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Class 10 Mathematics Chapter 3 & 4 Board Pattern Paper 2027 | Matrices and Determinants, Functions and Graphs
CLASS 10 Math Chapter 3 & 4 Board Pattern Paper 2027
Class 10 Mathematics Board Pattern Paper 2027 for Chapter 3: Matrices and Determinants and Chapter 4: Functions and Graphs is designed according to the latest Punjab Board-style examination pattern. This Mathematics paper includes objective and subjective-type questions covering important concepts, short questions, matrix operations, determinants, functions, inverse functions, domain and range, absolute value functions, and related problem-solving practice. Students preparing for the Class 10 Mathematics 2027 board examination can use this chapter-wise paper for revision, self-assessment, and exam preparation.
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BOARD PAPER PATTERN
MATHEMATICS
CHAPTER
WISE
WISE
Roll No. (in Figures):
………………………………….
(in Words):
………………………………….
Unit 3: Matrices and Determinants
Time : 20 Minutes
Unit 4: Functions and Graphs
Marks: 15
OBJECTIVE TYPE
1 ABCD
2 ABCD
3 ABCD
4 ABCD
5 ABCD
6 ABCD
7 ABCD
8 ABCD
9 ABCD
10 ABCD
11 ABCD
12 ABCD
13 ABCD
14 ABCD
15 ABCD
Note: Four possible answers A, B, C and D to each question are given.
The choice which you think is correct, fill that circle in front of that question with
Marker or Pen ink. Cutting or filling two or more circles will result in zero mark in
that question.
1.
A =
3 5 0
is a ______ matrix.
2.
B =
2
3 is a ______ matrix.
3 is a ______ matrix.
3.
If
A =
3 4
,
B =
7 8
,
then A + B =
4.
3 1
0 4 =
0 4 =
5. Identify the order of the matrix
7 8 9
.
6.
If
2x 1
=
10 1
then what is the value of x?
7. A square matrix A is symmetric if:
8. Commutative law of Addition of Matrices is:
9. A function f from X to Y is represented by:
10.
(fog)(x) =
11. What is the shape of the graph of an absolute value function?
12. If f(x) = x3, then
f(−2) =
13. If f(x) = x2 + 3x + 1,
what is the value of f(−2)?
14. If f(x) = x2 and
g(x) = 2x−1, then the value of
(f−g)(x) is:
15. Domain of f = __________.
Here is Subjective Part of paper.
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BOARD PAPER PATTERN
MATHEMATICS
CHAPTER
WISE
WISE
Roll No. (in Figures): ………………………………….
(in Words): ………………………………….
Unit 3: Matrices and Determinants
Time : 2:10 Hours
Unit 4: Functions and Graphs
Marks: 60
SUBJECTIVE TYPE (PART – I)
Q2. Write short answers to any SIX (6) questions:
(6×2=12)
(i)
If
2x + 1 4
7 5 = 9 4
7 y , then find the values of x and y.
7 5 = 9 4
7 y , then find the values of x and y.
(ii)
Find transpose of the matrix:
A =
2 3
4 5
4 5
(iii)
Find negative of the matrix:
A =
−3 0
5 6
5 6
(iv)
Show that
L =
2 3 4
3 −2 5
4 5 0 is a symmetric matrix.
3 −2 5
4 5 0 is a symmetric matrix.
(v)
If
A =
2 3
4 5 and B = 7 6
5 8 , then verify that (At)t = A.
4 5 and B = 7 6
5 8 , then verify that (At)t = A.
(vi)
If
A =
4 2
7 6 , B = 5 5
8 8 , then find (A − B)t.
7 6 , B = 5 5
8 8 , then find (A − B)t.
(vii)
If
A =
4 2
7 6 , B = 5 5
8 8 , then find Bt − At.
7 6 , B = 5 5
8 8 , then find Bt − At.
(viii)
If
A =
7 3
2 1 and B = 5 3
2 4 , then find |B|.
2 1 and B = 5 3
2 4 , then find |B|.
(ix)
If
A =
7 3
2 1 , B = 5 3
2 4 , then find Adj B.
2 1 , B = 5 3
2 4 , then find Adj B.
Q3. Write short answers to any SIX (6) questions:
(6×2=12)
(i)
Define a row in the context of a matrix.
(ii)
Define a column in context of a matrix.
(iii)
Define equal matrices.
(iv)
Find the value of x when
A =
x 6
5 15 is a singular matrix.
5 15 is a singular matrix.
(v)
What is a “square matrix”.
(vi)
Define “Scalar matrix”.
(vii)
Find the negative of matrix
B =
−1 0
4 7
4 7
(viii)
If
A =
9 −8
8 4 , then show that it is a symmetric matrix.
8 4 , then show that it is a symmetric matrix.
(ix)
Find the determinant of
A =
−7 35
−1 5
−1 5
Q4. Write short answers to any SIX (6) questions:
(6×2=12)
(i)
If f(x) = 2x + 5, g(x) = 3x − 2,
then find f(x) + g(x).
(ii)
If f(x) = 2x − 3 then find f−1(x).
(iii)
A function B(t) = 5,000 + 200t represents the total
balance (in rupees) after t months. What will be the
balance after 6 months?
(iv)
Describe the range of a function.
(v)
If g(x) = (x−1)3, then find g(−4).
(vi)
Find the domain and range for function:
f(x) = 3√x
(vii)
If f(x) = {(3,a),(7,b),(1,c)} then find f−1(x).
(viii)
Define an absolute value function.
(ix)
What is the characteristic shape of the graph of
f(x) = |x|?
(PART – II)
Note: Attempt any two (02) questions.
(2×8=16)
Q5. (a)
If
p + q 5
11 p − 2q = 6 5
11 0 , then find the values of p and q. 4
11 p − 2q = 6 5
11 0 , then find the values of p and q. 4
(b)
A shop employs, 5 men and 3 women, pays total daily wages
Rs. 3500. If the number of men is reduced to 2 and 3 extra
women are taken on, the daily wages amount to Rs. 5000.
Find daily wage of a man and a woman by using matrices.
4
Q6. (a)
If
A =
x 8
5 10 is a singular matrix, then find the value of x. 4
5 10 is a singular matrix, then find the value of x. 4
(b)
Find the value of x when
A =
x 6
5 15 is a singular matrix. 4
5 15 is a singular matrix. 4
Q7. (a)
Find the adjoint of the following matrices.
A =
a b
c d , B = 5 −2
3 7 , C = −3 5
−3 2 4
c d , B = 5 −2
3 7 , C = −3 5
−3 2 4
(b)
Find the inverse of f(x) = 2x + 3.
Also find domain and range of f−1(x).
4
(PART – III)
Note: Attempt any one (01) question.
(1×8=8)
Q8. (a)
If f(x) = x3, find f−1(x).
Also verify that
f(f−1(x)) = f−1(f(x)) = x.
4
(b)
Given that f(x) = x2 + 9 and g(x) = x + 21.
Find the values of a such that:
f(a) = g(a).
4
Q9. (a)
Solve 2|x − 3| = 16 and express the solution on number line.
4
(b)
Express the solution of
40|2x − 5| + 1 > 201
on number line.
4
