Tag: brackets

Questions Related to brackets

$24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$ using BODMAS rule to reduce the expression.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^2+23x+46$

  2. $-x^2+23x+46$

  3. $-x^2-23x+46$

  4. $-x^2+23x-46$

Show answer
Correct Option: B
Explanation:

$24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
$=$ $24x+24-x^2+24-x-2$
$=$ $-x^2+46+23x$
$=$ $-x^2+23x+46$

Solve the expression using BODMAS rule: $3x(x-2)+x(x^2\times 2x)-12x$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $2x^5-3x^2-18x$

  2. $2x^5+3x^2-18x$

  3. $2x^5+3x^2+18x$

  4. $-2x^5-3x^2-18x$

Show answer
Correct Option: B
Explanation:

$3x(x-2)+x(x^2\times 2x)-12x$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $3x(x-2)+x(x^2\times 2x)-12x$
$=$ $3x^2-6x+x^3\times2x^2-12x$
$=$ $3x^2-6x+2x^5-12x$
$=$ $2x^5+3x^2-18x$

If $1\le a\le 2$, then $\sqrt { a-2\sqrt { a-1 }  } -\sqrt { a+2\sqrt { a-1 }  } =$.......

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $2$

  2. $2\sqrt{a-1}$

  3. $-2$

  4. $1$

Show answer
Correct Option: C
Explanation:

$\sqrt{a - 2 \sqrt{a - 1}} - \sqrt{a + 2 \sqrt{a - 1}}$

$\Rightarrow \sqrt{(\sqrt{a - 1})^2 - 2 (1) \sqrt{a - 1} + 1^2} - \sqrt{(\sqrt{(a - 1)})^2 + 2 \sqrt{a - 1} + 1^2}$
$\Rightarrow \sqrt{(\sqrt{a - 1} - 1)^2} - \sqrt{(\sqrt{a - 1} + 1)^2}$
$\Rightarrow (\sqrt{a - 1} - 1) - ( \sqrt{a - 1} + 1)$
$= -2$

A number x is decreased by m% and some other number y is increased by m%. If both the results are equal, find m in terms of x and y. Also, find m if $\displaystyle 2x=3y$.


maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=10$

  2. $\displaystyle m=\frac{100\left ( x-y \right )}{x-y};m=20$

  3. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=30$

  4. $\displaystyle m=\frac{100\left ( x-y \right )}{x+y};m=20$

Show answer
Correct Option: D
Explanation:

Given $ \frac {100 - m}{100} \times x = \frac {100 + m}{100} \times y $
$ => 100x - mx = 100y + my $
$ => 100x - 100y = mx + my $
$ => 100 (x-y) = m (x + y) $
$ => m = \frac {100(x-y)}{x+y} $

When , $ 2x = 3y => x = \frac {3y}{2} $
We have, $ m = \frac {100(\frac {3y}{2} -y)}{\frac {3y}{2} +y} $
$ => m =\frac {100(\frac {y}{2})}{\frac {5y}{2}} $
$ => m =\frac {100}{5} = 20 $

 Make b the subject of formula : $\displaystyle a=\frac{1+b^2}{1-b^2}$. 

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle b=\sqrt{\frac{a+1}{a-1}}$

  2. $\displaystyle b=\sqrt{\frac{a-1}{a+1}}$

  3. $\displaystyle b=2\sqrt{\frac{a-1}{a+1}}$

  4. $\displaystyle b=2\sqrt{\frac{a+1}{a-1}}$

Show answer
Correct Option: B
Explanation:

Given, $ a = \frac {1 +{b}^{2}}{1 - {b}^{2}} $
$ => a -a{b}^{2} = 1 +{b}^{2} $
$ => a- 1 = {b}^{2} (1 + a) $
$ =>{b}^{2} = \frac {a-1}{1+a} $