to different topics/content units
S.No. Topic Marks
1. Relations and functions 10
2. Algebra 13
3. Calculus 44
4. Vectors and three-dimensional geometry 17
5. Linear programming 06
6. Probability 10
Total 100
(B) Weightage to different forms of questions:
S.No. Form of Questions Marks for Total No. of Total
each Question Questions Marks
1. MCQ/Objective type/VSA 01 10 10
2. Short Answer Questions 04 12 48
3. Long Answer Questions 06 07 42
Total 29 100
(C) Scheme of Option
There is no overall choice. However, an internal choice in four questions of
four marks each and two questions of six marks each has been provided.
Blue Print
Units/Type of Question MCQ/VSA S.A. L.A. Total
Relations and functions 2(2) 8 (2) – 10 (4)
Algebra 3 (3) 4 (1) 6 (1) 13 (5)
Calculus 2 (2) 24(6) 18(3) 44 (11)
Vectors and 3-dimensional
geometry 3 (3) 8 (2) 6 (1) 17 (6)
Linear programming – – 6 (1) 6 (1)
Probability – 4 (1) 6 (1) 10 (2)
Total 10 (10) 48 (12) 42 (7) 100 (29)
, DESIGN OF THE QUESTION PAPER SET-II 337
Section–A
Choose the correct answer from the given four options in each of the Questions 1 to 3.
1. If ∗ is a binary operation given by ∗: R × R → R, a ∗ b = a + b2, then –2∗5 is
(A) –52 (B) 23 (C) 64 (D) 13
π 3π 1
2. If sin–1 : [–1, 1] → , is a function, then value of sin–1 − is
2 2 2
−π −π 5π 7π
(A) 6 (B) 6 (C) 6 (D) 6
9 6 2 3 3 0
3. Given that = . Applying elementary row transformation
3 0 1 0 1 2
R1 → R1–2 R2 on both sides, we get
3 6 2 3 1 −4 3 6 0 3 3 0
(A) = (B) =
3 0 1 0 1 2 3 0 1 0 1 2
−3 6 2 3 3 0 −3 6 −4 3 3 0
(C) = (D) =
3 0 1 0 −3 2 3 0 1 0 1 2
4. If A is a square matrix of order 3 and |A| = 5, then what is the value of |Adj. A|?
5. If A and B are square matrices of order 3 such that |A| = –1 and |B| = 4, then
what is the value of |3(AB)|?
d y 3 d 2 y 2
6. The degree of the differential equation 1 + d x = 2 is_______.
d x
Fill in the blanks in each of the Questions 7 and 8:
dy
7. The integrating factor for solving the linear differential equation x d x – y = x2
is_______.
, 338 MATHEMATICS
2
8. The value of ˆi – ˆj is_______.
9. What is the distance between the planes 3x + 4y –7 = 0 and 6x + 8y + 6 = 0?
10. If a is a unit vector and (x – a) . (x + a) = 99, then what is the value of | x |?
Section–B
11. Let n be a fixed positive integer and R be the relation in Z defined as a R b if
and only if a – b is divisible by n, ∀ a, b ∈ Z. Show that R is an equivalence
relation.
12. Prove that cot–17 + cot–18 + cot–118 = cot–13.
OR
−1 −1 −1 2
Solve the equation tan (2 + x) + tan (2 − x) = tan ,− 3>x> 3.
3
x + 2 x + 6 x −1
13. Solve for x, x + 6 x − 1 x + 2 = 0
x −1 x + 2 x + 6
OR
1 2 1 −1 2
If A = and B = , verify that (AB)′ = B′ A′ .
3 4 3 2 –3
14. Determine the value of k so that the function:
k .cos 2 x
π − 4 x , π
if x ≠
f (x) = 4
5, π
if x =
4
π
is continuous at x = .
4
