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CBSE Questions for Class 7 Maths Simple Equations Quiz 2 - MCQExams.com
CBSE
Class 7 Maths
Simple Equations
Quiz 2
$$12, a, 6, 8, 2, 14$$
The average (arithmetic mean) of the numbers listed above is $$6$$. Calculate the value of $$a$$.
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$$-36$$
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$$-6$$
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$$0$$
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$$6$$
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$$36$$
Explanation
We know that average of a bunch of numbers is the sum of the numbers divided by how many numbers in the bunch.
We can set up an equation for the average from the given question,
$$\Rightarrow \dfrac { 12+a+6+8+2+14 }{ 6 } =6$$
$$\Rightarrow \dfrac { 42+a }{ 6 } =6$$
$$\Rightarrow 42+a=36$$
$$\Rightarrow a=-6$$
Sumeet guessed a number $$x$$ and then he added $$30$$ to it. Give the expression for double of it.
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$$2(x+30)$$
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$$\dfrac{1}{2(x+30)}$$
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$$2x+30$$
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$$x+60$$
Explanation
According to the question,
The expression is $$x+30$$.
$$\therefore$$ double of it will be $$ 2(x+30$$).
So. option $$A$$ is correct.
Frame the given statement into a mathematical expression: "Thrice of a number increased by $$150$$."
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$$150-x$$
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$$3x-150$$
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$$3x+150$$
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None of these
Explanation
Let $$x$$ be the required number.
$$\therefore $$ thrice of a number shall be
$$\displaystyle 3\times x=3x$$.
According to the question, if it is increased by $$150$$,
the number would be
$$\displaystyle (3x+150)$$.
What is an equation?
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A statement in which the values of two mathematical expressions are equal.
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An expression that computes the values of variables.
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A mathematical expression.
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None of these
Explanation
An equation is a mathematical statement which represents two things are equal. It consists of two expressions, one on either side of equal to symbol.
In other words, an equation is a statement in which the values of two mathematical expressions are equal.
$$3251+587+369-$$? $$=3007$$
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$$1250$$
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$$1300$$
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$$1375$$
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$$1200$$
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None of these
Explanation
$$3251$$ Let $$4207-x=3007$$
+$$587$$ Then, $$x=4207-3007=1200$$
+$$369$$
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$$4207$$
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Given that $$5x-2\left( 6+7x \right) =15$$, the value of $$x$$ is
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$$1\dfrac { 13 }{ 14 } $$
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$$1\dfrac { 8 }{ 19 } $$
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$$\dfrac { 1 }{ 3 } $$
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$$-3$$
Explanation
In order to simplify :- $$5x-2(6+7x)=15$$
Solving bracket first,
$$-2(6+7x)$$ = $$-12-14x$$ ........ eq $$(1)$$
using eq $$(1)$$,
$$5x-12-14x= 15$$
$$\Rightarrow 5x-14x= 15+12$$
$$\Rightarrow -9x = 27$$
$$\Rightarrow x =\dfrac{27}{-9}$$
$$\Rightarrow x = -3$$
Option $$D$$ is correct.
If the average of $$3, 4$$, and $$x$$ is $$2$$, then find $$x$$.
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$$-15$$
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$$-1$$
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$$-8$$
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$$-6$$
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$$-2$$
Explanation
Given: The average of $$3,4$$ and $$x$$ is $$2$$
we have to find $$x$$
$$\Rightarrow \dfrac { 3+4+x }{ 3 } =2$$
$$\Rightarrow 7+x=6$$
$$\Rightarrow x=-1$$
$$x$$ is $$-1$$
Hence, the answer is option $$B$$.
Find the value of $$p $$ in the equation
$$\dfrac{p}{9}-8=17$$
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$$225$$
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$$-225$$
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$$\dfrac{225}{9}$$
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$$\dfrac{9}{225}$$
Explanation
$$\frac { p }{ 9 } -8=17$$
$$\Longrightarrow\displaystyle \frac { p }{ 9 } =17+8$$
$$\Longrightarrow \dfrac { p }{ 9 } =25$$
Now, multiplying both sides by $$9$$ we get,
$$\Longrightarrow\displaystyle \frac { p }{ q } \times 9=25\times 9=225$$
$$\Longrightarrow\displaystyle p=225$$
Which of the following equations has $$x = 2$$ as a solution?
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$$x + 2 = 5$$
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$$x - 2 = 0$$
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$$2x + 1= 0$$
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$$x + 3 = 6$$
Explanation
$$\textbf{The value of the variable in an equation which satisfies the equation is called a solution to the}$$ $$\textbf{ equation.}$$
Let us now try and check the value of $$x=2$$ for all the four given equations
For option (A)
$$\begin{aligned}&x+2=5 \\&2+2 \neq 5\end{aligned}$$
$$\textbf{ Does not satisfy}$$
For option (B)
$$\begin{aligned}&x-2=0 \\&2-2=0\end{aligned}$$
$$\textbf{ Satisfies.}$$
For option (C)
$$\begin{aligned}&2 x+1=0 \\&(2 \times 2)+1 \neq 0\end{aligned}$$
$$\textbf{ Does not satisfy}$$
For option (D)
$$\begin{aligned}&x+3=6 \\&2+3 \neq 6\end{aligned}$$
$$\textbf{ Does not satisfy}$$
$$\textbf{Clearly option B is correct as it gives us the Left hand side equal to the Right hand side.}$$
Convert this statement in mathematical form.
Twice of remainder when 8 is subtracted from a number is 10.
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$$2x-8=10$$
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$$2(x-8)=10$$
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$$\dfrac{2x}{8}=10$$
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$$2x-10=8$$
Explanation
let number be $$x$$,then remainder$$=x-8$$
so $$2(x-8)=10$$
The value of x in the equation $$5x - 35 = 0$$ is:
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$$2$$
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$$7$$
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$$8$$
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$$11$$
Explanation
Given, $$5x-35=0$$
Transpose $$35$$ to R.H.S.,
$$5x=35$$
Divide throughout by $$5$$
$$\dfrac {5x}{5}=\dfrac {35}{5}$$
$$\Rightarrow x=7$$
$$12$$ times a number is $$4$$ less than the $$5$$ times the number. Write an equation representing the statement given.
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$$12x -4 = 5x$$
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$$12x+4 = 5x$$
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$$12+ 4x= 5$$
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$$12 -4x= 5$$
Explanation
Let the number be $$x$$
$$\Rightarrow 12\times x=5\times x-4 $$
$$\Rightarrow 12x+4=5x$$
Three times the number is $$300$$. Convert this statement in mathematical form.
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$$3x=100$$
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$$3+x=300$$
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$$3 =300+x$$
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$$3x=300$$
Explanation
$$3$$ times the number is $$300.$$
$$\Rightarrow$$ Let the number $$=x$$
$$\Rightarrow 3$$ times the number $$=3x$$
$$\Rightarrow$$ This is equal to $$3x=300.$$
Hence, the answer is $$3x=300.$$
If the mean of $$6, 8, 5, x $$ and $$4$$ is $$7$$, then the
value of $$x$$ is ______.
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$$11$$
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$$12$$
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$$13$$
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$$14$$
Explanation
Given, mean $$= 7$$ and data is $$6,8,5,x,4$$
Therefore, $$\dfrac {6+8+5+x+4}{5}$$ $$= 7$$
$$\Rightarrow$$ $$x + 23 = 35 $$
$$\Rightarrow$$ $$x = 12$$
The substraction of 3 from 2x is represent as
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2x-3
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3-2x
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2x+3
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$$\frac{2x}{3}$$
Explanation
Subtraction $$3$$ from $$2x=2x-3$$
Is this an equation $$21=z+11$$
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$$Yes$$
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$$NA$$
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$$No$$
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$$15$$
Explanation
$$21=z+11$$ is a equation
$$\dfrac{9}{5}$$ is the solution of the equation $$4X-1=8$$
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True
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False
Explanation
$$4 \times \dfrac{9}{5}=8$$
$$\dfrac{36}{5}=8$$
But,
$$\dfrac{36}{5}\neq8$$
Hence, $$\dfrac{9}{4}$$ is the solution of the given equation, not the $$\dfrac{9}{5}$$
State true (T) or false (F):
$$x=5$$ is a solution of the equation $$3x+2=13$$.
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True
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False
Explanation
Substituting $$x=5$$ in the given equation, we get,
$$3x+2=13$$
$$\Rightarrow 3\times 5+2=13\\ \Rightarrow 15+2=13\\ \Rightarrow 17=13$$
which is not true.
Hence the given statement is false.
The graph of the linear equation $$3x + 5y = 15$$ cuts the $$x-$$axis at the point
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(5, 0)
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(3, 0)
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(0, 5)
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(0, 3)
Explanation
For graph to cut x-axis;
we will substitute $$y=0$$ in $$3x+5y=15$$
as equation of x-axis is $$y=0$$.
So; $$3x+5(0) = 15$$
$$\Rightarrow 3x=15$$
$$\Rightarrow x = 5$$
$$\therefore $$ Point is $$(x, o) = (5,0)$$
$$\boxed{\text{Hence, answer is (a)}}$$
State weather the statement is true(T) or false (F):
In the equation $$3x-3=9$$, transposing $$-3$$ to RHS, we get $$3x=9$$.
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True
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False
Explanation
False,
It is given that, $$3x-3=9$$
$$\Rightarrow 3x=9+3$$ [Transposing $$-3$$ to RHS]
$$\Rightarrow 3x=12$$.
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