NCERT Exemplar Solutions: Algebraic Expressions | Mathematics (Maths) Class 7 PDF Download

 Page 1


Exercise 
 
In each of the questions 1 to 16, out of the four options, only one is 
correct. Write the correct answer. 
 
1. An algebraic expression containing three terms is called a  
(a) monomial       (b) binomial       (c) trinomial       (d) All of these 
 
Solution: 
 
(c) trinomial 
 
An algebraic expression containing one term is called monomial, two terms is called 
binomial and three terms is called trinomial. 
 
2. Number of terms in the expression 
2 2 2
3 2 5 x y y z z x - - + is  
(a) 2       (b) 3       (c) 4       (d) 5 
 
Solution:- 
 
(c) 4 
 
In the given expression there are 4 terms. 
 
3. The terms of expression 
2
4   3 x xy - are:  
2
2
2
2
  4   3
  4  
()
()
()
(
 3
  4   
  ) 
x and xy
x and xy
x and xy
x and xy
-
-
a
b
c
d
 
 
Solution:- 
 
(a) 4x
2
 and –3xy 
 
Terms in the expression 4x
2 
-3xy are 4x
2
 and -3xy. 
 
4. Factors of 
22
5x y z - are  
(a) – 5 × x × y × z       (b) – 5 × x
2
× y × z       (c) – 5 × x × x × y × y × z        
(d) – 5 × x × y × z
2
 
 
Solution:- 
 
Chapter - 10 
Algebraic Expressions
 
Page 2


Exercise 
 
In each of the questions 1 to 16, out of the four options, only one is 
correct. Write the correct answer. 
 
1. An algebraic expression containing three terms is called a  
(a) monomial       (b) binomial       (c) trinomial       (d) All of these 
 
Solution: 
 
(c) trinomial 
 
An algebraic expression containing one term is called monomial, two terms is called 
binomial and three terms is called trinomial. 
 
2. Number of terms in the expression 
2 2 2
3 2 5 x y y z z x - - + is  
(a) 2       (b) 3       (c) 4       (d) 5 
 
Solution:- 
 
(c) 4 
 
In the given expression there are 4 terms. 
 
3. The terms of expression 
2
4   3 x xy - are:  
2
2
2
2
  4   3
  4  
()
()
()
(
 3
  4   
  ) 
x and xy
x and xy
x and xy
x and xy
-
-
a
b
c
d
 
 
Solution:- 
 
(a) 4x
2
 and –3xy 
 
Terms in the expression 4x
2 
-3xy are 4x
2
 and -3xy. 
 
4. Factors of 
22
5x y z - are  
(a) – 5 × x × y × z       (b) – 5 × x
2
× y × z       (c) – 5 × x × x × y × y × z        
(d) – 5 × x × y × z
2
 
 
Solution:- 
 
Chapter - 10 
Algebraic Expressions
 
(c) – 5 × x × x × y × y × z 
 
-5x
2
y
2
z can be written as – 5 × x × x × y × y × z 
 
5. Coefficient of x in 
2
9xy z - is  
(a) 9yz       (b) – 9yz       (c) 9y
2
z       (d) – 9y
2
z 
 
Solution:- 
 
(d) – 9y
2
z 
 
Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the 
coefficient of the remaining part of the term. 
 
6. Which of the following is a pair of like terms?  
22
22
2 2 2
22
  7 , 7
  10 , 3
()
()
()
()
  3 , 3
  4 , 4
a xy z x yz
b xyz xyz
c xyz x y z
d xyz x yz
--
-
 
 
Solution:- 
 
(b) – 10xyz
2
, 3xyz
2
 
 
Like terms have the same algebraic factors.  
 
7. Identify the binomial out of the following:  
22
22
22
()
()
(
  3    5   –  
 5
     
  3   5
)
()
a xy y x y
b x y y x y
c xy yz zx
d xy y xy
+
--
++
+-
 
 
Solution:- 
 
(d) 3xy
2
 + 5y – xy
2
 
 
Expression with two unlike terms is called a ‘Binomial’. 
 
So, 
3xy
2 
+ 5y – xy
2
 = (3xy
2
 – xy
2
) + 5y 
                           = 2xy
2
 + 5y 
 
8. The sum of 
4 2 4 2
 –  2         2 x xy y and x xy y + - + + is  
Page 3


Exercise 
 
In each of the questions 1 to 16, out of the four options, only one is 
correct. Write the correct answer. 
 
1. An algebraic expression containing three terms is called a  
(a) monomial       (b) binomial       (c) trinomial       (d) All of these 
 
Solution: 
 
(c) trinomial 
 
An algebraic expression containing one term is called monomial, two terms is called 
binomial and three terms is called trinomial. 
 
2. Number of terms in the expression 
2 2 2
3 2 5 x y y z z x - - + is  
(a) 2       (b) 3       (c) 4       (d) 5 
 
Solution:- 
 
(c) 4 
 
In the given expression there are 4 terms. 
 
3. The terms of expression 
2
4   3 x xy - are:  
2
2
2
2
  4   3
  4  
()
()
()
(
 3
  4   
  ) 
x and xy
x and xy
x and xy
x and xy
-
-
a
b
c
d
 
 
Solution:- 
 
(a) 4x
2
 and –3xy 
 
Terms in the expression 4x
2 
-3xy are 4x
2
 and -3xy. 
 
4. Factors of 
22
5x y z - are  
(a) – 5 × x × y × z       (b) – 5 × x
2
× y × z       (c) – 5 × x × x × y × y × z        
(d) – 5 × x × y × z
2
 
 
Solution:- 
 
Chapter - 10 
Algebraic Expressions
 
(c) – 5 × x × x × y × y × z 
 
-5x
2
y
2
z can be written as – 5 × x × x × y × y × z 
 
5. Coefficient of x in 
2
9xy z - is  
(a) 9yz       (b) – 9yz       (c) 9y
2
z       (d) – 9y
2
z 
 
Solution:- 
 
(d) – 9y
2
z 
 
Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the 
coefficient of the remaining part of the term. 
 
6. Which of the following is a pair of like terms?  
22
22
2 2 2
22
  7 , 7
  10 , 3
()
()
()
()
  3 , 3
  4 , 4
a xy z x yz
b xyz xyz
c xyz x y z
d xyz x yz
--
-
 
 
Solution:- 
 
(b) – 10xyz
2
, 3xyz
2
 
 
Like terms have the same algebraic factors.  
 
7. Identify the binomial out of the following:  
22
22
22
()
()
(
  3    5   –  
 5
     
  3   5
)
()
a xy y x y
b x y y x y
c xy yz zx
d xy y xy
+
--
++
+-
 
 
Solution:- 
 
(d) 3xy
2
 + 5y – xy
2
 
 
Expression with two unlike terms is called a ‘Binomial’. 
 
So, 
3xy
2 
+ 5y – xy
2
 = (3xy
2
 – xy
2
) + 5y 
                           = 2xy
2
 + 5y 
 
8. The sum of 
4 2 4 2
 –  2         2 x xy y and x xy y + - + + is  
(a) Monomial and polynomial in y         (b) Binomial and Polynomial  
(c) Trinomial and polynomial                (d) Monomial and polynomial in x 
 
Solution:- 
 
(a) Monomial and polynomial in y 
 
Sum of two expressions = (x
4
 – xy + 2y
2
) + (–x
4
 + xy + 2y
2
) 
                                       = x
4
 – xy + 2y
2
 – x
4
 + xy + 2y
2
 
                                       = (x
4
 – x
4
)+ (-xy + xy) + (2y
2
 + 2y
2
) 
                                       = 0 + 0 + 4y
2
 
                                       = 4y
2
 
 
9. The subtraction of 5 times of y from x is  
(a) 5x – y       (b) y – 5x       (c) x – 5y       (d) 5y – x 
 
Solution:- 
 
(c) x – 5y 
 
10. – b – 0 is equal to  
(a) –1 × b       (b) 1 – b – 0       (c) 0 – (–1) × b       (d) – b – 0 – 1 
 
Solution:- 
 
(a) –1 × b 
 
As, 
– b – 0 = -b 
 
11. The side length of the top of square table is x. The expression for 
perimeter is:  
(a) 4 + x       (b) 2x       (c) 4x       (d) 8x 
 
Solution:- 
 
(c) 4x 
 
We have,  
Perimeter of the square = 4 × side 
 
Also, side length of the top of square table is x. 
Therefore,  
Perimeter = 4 × x 
                = 4x 
Page 4


Exercise 
 
In each of the questions 1 to 16, out of the four options, only one is 
correct. Write the correct answer. 
 
1. An algebraic expression containing three terms is called a  
(a) monomial       (b) binomial       (c) trinomial       (d) All of these 
 
Solution: 
 
(c) trinomial 
 
An algebraic expression containing one term is called monomial, two terms is called 
binomial and three terms is called trinomial. 
 
2. Number of terms in the expression 
2 2 2
3 2 5 x y y z z x - - + is  
(a) 2       (b) 3       (c) 4       (d) 5 
 
Solution:- 
 
(c) 4 
 
In the given expression there are 4 terms. 
 
3. The terms of expression 
2
4   3 x xy - are:  
2
2
2
2
  4   3
  4  
()
()
()
(
 3
  4   
  ) 
x and xy
x and xy
x and xy
x and xy
-
-
a
b
c
d
 
 
Solution:- 
 
(a) 4x
2
 and –3xy 
 
Terms in the expression 4x
2 
-3xy are 4x
2
 and -3xy. 
 
4. Factors of 
22
5x y z - are  
(a) – 5 × x × y × z       (b) – 5 × x
2
× y × z       (c) – 5 × x × x × y × y × z        
(d) – 5 × x × y × z
2
 
 
Solution:- 
 
Chapter - 10 
Algebraic Expressions
 
(c) – 5 × x × x × y × y × z 
 
-5x
2
y
2
z can be written as – 5 × x × x × y × y × z 
 
5. Coefficient of x in 
2
9xy z - is  
(a) 9yz       (b) – 9yz       (c) 9y
2
z       (d) – 9y
2
z 
 
Solution:- 
 
(d) – 9y
2
z 
 
Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the 
coefficient of the remaining part of the term. 
 
6. Which of the following is a pair of like terms?  
22
22
2 2 2
22
  7 , 7
  10 , 3
()
()
()
()
  3 , 3
  4 , 4
a xy z x yz
b xyz xyz
c xyz x y z
d xyz x yz
--
-
 
 
Solution:- 
 
(b) – 10xyz
2
, 3xyz
2
 
 
Like terms have the same algebraic factors.  
 
7. Identify the binomial out of the following:  
22
22
22
()
()
(
  3    5   –  
 5
     
  3   5
)
()
a xy y x y
b x y y x y
c xy yz zx
d xy y xy
+
--
++
+-
 
 
Solution:- 
 
(d) 3xy
2
 + 5y – xy
2
 
 
Expression with two unlike terms is called a ‘Binomial’. 
 
So, 
3xy
2 
+ 5y – xy
2
 = (3xy
2
 – xy
2
) + 5y 
                           = 2xy
2
 + 5y 
 
8. The sum of 
4 2 4 2
 –  2         2 x xy y and x xy y + - + + is  
(a) Monomial and polynomial in y         (b) Binomial and Polynomial  
(c) Trinomial and polynomial                (d) Monomial and polynomial in x 
 
Solution:- 
 
(a) Monomial and polynomial in y 
 
Sum of two expressions = (x
4
 – xy + 2y
2
) + (–x
4
 + xy + 2y
2
) 
                                       = x
4
 – xy + 2y
2
 – x
4
 + xy + 2y
2
 
                                       = (x
4
 – x
4
)+ (-xy + xy) + (2y
2
 + 2y
2
) 
                                       = 0 + 0 + 4y
2
 
                                       = 4y
2
 
 
9. The subtraction of 5 times of y from x is  
(a) 5x – y       (b) y – 5x       (c) x – 5y       (d) 5y – x 
 
Solution:- 
 
(c) x – 5y 
 
10. – b – 0 is equal to  
(a) –1 × b       (b) 1 – b – 0       (c) 0 – (–1) × b       (d) – b – 0 – 1 
 
Solution:- 
 
(a) –1 × b 
 
As, 
– b – 0 = -b 
 
11. The side length of the top of square table is x. The expression for 
perimeter is:  
(a) 4 + x       (b) 2x       (c) 4x       (d) 8x 
 
Solution:- 
 
(c) 4x 
 
We have,  
Perimeter of the square = 4 × side 
 
Also, side length of the top of square table is x. 
Therefore,  
Perimeter = 4 × x 
                = 4x 
 
12. The number of scarfs of length half metre that can be made from y 
metres of cloth is:  
(a) 2y       (b) y/2       (c) y + 2       (d) y + (1/2) 
 
Solution:- 
 
(a) 2y 
 
We have,  
Length of scarf is half meter = 
1
2
 m 
So, the number of scarfs can be made from y meters of cloth = 
1
2
y
 
                                                                                                           = 2y 
 
13. 
22
123 138 x y x y -  is a like term of :  
(a) 10xy       (b) –15xy       (c) –15xy
2
       (d) 10x
2
y 
 
Solution:- 
 
(d) 10x
2
y 
 
123x
2
y – 138x
2
y = (123 – 138) x
2
y 
                            = -15 x
2
y 
 
  So,  
-15x
2
y is a like term of 10x
2
y as both contain x
2
y. 
 
14. The value of 
2
3  – 5    3, xx + when x = 1 is 
 
(a) 1             (b) 0                  (c) –1              (d) 11 
 
Solution:- 
 
(a) 1 
 
We have, 
 x = 1 
 
So, 
 3x
2
 – 5x + 3 = (3 × (1)
2
) – (5 × 1) + 3 
                     = 3 – 5 + 3 
                     = 6 – 5 
Page 5


Exercise 
 
In each of the questions 1 to 16, out of the four options, only one is 
correct. Write the correct answer. 
 
1. An algebraic expression containing three terms is called a  
(a) monomial       (b) binomial       (c) trinomial       (d) All of these 
 
Solution: 
 
(c) trinomial 
 
An algebraic expression containing one term is called monomial, two terms is called 
binomial and three terms is called trinomial. 
 
2. Number of terms in the expression 
2 2 2
3 2 5 x y y z z x - - + is  
(a) 2       (b) 3       (c) 4       (d) 5 
 
Solution:- 
 
(c) 4 
 
In the given expression there are 4 terms. 
 
3. The terms of expression 
2
4   3 x xy - are:  
2
2
2
2
  4   3
  4  
()
()
()
(
 3
  4   
  ) 
x and xy
x and xy
x and xy
x and xy
-
-
a
b
c
d
 
 
Solution:- 
 
(a) 4x
2
 and –3xy 
 
Terms in the expression 4x
2 
-3xy are 4x
2
 and -3xy. 
 
4. Factors of 
22
5x y z - are  
(a) – 5 × x × y × z       (b) – 5 × x
2
× y × z       (c) – 5 × x × x × y × y × z        
(d) – 5 × x × y × z
2
 
 
Solution:- 
 
Chapter - 10 
Algebraic Expressions
 
(c) – 5 × x × x × y × y × z 
 
-5x
2
y
2
z can be written as – 5 × x × x × y × y × z 
 
5. Coefficient of x in 
2
9xy z - is  
(a) 9yz       (b) – 9yz       (c) 9y
2
z       (d) – 9y
2
z 
 
Solution:- 
 
(d) – 9y
2
z 
 
Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the 
coefficient of the remaining part of the term. 
 
6. Which of the following is a pair of like terms?  
22
22
2 2 2
22
  7 , 7
  10 , 3
()
()
()
()
  3 , 3
  4 , 4
a xy z x yz
b xyz xyz
c xyz x y z
d xyz x yz
--
-
 
 
Solution:- 
 
(b) – 10xyz
2
, 3xyz
2
 
 
Like terms have the same algebraic factors.  
 
7. Identify the binomial out of the following:  
22
22
22
()
()
(
  3    5   –  
 5
     
  3   5
)
()
a xy y x y
b x y y x y
c xy yz zx
d xy y xy
+
--
++
+-
 
 
Solution:- 
 
(d) 3xy
2
 + 5y – xy
2
 
 
Expression with two unlike terms is called a ‘Binomial’. 
 
So, 
3xy
2 
+ 5y – xy
2
 = (3xy
2
 – xy
2
) + 5y 
                           = 2xy
2
 + 5y 
 
8. The sum of 
4 2 4 2
 –  2         2 x xy y and x xy y + - + + is  
(a) Monomial and polynomial in y         (b) Binomial and Polynomial  
(c) Trinomial and polynomial                (d) Monomial and polynomial in x 
 
Solution:- 
 
(a) Monomial and polynomial in y 
 
Sum of two expressions = (x
4
 – xy + 2y
2
) + (–x
4
 + xy + 2y
2
) 
                                       = x
4
 – xy + 2y
2
 – x
4
 + xy + 2y
2
 
                                       = (x
4
 – x
4
)+ (-xy + xy) + (2y
2
 + 2y
2
) 
                                       = 0 + 0 + 4y
2
 
                                       = 4y
2
 
 
9. The subtraction of 5 times of y from x is  
(a) 5x – y       (b) y – 5x       (c) x – 5y       (d) 5y – x 
 
Solution:- 
 
(c) x – 5y 
 
10. – b – 0 is equal to  
(a) –1 × b       (b) 1 – b – 0       (c) 0 – (–1) × b       (d) – b – 0 – 1 
 
Solution:- 
 
(a) –1 × b 
 
As, 
– b – 0 = -b 
 
11. The side length of the top of square table is x. The expression for 
perimeter is:  
(a) 4 + x       (b) 2x       (c) 4x       (d) 8x 
 
Solution:- 
 
(c) 4x 
 
We have,  
Perimeter of the square = 4 × side 
 
Also, side length of the top of square table is x. 
Therefore,  
Perimeter = 4 × x 
                = 4x 
 
12. The number of scarfs of length half metre that can be made from y 
metres of cloth is:  
(a) 2y       (b) y/2       (c) y + 2       (d) y + (1/2) 
 
Solution:- 
 
(a) 2y 
 
We have,  
Length of scarf is half meter = 
1
2
 m 
So, the number of scarfs can be made from y meters of cloth = 
1
2
y
 
                                                                                                           = 2y 
 
13. 
22
123 138 x y x y -  is a like term of :  
(a) 10xy       (b) –15xy       (c) –15xy
2
       (d) 10x
2
y 
 
Solution:- 
 
(d) 10x
2
y 
 
123x
2
y – 138x
2
y = (123 – 138) x
2
y 
                            = -15 x
2
y 
 
  So,  
-15x
2
y is a like term of 10x
2
y as both contain x
2
y. 
 
14. The value of 
2
3  – 5    3, xx + when x = 1 is 
 
(a) 1             (b) 0                  (c) –1              (d) 11 
 
Solution:- 
 
(a) 1 
 
We have, 
 x = 1 
 
So, 
 3x
2
 – 5x + 3 = (3 × (1)
2
) – (5 × 1) + 3 
                     = 3 – 5 + 3 
                     = 6 – 5 
                     = 1 
 
15. The expression for the number of diagonals that we can make from one 
vertex of a n sided polygon is:  
(a) 2n + 1                  (b) n – 2                (c) 5n + 2              (d) n – 3 
 
Solution:- 
 
(d) n – 3 
 
There are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of 
diagonals that can be drawn is (n-3). 
 
16. The length of a side of square is given as 2x + 3. Which expression 
represents the perimeter of the square?  
(a) 2x + 16       (b) 6x + 9       (c) 8x + 3       (d) 8x + 12 
 
Solution:- 
 
(d) 8x + 12 
 
We have,  
Perimeter of the square = 4 × side 
 
Side length of the top of square table is 2x + 3. 
 
So,  
Perimeter = 4 × (2x + 3) 
                = (4 × 2x) + (4 × 3) 
                = 8x + 12 
 
In questions 17 to 32, fill in the blanks to make the statements 
true. 
 
17. Sum or difference of two like terms is ________.  
 
Solution:- 
 
Sum or difference of two like terms is a like term. 
 
18. In the formula, area of circle = 
2
r ? , the numerical constant of the 
expression 
2
r ? is ________.  
 
Solution:-