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Questions Related to maths

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

In the equation $4x+y=10$, if the value of $x$ ins increased by $3$, then what would be the effect on the corresponding value of $y$

  1. The value of $y$ is decreased by $12$
  2. The value of $y$ is decreased by $2$
  3. The value of $y$ is increased by $3$
  4. The value of $y$ will be $3$ times as large
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given 4x + y = 10, if x increases by 3, the new equation is 4(x + 3) + y_new = 10. This expands to 4x + 12 + y_new = 10, which simplifies to y_new = 10 - 4x - 12. Since the original y = 10 - 4x, the new y is y - 12.

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

Evaluate:
$( b - c + d + a ) ( d + a - b + c ) + ( c - d + a + b ) ( b + c + d - a )$

  1. $4 ( a d + b c )$
  2. $2 ( a d + b c )$
  3. $3 ( a d + b c )$
  4. $ ( a d + b c )$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$(b-c+d+a)(d+a-b+c)+(c-d+a+b)(b+c+d-a)$

$=[(d+a)+(b-c)][(d+a)-(b-c)]+[(b+c)+(a-d)][(b+c)-(a-d)]$

$[\because (a-d)^2=(d-a)^2]$

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

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

$=4ad+4bc$

$=4(ad+bc)$.
Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

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

  1. $a+b=c$
  2. $b+c=a$
  3. $c+a=b$
  4. $a=b=c$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given,

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

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

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

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

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

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

$\therefore a=b=c$
Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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)} $

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
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} $

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

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

  1. $92$
  2. $78$
  3. $96$
  4. $88$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $88$.