Tag: maths

Questions Related to maths

If $t = x+2$, find the value of x .If $2t-7 +\dfrac{3(t-1)}{2}=3$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $\frac{23}{7}$

  2. $\frac{3}{7}$

  3. $\frac{9}{7}$

  4. $\frac{37}{7}$

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Correct Option: C
Explanation:

$(2t-7)+(\frac{3t-3}{2})=3\\(\frac{4t-14+3t-3}{2})=3\\7t-17=6\\\therefore 7t=6+17\\t=(\frac{23}{7})\\then x+2=(\frac{23}{7})\\\therefore x=(\frac{23}{7})-2\\=(\frac{23-14}{7})\\=(\frac{9}{7})$

Which equation is  non- linear 

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x + 1 = 2x - 3$

  2. $9 - 5{x^2} = 4$

  3. $- 2x - 5 - \left( {x + 4} \right) = - 9$

  4. ${x} - \frac{1}{{15}} = 2$

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Correct Option: B
Explanation:

Linear equations are those which have the degree of equation as $1$


Here every equation has the degree as $1$

Except $9-5x^2=4$

So its is not a linear equation 

A triangular number which is the sum of the square of two consecutive odd numbers is?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $10$

  2. $15$

  3. $21$

  4. $28$

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Correct Option: A
Explanation:
Let the two consecutive odd numbers be $n-2,n$
$(n-2)^2+n\\ n^2+4-4n+n^2\\2n^2+4-4n$
If we put $n=1\\ 2(1)-4+4=2\\n=2\\ 2(4)+4-4=4\\n=3\\2(9)+4-4(3)\\=18+4-12\\=10$
$\therefore $ Triangular no. is $10$
For any other value of $n$ the triangular no. is not in the required options
$\therefore$ we take $n=3$ and triangular no. is $10$

If $\displaystyle \frac{a}{3y}+\frac{3b}{x}=7$ and $\displaystyle a+1=2b+1=x=5,$ find the value of $'y'.$


maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $\displaystyle \frac{10}{77}$

  2. $\displaystyle \frac{22}{69}$

  3. $\displaystyle \frac{20}{87}$

  4. $\displaystyle \frac{14}{93}$

Show answer
Correct Option: C
Explanation:

Since, $ a+1=2b+1=x=5 $
$ => a = 5 - 1 = 4 $
$ 2b = 5 - 1 = 4 => b = 2 $

$ x = 5 $

Substituting these values in $ \frac { a }{ 3y } +\frac { 3b }{ x } =7 $, we get $ \frac { 4 }{ 3y } +\frac { 6 }{ 5 } =7 $
$ => \frac { 4 }{ 3y } = 7 - \frac { 6 }{ 5 } $
$ => \frac { 4 }{ 3y } =  \frac { 29 }{ 5 } $
$ => \frac { 3y }{ 4 } =  \frac { 5 }{ 29 } $
$ => y = \frac {20}{87} $

If $(2ax + 1) (3x + 1) = 6a (x + 1)$ and $x = 1$, find the value of $a$.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $1$

  2. $4$

  3. $3$

  4. $2$

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Correct Option: A
Explanation:

    $(2ax + 1) (3x + 1) = 6a (x + 1) $
$=>[2a(1)+1][3(1)+1]=6a[(1+1)]$
$=>(2a+1)(3+1)=6a(2)$
$=>(2a+1)(4)=12a$
$=>8a+4=12a$
$=>8a-12a=-4$
$=>-4a=-4$
$=>a=1$

Solve for $x$ : $\displaystyle \sqrt{\frac{x\, -\,2}{x\, +\, 1}}\, =\, \frac{1}{2}$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. 3

  2. 2

  3. 1

  4. 0

Show answer
Correct Option: A
Explanation:
$\cfrac { \sqrt { x-2 }  }{ \sqrt { x+1 }  }  = \cfrac { 1 }{ 2 }$
Squaring on both sides we get
$\cfrac { x-2 }{ x+1 }  = \cfrac { 1 }{ 4 } \\ 4(x-2) = (x+1)\\ 4x - 8 = x +1\\ 3x = 9\\ x = 3$

Solve for $x$ : $\displaystyle \frac{4}{3\sqrt{x}}\, =\, \frac{1}{2}$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. ${5}\dfrac{6}{9}$

  2. ${7}\dfrac{1}{9}$

  3. $14$

  4. $27$

Show answer
Correct Option: B
Explanation:
$\cfrac{4}{3\sqrt{x}}=\cfrac{1}{2}$
Squre both the sides we get
$\cfrac{16}{9x}=\cfrac{1}{4}$
$\Rightarrow 9x=16\times 4$
$\Rightarrow 9x=64 \Rightarrow x=\cfrac{64}{9}$
$\Rightarrow x=7\cfrac{1}{9}$

Solve:
$x\, +\, y\, =\, 7xy$
$2x\, -\, 3y\, =\, -xy$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x\, =\, \displaystyle \frac{1}{8}$ and $y\, =\, \displaystyle \frac{1}{4}$

  2. $x\, =\, \displaystyle \frac{1}{7}$ and $y\, =\, \displaystyle \frac{1}{4}$

  3. $x\, =\, \displaystyle \frac{1}{2}$ and $y\, =\, \displaystyle \frac{1}{4}$

  4. $x\, =\, \displaystyle \frac{1}{3}$ and $y\, =\, \displaystyle \frac{1}{4}$

Show answer
Correct Option: D
Explanation:

Given equations are 

$x+y=7xy$ ....(1)
and $2x-3y=-xy$ ....(2)
Multiply equation (1) by $3$, we get
$3x+3y=21xy$ ....(3)
Add equations (2) and (3),
$5x=20xy$
$\Rightarrow y=\dfrac {1}{4}$
Put this value in equation (1), we get
$x+\dfrac {1}{4}=7x\times \dfrac {1}{4}$
$\Rightarrow x-\dfrac {7x}{4}=-\dfrac {1}{4}$
$\Rightarrow \dfrac {3x}{4}=\dfrac {1}{4}$
$\Rightarrow x=\dfrac {1}{3}$
Therefore, solution is $x=\dfrac {1}{3}, y=\dfrac {1}{4}$.

Find the value of $a$, if $x = 0.5$ is a solution of equation $ax^{2}\, +\, (a\, -\, 1)\,
x\, +\, 3\, =\, a$.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $24$

  2. $15$

  3. $10$

  4. $8$

Show answer
Correct Option: C
Explanation:

Given equation is $ax^2+(a-1)x+3=a$
The equation can be written as
$ax^2+(a-1)x+3-a=0$
Since $x=0.5$ is a solution of the equation, 
$a(0.5)^2 + (a-1)(0.5) + 3 - a = 0$
$\Rightarrow 0.25a + 0.5a - 0.5 + 3 - a = 0$
$\Rightarrow   (0.25 + 0.5 -1)a - 0.5+3 = 0$
$\Rightarrow  -0.25a + 2.5 = 0$
$\Rightarrow  0.25a = 2.5$
$\Rightarrow  a = \dfrac{2.5}{0.25}$
$\Rightarrow a = 10$

The solution of the equation $\displaystyle \frac{2x+4}{3x-1}=\frac{4}{3}$ is 

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. 6

  2. 4

  3. $\displaystyle \frac{8}{3}$

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

Show answer
Correct Option: C
Explanation:

Given equation is $\displaystyle \frac{2x+4}{3x-1}=\frac{4}{3}$
Cross multiplying, we get
$3(2x+4)=4(3x-1)$
$\Rightarrow 6x+12=12x-4\Rightarrow 6x=16$
$\Rightarrow \displaystyle x=\frac{16}{6}=\frac{8}{3}$.
Hence, the solution is $x=\cfrac{8}{3}$.