Tag: brackets

Questions Related to brackets

$x^2+y^2 =100$ find $x$ if $y=6$

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

  1. $\pm 8$

  2. $\pm \sqrt 8$

  3. $\pm 64$

  4. $\pm 4$

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Correct Option: A
Explanation:

$x^2+y^2=100\y=6\x^2+6^2=100\x^2=100-36\x^2=64\x=\pm 8$

If ${a}^{2}+{b}^{2}+{c}^{2}-ab-bc-ca=0$, then

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

  1. $a+b=c$

  2. $b+c=a$

  3. $c+a=b$

  4. $a=b=c$

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Correct Option: D
Explanation:
Given,

$a^2+b^2+c^2-ab-bc-ca=0$

$\Rightarrow 2(a^2+b^2+c^2-ab-bc-ca)=2(0)$

$\Rightarrow 2a^2+2b^2+2c^2-2ab-2bc-2ca=0$

$\Rightarrow (a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)=0$

$(a-b)^2+(b-c)^2+(c-a)^2=0$

$\Rightarrow a-b=b-c=c-a=0$

$\therefore a=b=c$

If $\displaystyle b=6-\left [ \frac{4b+3}{2a-5} \right ]$, express a in terms of b.

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

  1. $\displaystyle a=\frac{33-b}{2\left ( 6-b \right )}$

  2. $\displaystyle a=\frac{b-33}{2\left ( 6-b \right )}$

  3. $\displaystyle a=\frac{33-b}{2\left ( b-6 \right )}$

  4. none of the above

Show answer
Correct Option: A
Explanation:

Given,
$ b = 6 - \left[ \frac { 4b+3 }{ 2a-5 }  \right]  $
$ => \left[ \frac { 4b+3 }{ 2a-5 }  \right] = 6 - b $
$ => 4b + 3 = (6-b)(2a-5) $
$ => 4b + 3 = 12a - 30 - 2ab +5b $
$ => 12a - 33  -2ab + b = 0 $
$ =>  a(12 -2b) = 33 - b $
$ => 2a(6-b) = 33-b $
$ => a = \frac {33-b}{2(6-b)} $

Given $\displaystyle b=\frac{2a}{a-2}$ and $\displaystyle c=\frac{3b-4}{4b+3}$, express c in terms of a.

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

  1. $\displaystyle c=\frac{2a+8}{11a+6}$

  2. $\displaystyle c=\frac{2a-8}{11a-6}$

  3. $\displaystyle c=\frac{2a+8}{11a-6}$

  4. none of the above

Show answer
Correct Option: C
Explanation:

Given, $ c = \frac {3b-4}{4b + 3} $

But, $ b = \frac {2a}{a-2} $
Hence, $ c = \frac {3(\frac {2a}{a-2} )-4}{4(\frac {2a}{a-2} ) + 3} $
$ => c = \frac {6a-4a + 8}{8a +3a - 6} $
$ => c = \frac {2a+8}{11a -6} $

The value of $100 - { ( 7 $of $8 + 4 ) \div 5 } $ is

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

  1. $92$

  2. $78$

  3. $96$

  4. $88$

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Correct Option: D
Explanation:

We apply BODMAS rule to find the value of the given expression. According to BODMAS rule, if an expression contains brackets we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.


Since 'of' stands for multiplication, therefore the given expression becomes 
$100-[(7\times 8+4)\div 5]$ and apply BODMAS rule as shown below:
$ \Rightarrow 100-[(56+4)\div 5]\ \Rightarrow 100-(60\div 5)\ \Rightarrow 100-12\ \Rightarrow 88$
Hence, the value of $100-[(7\times 8+4)\div 5]$ is $88$.

The value of $12\div \dfrac {1}{2}+0.5\times \dfrac {5}{2}-2$ is

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

  1. 23.25

  2. 12.25

  3. 13.25

  4. none

Show answer
Correct Option: A
Explanation:

 

$12\div \dfrac {1}{2}+0.5\times \dfrac {5}{2}-2 = 24 + 1.25 - 2 = 23.25$

Find the value of $\displaystyle \frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times\frac{3}{\frac{5}{6}of\frac{3}{2}\div 1\frac{1}{4}}$.

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

  1. 4

  2. 3

  3. 2

  4. 1

Show answer
Correct Option: C
Explanation:

Given exp.$\displaystyle \frac{2}{1+\frac{1}{\frac{1}{2}}}\times\frac{3}{\frac{15}{12}\div \frac{5}{4}}=\frac{2}{1+2}\times\frac{3}{\frac{15}{12}\times\frac{4}{5}}=\frac{2}{3}\times\frac{3}{1}=2$

If $a$ and $ b $ are any two real numbers with opposite signs, which of the following is the greatest?

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

  1. $\displaystyle (a-b)^{2}$

  2. $\displaystyle (|a|-|b|)^{2}$

  3. $\displaystyle |a^{2}-b^{2}|$

  4. $\displaystyle a^{2}+b^{2}$

Show answer
Correct Option: A
Explanation:

$(a-b)^2=a^2+b^2-2ab$

as a and b are of oppsite sign ab<0 and -2ab>0,it means $(a-b)^2>a^2+b^2-2|a||b|=(|a|-|b|)^2>(|a2+b^2|)>(|a^2-b^2|)$

What is the value of $((x^3-2)\div2^2)\times 4+16$?

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

  1. $x^3+14$

  2. $x^3-14$

  3. $-x^3+14$

  4. $x^3+16$

Show answer
Correct Option: A
Explanation:

$((x^3-2)\div2^2)\times 4+16$
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.
$=$ $((x^3-2)\div2^2)\times 4+16$
$=$ $\dfrac{x^3-2}{4}\times 4+16$
$=$ $x^3+14$

Simplify: $3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$

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

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

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

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

  4. $x^3+3x^2+5x-1$

Show answer
Correct Option: B
Explanation:

$3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$
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.
$3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$
$=$ $3x.x^2+3x.1-[2x.x^2+2x.x-2x.1+1]-x^2$
$=$ $3x^3+3x-2x^3-2x^2+2x-1-x^2$
$=$ $x^3-3x^2+5x-1$