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

6th Grade > Mathematics

ALGEBRA MCQs

Total Questions : 96 | Page 7 of 10 pages

Question 61.

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 62.

Raju's age is 5 more than twice of Ram's age. If Ram's age is represented by $x$ , then the expression which represents Raju's age is ________.

$2 x$
$2 x$ + 5
$5 x + 2$
$2 x - 5$

Discuss Question

Answer: Option B. ->

2 x

+ 5
:
B
Given Ram's age is

x

.
Twice of Ram's age is

2 x

∴

5 more than twice Ram's age is

2 x + 5

which gives Raju's age.

Question 63.

Which of the pairs given in options will add up to give (9x+5y)?

$3 x + 2 y$ , $2 x + 7 y$
$4 x + 4 y$ , $5 x + y$
$3 x + 7 y$ , $6 x - 2 y$
$3 x + 3 y$ , $4 x + 7 y$

Discuss Question

Answer: Option B. ->

4 x + 4 y

5 x + y

:
B and C

3 x + 2 y

2 x + 7 y

5 x + 9 y

\neq 9 x + 5 y

4 x + 4 y

5 x + y

9 x + 5 y

= 9 x + 5 y

3 x + 7 y

6 x - 2 y

9 x + 5 y

= 9 x + 5 y

3 x + 3 y

4 x + 7 y

7 x + 10 y

\neq 9 x + 5 y

Question 64.

Which of the given expressions represent/s the pattern 1, 4, 7, 10, 13..... ?

3n+1
3n+2
3n-2
3n

Discuss Question

Answer: Option A. -> 3n+1
:
A and C
On careful observation, you can see that each term in the pattern is one more than multiples of three.
Since the multiples of 3 can be represented by 3n, the pattern can be represented by 3n+1 (where n is 0, 1, 2...)
But each term can also be thought of two less than multiples of 3.
So, the pattern can also be represented by 3n-2 (where n is 1, 2, 3....)
Hence 3n + 1 and 3n -2 are the correct options.

Question 65.

If $3 x - 2 = 13$ , then $x$ is

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 66.

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 67.

Express the following statement in the algebraic form "the sum of $3 x$ and $4 y$ is $8$ ." [1 MARK]

Discuss Question

Answer: Option B. -> 3
:
Solution: 1 Mark
The algebraic form of the given statement is:

3 x + 4 y = 8

Question 68.

Add: [2 MARKS]
(i) $3 x^{3} - 5 x^{2} + 8 x + 10$ ,
$15 x^{3} - 6 x - 23$ and
$9 x^{2} - 4 x + 15$
(ii) $3 a b^{2} - 2 b^{2} + a^{2}$ ,
$5 a^{2} b - 2 a b^{2} - 3 a^{2}$ and
$8 a^{2} - 5 b^{2}$

Discuss Question

Answer: Option B. -> 3
:
Each Point: 1 Mark
(i)

(3 x^{3} - 5 x^{2} - + 8 x + 10) + (15 x^{3} - 6 x - 23) + (9 x^{2} - 4 x + 15)

= 3 x^{3} - 5 x^{2} + 8 x + 10 + 15 x^{3} - 6 x - 23 + 9 x^{2} - 4 x + 15

Bringing like terms together, we get,

= 3 x^{3} + 15 x^{3} - 5 x^{2} + 9 x^{2} + 8 x - 6 x - 4 x + 10 - 23 + 15

= 18 x^{3} + 4 x^{2} - 2 x + 2

(ii)

(3 a b^{2} - 2 b^{2} + a^{2}) + (5 a^{2} b - 2 a b^{2} - 3 a^{2}) + (8 a^{2} - 5 b^{2})

= 3 a b^{2} - 2 b^{2} + a^{2} + 5 a^{2} b - 2 a b^{2} - 3 a^{2} + 8 a^{2} - 5 b^{2}

Bringing like terms together, we get,

= 3 a b^{2} - 2 a b^{2} - 2 b^{2} - 5 b^{2} + a^{2} - 3 a^{2} + 8 a^{2} + 5 a^{2} b

= 5 a^{2} b + a b^{2} + 6 a^{2} - 7 b^{2}

Question 69.

One-third of a number added to one-fifth gives 32. Find the number.[3 MARKS]

Discuss Question

Answer: Option B. -> 3
:

Steps: 2 Marks
Answer: 1 Mark
Let the number be $x$ .
One-third of the number $\Rightarrow \frac{1}{3} x$
One-fifth of the number $\Rightarrow \frac{1}{5} x$
Given: $\frac{1}{3} x + \frac{1}{5} x = 32$
$\Rightarrow \frac{5 x + 3 x}{15} = 32$
$\Rightarrow \frac{8 x}{15} = 32$
$\Rightarrow x = \frac{32 \times 15}{8} = 60$
$∴$ The required number = $60$

Question 70.

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

Answer: Option B. -> 3
:
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.