Algebra(6th Grade > Mathematics ) Questions and answers for exam Preparation

6th Grade > Mathematics

ALGEBRA MCQs

Total Questions : 96 | Page 8 of 10 pages

5x + 4y + 6pq - 2y + 3x + 4xy - 3pq - 2xy is equal to: [2 MARKS]

Discuss Question

Answer: Option A. ->
:
Steps: 1 Mark
Answer: 1 Mark
Like terms can be added and subtracted.
So,

5 x + 3 x = 8 x

Similarly,

4 y - 2 y = 2 y

4 x y - 2 x y = 2 x y

6 p q - 3 p q = 3 p q

$\Rightarrow 5 x + 4 y + 6 p q - 2 y + 3 x + 4 x y - 3 p q - 2 x y$
= $8 x + 2 y + 2 x y + 3 p q$

Question 72.

Find the value of: [4 MARKS]
(i) $p + q + 3 r$
$w h e n p = 1, q = 5, r = 2$
(ii) $2 a + 4 b + 5 c$
$w h e n a = 5, b = 10, c = 20$
(iii) $3 a - 2 b$
$w h e n a = 8, b = 10$
(iv) $5 x + 3 y - 6 z$ ,
$w h e n x = 3, y = 5, z = 4$

Discuss Question

Answer: Option A. ->
:
Each option: 1 Mark
(i)

p + q + 3 r, w h e n p = 1, q = 5, r = 2

p + q + 3 r = 1 + 5 + 3 (2) = 12

(ii)

2 a + 4 b + 5 c, w h e n a = 5, b = 10, c = 20

2 a + 4 b + 5 c = 2 (5) + 4 (10) + 5 (20)

= 10 + 40 + 100 = 150

(iii)

3 a - 2 b, w h e n a = 8, b = 10

3 a - 2 b = 3 (8) - 2 (10)

= 24 - 20 = 4

(iv)

5 x + 3 y - 6 z, w h e n x = 3, y = 5, z = 4

5 x + 3 y - 6 z = 5 (3) + 3 (5) - 6 (4) = 15 + 15 - 24

= 30 - 24 = 6

Question 73.

A pattern is made using matchsticks. What is the number of matchsticks needed to create the next member in the pattern? [3 MARKS]

Discuss Question

Answer: Option A. ->
:
Visualisation of question: 1 Mark
Identifying the pattern: 1 Mark
Solution: 1 Mark
Number of sticks used for the first member = 6

Number of sticks used for the second member = 6 + 5 = 11

Number of sticks used for the third member = 6 + 5 + 5 = 16

Therefore, number of sticks required for the fourth member = 16 + 5 = 21

Question 74.

Translate each of the following statements into an equation: [4 MARKS]
a) The perimeter (p) of an equilateral triangle is three times of its side (a).
b) The diameter (d) of the circle is twice its radius (r).
c) The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned.
d) Amount (a) is equal to the sum of principal (p) and interest (i).

Discuss Question

Answer: Option A. ->
:

Each Option: 1 Mark
(a) Side of a equilateral triangle = a
According to question, p = 3a
(b) Diameter of circle = d
Radius of circle = r
According to question, d = 2r.
(c) Selling price = s, cost price = c and profit = p
According to question, s = c + p.
(d) Amount = a, Principal = p and Interest = i
According to question, a = p + i.

Question 75.

(a) Sunita is half the age of her mother Geeta. Find their ages.
(i) After 4 years
(ii) Before 3 years
(b) A bus travels at 'v' km per hour. It is going from Daspur to Beespur. After the bus has travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using $v$ .
(c) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father's age?
[4 MARKS]

Discuss Question

Answer: Option A. ->
:
(a) Solution: 2 Marks (1 Mark for Geeta and 1 mark for Sunita)
(b) Solution: 1 Mark
(c) Solution: 1 Mark
(a) Let the present age of Sunita’s mother Geeta =

2 x

years
Present age of Sunita

= \frac{2 x}{2} = x y e a r s

(i) After 4 years:
Age of Geeta

= (2 x + 4) y e a r s

Age of Sunita

= (x + 4) y e a r s

(ii) Before 3 years
Age of Geeta

= (2 x - 3) y e a r s

Age of Sunita

= (x - 3) y e a r s

(b) Speed of the bus =

v \frac{k m}{h r}

i.e. (in 1 hr bus travels

v

km )

∴

Distance travelled by bus after 5 hrs =

5 v k m

Distance remaining to Beespur =

20 k m

Distance from Daspur to Beespur
= Distance travelled by bus in 5 hrs + Distance remaining
=

(5 v + 20) k m

∴

three times of Sarita's age =3x years

∴

Sarita's father age = 3x + 5 years

Question 76.

Length and breadth of a bulletin board are $r c m$ and $t c m$ respectively. [4 MARKS]
(i) What will be the length (in cm) of the aluminium strip required to frame the board, if 10 cm extra strip is required to fix it properly.?
(ii) If $x$ nails are used to repair each board, how many nails will be required to repair 15 such board?
(iii) If $500 c m^{2}$ extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?
(iv) What will be the expenditure for making 23 boards, if the carpenter charges Rs $x$ per board?

Discuss Question

Answer: Option A. ->
:

Each Point: 1 Mark
Perimeter of the bulletin board $= 2 (r + t) c m$
Area of the bulletin board $= r t c m^{2}$
(i) Length (in cm) of the aluminium strip required to frame the board = Perimeter + extra strip
= $2 (r + t) + 10 c m$
(ii) Repairing 1 board requires $x$ nails.
$∴$ Number of nails required to repair 15 boards = $15 x$
(iii) Total area of cloth required = Area of 8 bulletin boards + Area of extra cloth required for 8 boards
= ( $8 \times r \times t c m^{2}$ ) + ( $8 \times 500 c m^{2}$ )
= ( $8 r t + 4000) c m^{2}$
(iv) Carpenter's charge for making 1 board = Rs $x$
$∴$ Expenditure for making 23 boards = Rs $23 x$

Question 77.

The branch of mathematics in which we study the use of letters to write rules and formulae in a general way is known as _______.

Arithmetic
Algebra
Statistics
Geometry

Discuss Question

Answer: Option B. -> Algebra
:
B

Algebra is the branch of mathematics in which we study the use of letters to represent numbers/quantities.
For example, ram bought mangoes, but we don't know the number of mangoes he bought. So, let's say he bought x number of mangoes.
Here x is an alphabet but represents the number of mangoes.

Question 78.

All integers are constants not variables.

True
False
Statistics
Geometry

Discuss Question

Answer: Option A. -> True
:
A
All integers are constants since they have a fixed value which will not change with time.
Example: 5,6, -7,....

Question 79.

35xy + 45x + 5y² + 25xyz is a

Monomial
Binomial
Trinomial
Polynomial

Discuss Question

Answer: Option D. -> Polynomial
:
D
35xy, 45x, 5y² and 25xyz are unlike terms.

Therefore, there are 4 unlike terms. So it is a polynomial.

Question 80.

Rahul's dad's age is 4 more than 3 times of his present age. If Rahul is 11 years old, then his dad is _____.

35 years old
36 years old
34 years old
37 years old

Discuss Question

Answer: Option D. -> 37 years old
:
D
Rahul's dad's age is 4 more than 3 times of his age.
Let Rahul's present age be x years.
Then his dad's age = (3x + 4) years.
Given that Rahul's present age is 11, x = 11.

Hence, his dad's present age = (3 × 11) + 4 = 37 years.