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

6th Grade > Mathematics

ALGEBRA MCQs

Total Questions : 96 | Page 4 of 10 pages

Question 31. Kimmy went to play with her friends. If Kimmy rolls a die, say 13 times, her score will be the addition of all the numbers appearing on the die each time. Kimmy got 'a' 2 times, 'b' 5 times and 'd' 6 times. What is the total score of Kimmy? [2 MARKS]

Discuss Question

:
Concept: 1 Mark
Solution: 1 Mark
Total score of Kimmy

= 2 a + 5 b + 6 d

Question 32. The

n^{t h}

term in a pattern is

2 n^{2} + 5

. What is the difference between

6^{t h}

and

4^{t h}

terms in the pattern? [3 MARKS]

Discuss Question

6^{t h}

: 1 Mark

4^{t h}

: 1 Mark
Answer: 1 Mark
Given that,

n^{t h}

term is

2 n^{2} + 5

Therefore,

6^{t h} t e r m = 2 \times 6^{2} + 5

2 \times 36 + 5 = 77

4^{t h} t e r m = 2 \times 4^{2} + 5

2 \times 16 + 5 = 32 + 5 = 37

Difference

= 77 - 37 = 40.

Question 33. Solve the equation

\frac{5 x - 3}{12} = 1

2
3
4
-3

Discuss Question

Answer: Option B. -> 3
:
B

\frac{5 x - 3}{12} = 1 \Rightarrow 5 x - 3 = 1 \times 12 \Rightarrow 5 x - 3 = 12 \Rightarrow 5 x = 12 + 3 \Rightarrow 5 x = 15 \Rightarrow x = \frac{15}{5} \Rightarrow x = 3

Question 34. Tulika is 3 times as old as her cousin. The sum of their ages is 36 years. How old is Tulika?

8 years
9 years
27 years
32 years

Discuss Question

Answer: Option C. -> 27 years
:
C
Let Tulika’s cousin's age be

x .

Then Tulika’s age will be

3 x .

Given that the sum of their ages is 36.

∴ x + 3 x = 36

\Rightarrow 4 x = 36

\Rightarrow x = \frac{36}{4} = 9

\Rightarrow Tulika's age = 3 x = 3 \times 9 = 27 years.

Question 35. The cost of two red balls and five blue balls is ₹160. Then the correct equation for this situation among the given options is _______.

(r : price of one red ball)

(b : price of one blue ball)

2r+5b=₹160
3r+5b=₹160
r+5b=₹80
2r−5b=₹160

Discuss Question

Answer: Option A. -> 2r+5b=₹160
:
A
Let the cost of one Red ball be

r

.
Let the cost of oneBlue ball be

b

.
So, the algebraic equation will be

2 r + 5 b = ₹ 160

Question 36.

(2 x^{2} + 3 x y + 4 x y^{2} + 5 z) is an algebraic expression.

True
False
r+5b=₹80
2r−5b=₹160

Discuss Question

Answer: Option A. -> True
:
A
2x², 3xy, 4xy²and 5z are terms and they are combined using the operator "+”.
Therefore, it is an algebraic expression.

Question 37. If

3 x - 2 = 13

, then

x

Discuss Question

Answer: Option D. -> 5
:
D

Given, 3 x - 2 = 13

\Rightarrow 3 x = 13 + 2

[Transposing 2 to the other side]

\Rightarrow 3 x = 15

\Rightarrow x = \frac{15}{3}

[Transposing 3 to the other side]

\Rightarrow x = 5

Question 38. Rahul and his cousins spent ₹ (5x + 6y) for the clothes they bought, where ₹ x is the price of a pant and ₹ y is the price of a shirt. They wanted to return 2 shirts because the shirts were damaged and they wanted a refund. Then the money they spent on clothes will be equal to? [3 MARKS]

Discuss Question

:
Steps: 2 Marks
Answer: 1 Mark
Price of one shirt = ₹y
So, price of two shirts = ₹ 2y
Rahul and his cousins will get ₹ 2y after giving back two shirts.
Now, the money they spent on clothes = (Money they spent before giving back the shirts) - (Cash they get back)
= (5x + 6y) - (2y)
Like terms can be subtracted.

\Rightarrow 6 y

and

2 y

are like terms,

∴

The money they spent on clothes
= ₹(5x + 6y - 2y)
= ₹ (5x + 4y)

Question 39. 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

:
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 40. Express the following statement in the algebraic form "the sum of