## 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:

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:

**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:

Question 4.

Which of the following is an equation?

(a) x + 5

(b) 7x

(c) 2y + 3 = 11

(d) 2p < 1

Solution:

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:

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:

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:

Question 8.

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

(a) x = 1

(b) x = 2

(c) x = 3

(d) x = 4

Solution:

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:

Question 10.

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

Solution:

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:

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:

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:

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:

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:

Question 16.

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

(a) 3

(b) 4

(c) 5

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

Solution:

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:

Question 18.

(-5)^{2} × (-1)^{3} is equal to

(a) 25

(b) -25

(c) 10

(d) -10

Solution:

Question 19.

(-2)^{3} × (-3)^{2} is equal to

(a) 6^{5}

(b) (-6)^{5}

(c) 72

(d) -72

Solution: