Tag: maths

Questions Related to maths

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 $y$

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

  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

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Correct Option: A

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

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

  1. $4 ( a d + b c )$

  2. $2 ( a d + b c )$

  3. $3 ( a d + b c )$

  4. $ ( a d + b c )$

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Correct Option: A
Explanation:
$(b-c+d+a)(d+a-b+c)+(c-d+a+b)(b+c+d-a)$

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

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

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

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

$=4ad+4bc$

$=4(ad+bc)$.

Evaluate $\sqrt {13+\sqrt {44+10^2}}$.

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

  1. $12$

  2. $5$

  3. $25$

  4. None

Show answer
Correct Option: B
Explanation:

$\sqrt {13+\sqrt {44+10^2}}\$

$=\sqrt{13+\sqrt {44+100}}\$
$=\sqrt {13+144}\$
$=\sqrt {13+12}\$
$=\sqrt {25}=5$

If $f(x)=x^2+x+5$ then find $f(1)$
maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $7$

  2. $5$

  3. $4$

  4. None of the above

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Correct Option: A
Explanation:
$f(x)=x^2+x+5$

Put $x=1$

$\Rightarrow$$f(1)=1+1+5$

$\Rightarrow$$f(1)=7$

$x^2+y^2 =100$ 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. $88$

Show answer
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:

 

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