Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 16

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Question 1
1 / -0

A student divided a number by two when he was required to multiply it by $$2$$. The answer he got was $$2$$. The correct answer should have been

A
$$8$$

B
$$1$$2

C
$$6$$

D
$$4$$

Solution

Let the number be $$x$$
As per the given condition, we have:
$$\cfrac { x }{ 2 } =2 $$
$$\Rightarrow x=4$$
$$ \therefore$$ the number is $$4$$.
This number was supposed to be multiplied by $$2$$.
Hence, the correct answer is $$4\times 2=8$$.
Question 2
1 / -0

Solve the following:
$$ 3\left ( 3x-4 \right )-2\:\left ( 4x-5 \right )=\:6 $$

A
$$4$$

B
$$8$$

C
$$12$$

D
$$6$$

Solution

Given, $$3(3x-4)-2(4x-5)=6$$
$$\Rightarrow 9x-12-8x+10=6$$
$$\Rightarrow x-2=6$$
Add $$2$$ on both the sides, we get
$$x-2+2=6+2$$
$$\Rightarrow x=8$$
Question 3
1 / -0

If $$\displaystyle \frac{1}{3}\, =\, \frac {\sqrt{x}}{2}$$, then value of $$x$$ is

A
$$\displaystyle \frac{6}{7}$$

B
$$\displaystyle \frac{7}{2}$$

C
$$\displaystyle \frac{4}{9}$$

D
$$\displaystyle \frac{12}{7}$$

Solution

$$\dfrac { 1 }{ 3 } = \dfrac { \sqrt { x } }{ 2 } \\ \sqrt { x } =\dfrac { 2 }{ 3 }$$
On squaring both the sides.
$$\Rightarrow x = \dfrac { 4 }{ 9 } $$
Question 4
1 / -0

Solve for $$x$$ : $$\sqrt[3]{x}\,- 4\, =\, 0$$

A
$$64$$

B
$$36$$

C
$$81$$

D
$$49$$

Solution

$$\sqrt [ 3 ]{ x } - 4 = 0\\ \sqrt [ 3 ]{ x } = 4$$
Cubing on both sides
$$x = { 4 }^{ 3 } = 64$$
Question 5
1 / -0

Solve for $$x$$ : $$5\, -\, \sqrt{x}\, =\, 0$$

A
$$25$$

B
$$54$$

C
$$15$$

D
$$20$$

Solution

Given, $$5 - \sqrt { x } = 0$$
$$ \sqrt { x } = 5$$
Squaring on both sides, we get
$$ x = { 5 }^{ 2 } = 25$$
Question 6
1 / -0

Two distinct natural numbers are such that the one number is twice the other number and their sum is $$6$$. The two numbers are ____

A
$$8$$ and $$3$$

B
$$2$$ and $$7$$

C
$$4$$ and $$2$$

D
$$6$$ and $$3$$

Solution

Let the number be $$x$$.
Then, according to question, we have $$x+2x=6$$
$$\Rightarrow 3x=6$$
$$\Rightarrow x=2$$
$$\Rightarrow 2x=4$$
Therefore, the two numbers are $$2$$ and $$4$$.
Question 7
1 / -0

Mohan gets $$3$$ marks for each correct sum and loses $$2$$ marks for each wrong sum. He attempts $$30$$ sums and obtains $$40$$ marks. The number of sums solved correctly is

A
$$10$$

B
$$15$$

C
$$20$$

D
$$25$$

Solution

It is given that, Mohan gets $$3$$ marks for each correct answer and loses $$2$$ marks for each wrong answer.
He attempted $$30$$ sums and got $$40$$ marks.
Let the number of sums solved correctly be $$n$$.
Then number of wrong sums $$= 30 - n$$
$$\therefore 3n-2.(30-n) = 40$$
$$\Rightarrow 3n-60+2n=40$$
$$\Rightarrow 5n=100$$
$$\Rightarrow n=20$$
Question 8
1 / -0

Twice a number decreased by $$15$$, equals $$25$$. Find the number.

A
$$25$$

B
$$20$$

C
$$18$$

D
$$21$$

Solution

Let the number be $$x$$
In the question, it is given that twice a number, i.e. $$2x$$ and decreased by $$15$$.
That means, $$2x-15$$. This is further equals to
$$2x-15=25$$
$$2x=40$$
$$x=20$$
Therefore, the number is $$20$$.
Question 9
1 / -0

You take $$5$$ less than thrice a number and add $$7$$. The result is $$14$$. The number is

A
$$5$$

B
$$4$$

C
$$6$$

D
$$2$$

Solution

Let the number be $$x$$.
Then according to the given condition,
$$(3x-5)+7=14$$
$$\Rightarrow 3x+2=14$$
$$\Rightarrow \displaystyle 3x=12$$
$$\Rightarrow x=\dfrac{12}{3}$$
$$\Rightarrow x=4$$
Hence, the required number is $$4$$.
Question 10
1 / -0

The difference between $$\displaystyle \frac{3}{4}$$ of a line and $$\displaystyle \frac{2}{5}$$ of the same line is $$28$$ cm. Find the length of the line.

A
$$60$$ cm

B
$$90$$ cm

C
$$20$$ cm

D
$$80$$ cm

Solution

Let the length of the line be $$x$$.
$$\cfrac { 3 }{ 4 } x - \cfrac { 2 }{ 5 } x = 28$$
L.C.M. of $$4$$ and $$5$$ is $$20$$.
$$\therefore 15x - 8x = 28(20)$$
$$\therefore 7x = 28(20)$$
$$\therefore x = 80$$
Therefore, length of the line is $$80$$ cm.

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 16

Result

Linear Equations in One Variable Test - 16

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SHARING IS CARING

Question 1

$$8$$

$$1$$2

$$6$$

$$4$$

Solution

Question 2

$$4$$

$$8$$

$$12$$

$$6$$

Solution

Question 3

$$\displaystyle \frac{6}{7}$$

$$\displaystyle \frac{7}{2}$$

$$\displaystyle \frac{4}{9}$$

$$\displaystyle \frac{12}{7}$$

Solution

Question 4

$$64$$

$$36$$

$$81$$

$$49$$

Solution

Question 5

$$25$$

$$54$$

$$15$$

$$20$$

Solution

Question 6

$$8$$ and $$3$$

$$2$$ and $$7$$

$$4$$ and $$2$$

$$6$$ and $$3$$

Solution

Question 7

$$10$$

$$15$$

$$20$$

$$25$$

Solution

Question 8

$$25$$

$$20$$

$$18$$

$$21$$

Solution

Question 9

$$5$$

$$4$$

$$6$$

$$2$$

Solution

Question 10

$$60$$ cm

$$90$$ cm

$$20$$ cm

$$80$$ cm

Solution

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