Test Details

Expansion Formulae

Feb 10, 7:15 PM

60 minutes

Feb 10, 10:00 PM

49.0 marks

MCQ

31 questions

vinayak sir

Hi good morning students सर्व विद्यार्थी सकाळी आठ ते अकरा या वेळेत येथे उपस्थित राहतील काही अडचणी असल्यास आपण विचारू शकता सर्व विषयाचे तास सुरू आहेत

Class Details

Mathematics

Class 8th Scolership Exam

Mathematics

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Question Text

Question 2 :
Solve: $\cfrac { { x }^{ 2 }-{ \left( y-z \right) }^{ 2 } }{ { \left( x+z \right) }^{ 2 }-{ y }^{ 2 } } +\cfrac { { y }^{ 2 }{ -\left( x-z \right) }^{ 2 } }{ { \left( x+y \right) }^{ 2 }-{ z }^{ 2 } } +\cfrac { { z }^{ 2 }{ -\left( x-y \right) }^{ 2 } }{ { \left( y+z \right) }^{ 2 }-{ x }^{ 2 } } =$

Question 7 :
If $ a^2+b^2=29 $ and $ ab=10 $, then find $ a-b $.

Question 8 :
If $x + \displaystyle \frac{1}{x} = a+ b$ and $x - \displaystyle \frac{1}{x} = a - b$, then

Question 10 :
The coefficient of $x$ in the expansion of $(x + 3)^3$ is

Question 11 :
<span>If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find </span>$a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$

Question 13 :
<b></b>If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a+b $.

Question 14 :
If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a-b $.

Question 15 :
If $\displaystyle a+b=7 \ and \ ab=6 \, ,find \ a^{2}-b^{2}$<br/>

Question 17 :
<span>Find the value of 'a' in </span>$4x^{2}\, +\, ax\, +\, 9\, =\, (2x\, -\, 3)^{2}$

Question 18 :
<span>State whether the statement is True or False.</span><div>The square of $(3x+\dfrac{2}{y} )$ is equal to $9x^2+\dfrac{12x}{y}+\dfrac{4}{y^2} $.<br/></div>

Question 19 :
<span>If $\displaystyle a \neq 0$ and $\displaystyle a - \dfrac{1}{a} = 4$, find:</span><div>$\displaystyle a^{2} + \dfrac{1}{a^{2}}$<br/></div>

Question 20 :
$\displaystyle \left ( x+4 \right )\left ( x-4 \right )\left ( x^{2}+16 \right )$ is equal to

Question 22 :
The simplified value of the experession$\displaystyle \left ( a+b-c \right )^{2}+2\left ( a+b-c \right )\left ( a-b+c \right )+\left ( a-b+c \right )^{2}$ is

Question 24 :
If the sum and difference of two numbers are 20 and 8 respectively then the difference of their squares is :

Question 25 :
$9a^4+12a^2b^2+4b^4$<br>Which of the following is equivalent to the expression shown above?<br>

Question 28 :
If $x - \dfrac{1}{x}= 2$, then the value of $x^{4} + \dfrac{1}{x^{4}}$ is<br/>

Question 29 :
If $a = \dfrac{1}{3 - 2\sqrt{2}}, b = \dfrac{1}{3 + 2\sqrt{2}}$, then the value of $a^{3} + b^{3}$ is<br/>

Question 30 :
<span>State whether the statement is True or False.</span><div>The square of $ (\dfrac{5a}{6b}+ \dfrac{6b}{5a} )$ is equal to $\dfrac{25a^2}{36b^2} -2+\dfrac{36b^2}{25a^2} $.<br/></div>

Question 31 :
The value of $\displaystyle \left ( x-y \right )^{3}+\left ( x+y \right )^{3}+3\left ( x-y \right )^{2}\left ( x+y \right )+3\left ( x+y \right )^{2}\left ( x-y \right )$ is

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