## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) The terms with different algebraic factors are called ……….

(ii) The number of terms in a monomial is ………

(iii) An algebraic expression having two unlike terms is called a ……..

(iv) 3a^{2}b and -7ba^{2} are ……….. terms.

(v) -6a^{2}b and -6ab^{2} are ……… terms.

(vi) The number of unlike terms in the algebraic expression 3x^{2} – 2xy + 5x^{2} is ………

(vii) The factors of the term -3p^{2}q^{2} are ……..

(viii) The perimeter of a triangle whose sides measure 2a, b and a + b is ………

(ix) The value of the expression 2x^{3} – 7x^{2} + 5x – 3 when x = 1 is ………..

(x) In the term -7a^{2}bc, the coefficient of a is ……..

(xi) The degree of the polynomial 3 – 5x^{2} + 7x^{3} – x^{4} is ……….

(xii) The degree of the polynomial 3x^{2} – 2xy^{2} + 5 is ………

Solution:

(i) The terms with different algebraic factors

are called unlike terms.

(ii) The number of terms in a monomial is one.

(iii) An algebraic expression having two unlike terms

is called a bionomial.

(iv) 3a^{2}b and -7ba^{2} are like terms.

(v) -6a^{2}b and -6ab^{2} are unlike terms.

(vi) The number of unlike terms in the algebraic expression

3x^{2} – 2xy + 5x^{2} is 2.

(vii) The factors of the term -3p^{2}q^{2} are -3, p, p, q, q.

(viii) The perimeter of a triangle whose sides measure

2a, b and a + b is 2a + b + a + b = 3a + 2b.

(ix) The value of the expression 2x^{3} – 7x^{2} + 5x – 3

when x = 1 is -3.

2(1)^{3} – 7(1)^{2} + 5(1) – 3

= 2 – 7 + 5 – 3

= -3

(x) In the term -7a^{2}bc, the coefficient of a is -7abc.

(xi) The degree of the polynomial 3 – 5x^{2} + 7x^{3} – x^{4} is 4.

3 – 5x^{2} + 7x^{3} – x^{4} is 4

(xii) The degree of the polynomial 3x^{2} – 2xy^{2} + 5 is 3.

3x^{2} – 2xy^{2} + 5 is 1 + 2 = 3

Question 2.

State whether the following statements are true (T) or false (F).

(i) The expression 5x + 7 – 2x is a trinomial.

(ii) (7x – 10) – (3x – 5) = 4x – 15.

(iii) The coefficient of 3x in -3x^{3}y is -xy.

(iv) The constant term in the expression 2x^{2} – 3xy – 7 is 7.

(v) If x = 3 and y = \(\frac { 1 }{ 3 }\) then the value of xy (x^{2} + y^{2}) is 9\(\frac { 1 }{ 9 }\).

(vi) (3x – y + 5) – (x + y) is a binomial.

(vii) Sum of 2 and p is 2p.

(viii) Sum of x^{2} + x and y^{2} + y is 2x^{2} + 2y^{2}.

(ix) In like terms, variables and their powers are the same.

(x) Every polynomial is a monomial.

(xi) If we add a monomial and a binomial, then answer can never be a monomial.

(xii) If we subtract a monomial from a binomial, then the answer is at least a binomial.

(xiii) if we add a monomial and a trinomial, then the answer can be a monomial.

(xiv) If we add a monomial and a binomial, then the answer can be a trinomial.

Solution:

(i) The expression 5x + 7 – 2x is a trinomial. (False)

Correct:

As 5x + 7 – 2x = 3x + 7 which has two terms.

(ii) (7x – 10) – (3x – 5) = 4x – 15. (False)

Correct:

(7x – 10) – (3x – 5) = 4x – 5

(iii) The coefficient of 3x in -3x^{3}y is -xy. (False)

Correct:

As co-efficient of 3x is -x^{2}y

(iv) The constant term in the expression

2x^{2} – 3xy – 7 is 7. (False)

Correct:

2x^{2} – 3xy – 7 is -7

(v) If x = 3 and y = \(\frac { 1 }{ 3 }\)

then the value of xy(x^{2} + y^{2}) is 9\(\frac { 1 }{ 9 }\). (True)

(vi) (3x – y + 5) – (x + y) is a binomial. (False)

Correct:

= 3x – y + 5 – x + y

= 2x – 2y + 5

It is trinomial.

(vii) Sum of 2 and p is 2p. (False)

Correct:

Sum of 2 and p is 2 + p not 2p.

(viii) Sum of x^{2} + x and y^{2} + y is 2x^{2} + 2y^{2}. (False)

Correct:

Sum of x^{2} + x and y^{2} + y = x^{2} + y^{2} + x + y not 2x^{2} + 2y^{2}

(ix) In like terms, variables and their powers are same. (True)

(x) Every polynomial is a monomial. (False)

It could be binomial, trinomial or polynomial.

(xi) If we add a monomial and a binomial,

then answer can never be a monomial. (False)

Correct:

It can be monomial.

For example :

3x + (5 – 3x) = 3x + 5 – 3x = 5 which is monomial.

(xii) If we subtract a monomial from a binomial,

then the answer is at least a binomial. (False)

Correct:

It can be monomial also, for example

2x – (7 + 2x) = 2x – 2 – 2x = -7 which is a monomial.

(xiii) if we add a monomial and a trinomial,

then the answer can be a monomial. (False)

Correct:

It can be binomial also.

(xiv) If we add a monomial and a binomial,

then the answer can be a trinomial. (True)

**Multiple Choice Questions**

Choose the correct answer from the given four options (3 to 16):

Question 3.

The algebraic expression for the statement ‘Thrice square of a number x subtracted from five times the sum of y and 2’ is

(a) 5y + 2 – 3x^{2}

(b) 3x^{2} – (5y + 2)

(c) 5(y + 2) – 3x^{2}

(d) 5(y + 2) – (3x)^{2}

Solution:

For the statement, thrice square of a number x

subtracted from five times the sum of y and 2 is 5(y + 2) – 3x^{2} (c)

Question 4.

The expression 7x – 5(x^{2} + y^{2}) is a

(a) monomial

(b) binomial

(c) trinomial

(d) none of these

Solution:

7x – 5(x^{2} + y^{2}) = 7x – 5x^{2} – 5y^{2}

It is trinomial. (c)

Question 5.

The coefficient of 5a^{2} in -5a^{3}bc is

(a) -bc

(b) a^{2}bc

(c) -a^{2}bc

(d) -abc

Solution:

Co-efficient of 5a^{2} in -5a^{3}bc is -abc (d)

Question 6.

Which of the following is a pair of like terms?

(a) -5xy, 5x

(b) -5xy, 3yz

(c) -5xy, -5y

(d) -5xy, 7yx

Solution:

-5xy, 7yx is a pair of like terms. (d)

Question 7.

The like terms is the expressions 3x(3 – 2y) and 2(xy + x^{2}) are

(a) 9x and 2x^{2}

(b) -6xy and 2xy

(c) 9x and 2xy

(d) -6xy and 2x^{2}

Solution:

Like terms in the expression

3x(3 – 2y) = 9x – 6xy and 2(xy + x^{2}) = 2xy + 2x^{2}

are -6xy and 2xy (b)

Question 8.

Identify the binomial out of the following:

(a) 3xy^{2} + 5y – x^{2}y

(b) 2x^{2}y – 5y – 2x^{2}y

(c) 3xy^{2} + 5y – xy^{2}

(d) xy + yz + zx

Solution:

(a) 3xy^{2} + 5y – x^{2}y trinomial

(b) 2x^{2}y – 5y – 2x^{2}y = -5y monomial

(c) 3xy^{2} + 5y – xy^{2} = 2xy2 + 5y binomial (c)

Question 9.

The number of (unlike) terms in the expression 3xy^{2} + 2y^{2}z – y^{2}x + y(xz + yz) – 5

(a) 3

(b) 4

(c) 5

(d) 6

Solution:

The number of unlike terms in the expression

= 3xy^{2} + 2y^{2}z – y^{2}x + y(xz + yz) – 5

= 3xy^{2} + 2y^{2}z – y^{2}x + xyz + y^{2}z – 5

= 2xy^{2} + 3y^{2}z^{2} + xyz – 5

= 4 (b)

Question 10.

The value of the expression x^{3} + y^{3} when x = 2 and y = -2 is

(a) 0

(b) 8

(c) 16

(d) -16

Solution:

Value of x^{3} + y^{3} = (2)^{3} + (-2)^{3} = 8 – 8 = 0 (a)

Question 11.

-xy – (-5xy) is equal to

(a) -6xy

(b) 6xy

(c) -4xy

(d) 4xy

Solution:

-xy – (-5xy) = -xy + 5xy = 4xy (d)

Question 12.

On subtracting 7x + 5y – 3 from 5y – 3x – 9, we get

(a) 10x + 6

(b) -10x – 6

(c) 10x + 10y – 12

(d) -10x – 12

Solution:

(5y – 3x – 9) – (7x + 5y – 3)

= 5y – 3x – 9 – 7x – 5y + 3

= -10x – 6 (b)

Question 13.

The value of the expression \(\frac { 5 }{ 3 }\) x^{2} + 1 when x = -2 is

(a) \(\frac { -17 }{ 3 }\)

(b) \(\frac { -7 }{ 3 }\)

(c) \(\frac { 21 }{ 3 }\)

(d) \(\frac { 23 }{ 3 }\)

Solution:

Question 14.

The number of sides in a pattern having 3 hexagons arranged in a row as shown in the given figure is

(a) 18

(b) 17

(c) 16

(d) 15

Solution:

Number of sides are = 16 (c)

Question 15.

The degree of the polynomial 3x^{3}y – 5xy^{4} – 2x + 1 is

(a) 5

(b) 4

(c) 3

(d) 2

Solution:

The degree of the polynomial

3x^{3}y – 5xy^{4} – 2x + 1 is of

-5xy^{4} = 1 + 4 = 5 (a)

**Higher Order Thinking Skills (HOTS)**

Question 1.

The length of a rectangle is 3x – 4y + 6z and the perimeter is 7x + 8y + 17z, find the breadth of the rectangle.

Solution:

Length of rectangle = 3x – 4y + 6z

2 × length = 6x – 8y + 12z

and perimeter = 7x + 8y + 17z = 2(Length + Breadth)

2 × Breadth = 7x + 8y + 17z – 6x + 8y – 12z = x + 5 z + 16y

Breadth = \(\frac { x }{ 2 }\) + 8y + \(\frac { 5 }{ 2 }\) z

Question 2.

Solution:

Question 3.

If a = 3, b = -1, then find the value of each of the following:

Solution: