## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) In algebra, we use …………… to represent variables (generalized numbers).

(ii) A symbol or letter which can be given various numerical values is called a ……………

(iii) If Jaggu’s present age is x years, then his age 7 years from now is ……………

(iv) If one pen costs ₹X x, then the cost of 9 pens is ……………

(v) An equation is a statement that the two expressions are ……………

(vi) Trial an error is one of methods to obtain …………… of an equation.

(vii) 7 less than thrice a number y is ……………

(viii) If 3x + 4 = 19, then the value of x is ……………

(ix) The number of pencils bought for ₹ x at the rate of ₹2 per pencil is ……………

(x) In the expression (-7)^{5}, base = …………… and exponent = ……………

(xi) If base = 6 and exponent = 5, then the exponential form = …………… .

Solution:

(i) In algebra, we use letters to represent variables (generalized numbers).

(ii) A symbol or letter which can be given various numerical values is called a variable.

(iii) If Jaggu’s present age is x years, then his age 7 years from now is (x + 7) years.

(iv) If one pen costs ₹ x, then the cost of 9 pens is ₹9x.

(v) An equation is a statement that the two expressions are equal.

(vi) Trial an error is one of methods to obtain the solution of an equation.

(vii) 7 less than thrice a num bery is 3y – 7.

(viii) If 3x + 4 = 19, then the value of x is 5.

(ix) The number of pencils bought for ₹ x at the rate of ₹2 per pencil is \(\frac{x}{2}\).

(x) In the expression (-7)^{5}, base = -7 and exponent = 5.

(xi) If base = 6 and exponent = 5, then the exponential form = 6^{5}.

Question 2.

State whether the following statements are ture (T) or false (F):

(i) If x is variable then 5x is also variable.

(ii) If y is variable then y – 5 is also variable.

(iii) The number of angles in a triangle is a variable.

(iv) The value of an algebraic expression changes with the change in the value of the variable.

(v) If the length of a rectangle is twice its breadth, then its area is a constant.

(vi) An equation is satisfied only for a definite value of the variable.

(vii) If x toffees are distributed equally among 5 children, then each child gets 5x toffees.

(viii) t minutes are equal to 60 t seconds.

(ix) If x is a negative integer, then -x is a positive integer.

(x) x = 5 is a solution of the equation 3x + 2 = 13.

(xi) 2y- 7 > 13 is an equation.

(xii) ‘One third of a number x added to itself gives 8’ can be expressed as \(\frac{x}{3}\) + 8 = x.

(xiii)The difference between the ages of two sisters Lata and Asha is a variable.

Solution:

(i) If x is variable then 5x is also variable. True

(ii) If y is variable then y – 5 is also variable. True

(iii) The number of angles in a triangle is a variable. False

(iv) The value of an algebraic expression changes with the change in the value of the variable. True

(v) If the length of a rectangle is twice its breadth, then its area is a constant. False

(vi) An equation is satisfied only for a definite value of the variable. True

(vii) If x toffees are distributed equally among 5 children, then each child gets 5x toffees. False

(viii) t minutes are equal to 60 t seconds. True

(ix) If x is a negative integer, then -x is a positive integer. True

(x) x = 5 is a solution of the equation 3x + 2 = 13. False

(xi) 2y – 1 > 13 is an equation. False

(xii) ‘One third of a number x added to itself gives 8’ can be expressed as \(\frac{x}{3}\) + 8 = x. False

(xiii)The difference between the ages of two sisters Lata and Asha is a variable. False

**Multiple Choice Questions**

**Choose the correct answer from the given four options (3 to 19): **Question 3.

I think of a number x, add 5 to it. The result is then multiplied by 2 and the final result is 24. The correct algebraic statement is

(a) x + 5 × 2 = 24

(b) (x + 5) × 2 = 24

(c) 2 × x + 5 = 24

(d) x + 5 = 2 × 24

Solution:

Let number = x

Add 5 to the number

⇒ i.e. x + 5

Now multiply result with 2

i.e. (x + 5) × 2

Now, final result is 24

i.e. (x + 5) × 2 = 24 (b)

Question 4.

Which of the following is an equation?

(a) x + 5

(b) 7x

(c) 2y + 3 = 11

(d) 2p < 1

Solution:

2y + 3 = 11 (c)

Question 5.

If each matchbox contains 48 matchsticks, then the number of matchsticks required to fill n such boxes is

(i) 48 + n

(b) 48 – n

(c) 48 ÷ n

(d) 48n

Solution:

Matchstick required to fill 1 matchbox

= 48 × 1 = 48

Matchstick required to fill 2 matchbox

= 48 × 2 = 96

Matchstick required to fill 3 matchbox

= 48 × 3 – 144

∴ Matchstick required to fill n matchbox

= 48 n (d)

Question 6.

If the perimeter of a regular hexagon is x metres, then the length of each of its sides is

(a) (x + 6) metres

(b) (x – 6) metres

(c) (x ÷ 6) metres

(d) (6 ÷ x) metres

Solution:

Perimeter of hexagon = x metres

6(side) = x metres

Side = (x ÷ 6) metres

∴ Side = (x ÷ 6) metres (c)

Question 7.

x = 3 is the solution of the equation

(a) x + 7 = 4

(b) x + 10 = 7

(c) x + 7 = 10

(d) x + 3 = 7

Solution:

When put the value of x = 3

3 + 7=10 (c)

Question 8.

The solution of the equation 3x – 2 = 10 is

(a) x = 1

(b) x = 2

(c) x = 3

(d) x = 4

Solution:

3x – 2 = 10

3x = 10 + 2

\(x=\frac{12}{3}=x=4\) (d)

Question 9.

The operation not involved in forming the expression 5x + \(\frac{5}{x}\) from the variable x and number 5 is

(a) addition

(b) subtraction

(c) multiplication

(d) division

Solution:

Subtraction (b)

Question 10.

The quotient of x by 3 added to 7 is written as

Solution:

\(\frac{x}{3}+7\) (a)

Question 11.

If there are x chairs in a row, then the number of persons that can be seated in 8 rows are

(a) 64

(b) x + 8

(c) 8x

(d) none of these

Solution:

Let the no. of chairs in a row = x

⇒ Number of persons that can be seated in a row = x

Hence, number of persons that can be seoted in 8 row = 8x (c)

Question 12.

If Arshad earns ₹ x per day and spends ₹ y per day, then his saving for the month of March is

(a) ₹(31x – y)

(b) ₹31(x – y)

(c) ₹31 (x + y)

(d) ₹31 (y – x)

Solution:

Earning of Arshad for 1 day = ₹ x

Spending of Arshad for 1 day = ₹ y

Saving for 1 day = ₹(x – y)

Saving for 31 days = ₹31 (x – y) (b)

Question 13.

If the length of a rectangle is 3 times its breadth and the breadth is x units, then its perimeter is

(a) 4x units

(b) 6x units

(c) 8x units

(d) 10x units

Solution:

Breadth of rectangle = x units

Length of rectangle = 3(Breadth) = 3x

Perimeter of rectangle = 2(l + b)

= 2(3x + x)

= 2(4x) = 8x units (c)

Question 14.

Rashmi has a sum of ₹ x. She spend ₹800 on grocery, ₹600 on cloths and ₹500 on education and received as ₹200 as a gift. How much money (in ₹) is left with her?

(a) x – 1700

(b) x – 1900

(c) x + 200

(d) x – 2100

Solution:

Total money = ₹ x

Money spent = ₹800 on grocery

Money spent = ₹600 on cloths .

Money spent = ₹500 on education

Money left with Rashmi

= x – ₹800 + ₹600 + ₹500

= x – 1900

She received a gift of = ₹200

∴ Money left = x – 1900 + 200

= x – 1700 (a)

Question 15.

For any two integers a and b, which of the following suggests that the operation of addition is commutative?

(a) a × b = b × a

(b) a + b = b + a

(c) a – b = b – a

(d) a + b > a

Solution:

a + b = b + a

Question 16.

In \(\left(\frac{3}{4}\right)^{5}\), the base is

(a) 3

(b) 4

(c) 5

(d) \(\frac{3}{4}\)

Solution:

\(\frac{3}{4}\)

Question 17.

a × a × b × b × b can be written as

(a) a^{2}b^{3}

(b) a^{3}b^{2}

(c) a^{3}b^{3}

(d) a^{5}b^{5}

Solution:

a × a × b × b × b

= a^{2} × b^{3} = a^{2}b^{3} (a)

Question 18.

(-5)^{2} × (-1)^{3} is equal to

(a) 25

(b) -25

(c) 10

(d) -10

Solution:

(-5)^{2} × (-1)3

⇒ (-5) × (-5) x (-1) × (-1) × (-1)

⇒ 25 × (-1) = -25 (b)

Question 19.

(-2)^{3} × (-3)^{2} is equal to

(a) 6^{5}

(b) (-6)^{5}

(c) 72

(d) -72

Solution:

(-2)^{3} × (-3)^{2}

⇒ (-2) × (-2) × (-2) × (-3) × (-3)

⇒ -8 × 9 = -72 (d)