Tag: solving linear equations

Questions Related to solving linear equations

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

  1. $64$

  2. $36$

  3. $81$

  4. $49$


Correct Option: A
Explanation:

$\displaystyle \sqrt[3]{x}\,- 4\, =\, 0\, \Rightarrow\, \sqrt[3]{x}\, =\, 4$.
$\Rightarrow\, x\, =\, 4^{3}\, =\, 64$

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

  1. $25$

  2. $54$

  3. $15$

  4. $20$


Correct Option: A
Explanation:
Given, $5 - \sqrt { x }  = 0$
$ \sqrt { x }  = 5$
Squaring on both sides, we get
$ x = { 5 }^{ 2 } = 25$

Simplify: 
$\displaystyle 6x-\left( -4y-8x \right) $

  1. $2x+y$

  2. $14x+4y$

  3. $12x+3y$

  4. $15x+5y$


Correct Option: B
Explanation:

On simplifying, we have

$\displaystyle 6x-\left( -4y-8x \right) =6x+4y+8x$
$=14x+4y$
Hence simplified form of the given expression is $14x+4y$.

Simplify: 
$\displaystyle x-\left[ y-{ x-\left( y-1 \right) -2x}  \right] $

  1. $2y+1$

  2. $-2y+1$

  3. $2x+y-1$

  4. $2x-y-1$


Correct Option: B
Explanation:

On simplified, we have

$\displaystyle x-\left[ y-{ x-\left( y-1 \right) -2x}  \right] $
$=x-\left[ y-{ x-y+1-2x}  \right] $
=$\displaystyle x-\left[ y-{ -x-y+1}  \right] =x-\left[ y+x+y-1 \right] $
=$\displaystyle x-\left[ 2y+x-1 \right] =x-2y-x+1=-2y+1$
Hence, simplified form of the given expression is $-2y+1$.

Number of variables in a simple linear equation

  1. Two

  2. One

  3. 0

  4. None


Correct Option: B
Explanation:

A linear equation can comprise of many variables. The most simple linear equation is in $one$ variable ,i.e, $ax+b=0$.

The value of $\displaystyle \sqrt{2\sqrt{2}\sqrt{2}}...\infty $ is 

  1. 0

  2. 1

  3. $\displaystyle 2\sqrt{2}$

  4. 2


Correct Option: D
Explanation:

Let  $ x =\sqrt{2\sqrt{2\sqrt{2.. }}}\infty$
square both side
$x^2=\sqrt{2\sqrt{2\sqrt{2...}}}\infty = 2x$
$x=2$



If $Rs.50$ is distributed among $150$ children giving $50p$ to each boy and $25p$ to each girl, then the number of boys is:

  1. $25$

  2. $40$

  3. $36$

  4. $50$


Correct Option: D
Explanation:
Let the number of boys $= x$
then number of girls $= 150-x$ 
According to the problem, the total money divided between girls and boys are:
$\cfrac { 50 }{ 100 } \times  (x)+\cfrac { 25 }{ 100 } (150x)=50$
Multiply equation by $100$, we get
$50x+(150x)25 = 5000$
$\Rightarrow 50x+375025x = 5000$
$\Rightarrow 25x = 1250$
$\Rightarrow x = 50$

If $\sqrt{x+1}=\sqrt{x-1}=1$, then x is equal to __________________.

  1. $\displaystyle\frac{5}{4}$

  2. $\displaystyle\frac{2}{3}$

  3. $\displaystyle\frac{4}{5}$

  4. $\displaystyle\frac{3}{5}$


Correct Option: A

The number of solution of the equation $\sqrt{x^{2}}=x-2$ is

  1. $0$

  2. $1$

  3. $2$

  4. $4$


Correct Option: B
Explanation:

Given equation:

$ \sqrt {x^2} = x-2$
$ =  |x-2|$ 
For $x>2$,  $ x=x-2$ No solution
For $x<2$,  $ 2x-2=0      \quad x=1$ 
One solution exists.

IF the lines $ \displaystyle y=m _{1}x+c $  and $  y=m _{2}x+c _{2}  $ are parallel , then 

  1. $ \displaystyle m _{1}=m _{2} $

  2. $ \displaystyle m _{1}=m _{2} =1 $

  3. $ \displaystyle m _{1}=m _{2} =-1 $

  4. $ \displaystyle m _{1}=m _{2} =0 $


Correct Option: A
Explanation:

Two lines are said to be parallel if the slopes of two line will be equal
$m _1=m _2$