Tag: maths

Questions Related to maths

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

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

  1. 0

  2. 1

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

  4. 2

Show answer
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:

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

  1. $25$

  2. $40$

  3. $36$

  4. $50$

Show answer
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 __________________.

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

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

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

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

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

Show answer
Correct Option: A

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

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

  1. $0$

  2. $1$

  3. $2$

  4. $4$

Show answer
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 

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

  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 $

Show answer
Correct Option: A
Explanation:

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

If $\sqrt {x-1}-\sqrt {x + 1} + 1= 0$, then $4x$ equals

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

  1. $5$

  2. $4$

  3. $3$

  4. $2$

Show answer
Correct Option: A
Explanation:

$\sqrt {x-1}-\sqrt {x+1}+1=0$
or $\sqrt {x-1}=\sqrt {x+1}=-1$
Squaring, we get
$x-1=x+1+1-2\sqrt {x+1}$
or $2\sqrt {x+1}=3$
or $4(x+1)=9$ or $4x=9-4=5$

Seamus has $3$ times as many marbles as Ronit, and Taj has $7$ times as many marbles as Ronit. If Seamus has $s$ marbles then, in terms of $s$, how many marbles do Seamus, Ronit and Taj have together?

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

  1. $\cfrac{3}{7}s$

  2. $\cfrac{7}{3}s$

  3. $\cfrac{11}{3}s$

  4. $7s$

  5. $11s$

Show answer
Correct Option: C
Explanation:
The problem will be easier to solve if you can choose numbers that will give you all integers as you solve. both Seamus and Taj have a multiple of the number of marbles that Ronit has, so begin by picking for Ronit, not for Seamus.
If Ronit has $2$ marbles, then Seamus has $(3)(2)=6$ marbles and Taj has $(7)(2)=14$ marbles. Together, the three have $22$ marbles.
plug $s=6$ into the answer (remember that the problem asks about Seamus's starting number, not Ronit's and look for a match of $22$:
(A) $\cfrac{3}{7}s=$ not an integer
(B) $\cfrac{7}{3}s=\cfrac{7}{3}(6)=14$. Not a match
(C) $\cfrac{11}{3}s=\cfrac{11}{3}(6)=22$. Match!!
(D) $7s=42$. Not a match
(E) $11s=$ Too large
Alternately, you can use an algebraic approach. Begin by translating the first sentence into equations:
$s=3r$
$t=7r$
The question asks for the sum of the three:
$s+r+t=$?
The answer use only $s$, so figure out how to substitute to leave only $s$ in the equation
$r=\cfrac{s}{3}$
$t=7r=7(\cfrac{s}{3})$
Substitute those into the equation
$s+r+t$
$s+\cfrac{s}{3}+7(\cfrac{s}{3})$
$\cfrac{3s}{3}+\cfrac{s}{3}+\cfrac{7s}{3}$
$\cfrac{11s}{3}$
The correct answer is (C)

Solve the equation: $\dfrac{2z}{1-z}=6$

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

  1. $z = \dfrac{1}{4}$

  2. $z = \dfrac{3}{4}$

  3. $z = \dfrac{2}{4}$

  4. $z = \dfrac{3}{7}$

Show answer
Correct Option: B
Explanation:

Given, $\dfrac{2z}{1-z}=6$
On multiplying both sides by $1 - z$, we get
$2z = 6(1 - z)$
$2z = 6 - 6z$
$8z = 6$
$z = \dfrac{3}{4}$

Solve the equation: $\dfrac{7x - 3}{3x}=2$

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

  1. $x=3$

  2. $x=2$

  3. $x=1$

  4. $x=-1$

Show answer
Correct Option: A
Explanation:

$\dfrac{7x - 3}{3x}=2$
$7x - 3 = 6x$
On transposing $6x$ to the L.H.S and $3$ to the R.H.S we obtain
$7x - 6x = 3$
$x = 3$

Find the value of $ p$ in the linear equation: $4p + 2 = 6p + 10$

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

  1. $p=-4$

  2. $p=-3$

  3. $p=-2$

  4. $p=-1$

Show answer
Correct Option: A
Explanation:

$4p + 2 = 6p + 10$

On transposing $4p+ 2$ to the R.H.S we obtain
$6p - 4p + 10 - 2 = 0$
$2p + 8 = 0$
$2p = -8$
$p = -4$