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Algebraic Expressions and Identities

Dec 04, 8:55 PM

60 minutes

Dec 10, 9:00 PM

50.0 marks

MCQ

50 questions

Mastermind Institute

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Maths

Science

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Class 8 CBSE

Maths

Science

English

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Question Text

Question 1 :
State whether the statement is True or False.Expand: $(2x-\dfrac{1}{2x})^2 $ is equal to $4x^2-2+\dfrac{1}{4x^2} $.

Question 3 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate: $21\times 19 $

Question 6 :
State whether the statement is True or False.Evaluate: $(4x^2-5y^2)(4x^2+5y^2)$ is equal to $16x^4-25y^4$.

Question 10 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.

Question 11 :
If $x+\dfrac { 1 }{ x } =3$, then ${ x }^{ 4 }+\dfrac { 1 }{ x^{ 4 } }$=

Question 14 :
State whether the statement is True or False.Expand: $(a-2b)^2 $ is equal to $a^2-4ab+4b^2$.

Question 15 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.

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

Question 19 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$

Question 21 :
State whether the statement is True or False.Find the square: $(a+\dfrac{1}{5a})$, then answer is $a^2+1+\dfrac{1}{4a^2}$.

Question 22 :
Simplify the following:  $(\sqrt{3}-\sqrt{2})^{2}$ is equal to $5-2\sqrt{6}$  If true then enter $1$ and if false then enter $0$

Question 23 :
If $\displaystyle \left (x - \frac{1}{x} \right ) = 5$  find the value of $\displaystyle \left (x^4 + \frac{1}{x^4} \right )$.

Question 27 :
State whether the statement is True or False.The square of $(x+3y)$ is equal to $x^2+6xy+9y^2$.

Question 29 :
State whether the statement is True or False.Evaluate: $(2x-\dfrac{3}{5})(2x+\dfrac{3}{5})$ is equal to $4x^2-\dfrac{9}{25}$.

Question 30 :
If $\displaystyle x \neq 0$, $\displaystyle x + \dfrac{1}{2x} = p$ and $\displaystyle x - \dfrac{1}{2x} = q$; find a relation between $\displaystyle p$ and $\displaystyle q$.

Question 31 :
State whether the statement is True or False.Evaluate: $(1.6x+0.7y)(1.6x-0.7y)$ is equal to $2.56x^2-0.49y^2$.

Question 32 :
If $a-b=3$ and $ \displaystyle a^{3}-b^{3}=117 $ then $a+b$ is equal to 

Question 33 :
$(2x + 3y)^{2} = 4x^{2} + 9y^{2} + M$, find M.

Question 36 :
If $x + \displaystyle \frac{1}{x} = a+ b$ and $x - \displaystyle \frac{1}{x} = a - b$, then

Question 38 :
The product of $(2x^2 -3x + 1)$ and (x -3) is.equal to

Question 39 :
If $\displaystyle a+b=7 \ and \ ab=6 \, ,find \ a^{2}-b^{2}$

Question 41 :
State whether the statement is True or False.Evaluate: $(a+bc)(a-bc)(a^2+b^2c^2)$ is equal to $a^4-b^4c^4$.

Question 46 :
State whether the statement is True or False.$\left(3x-\dfrac{1}{2y}\right)\left(3x+\dfrac{1}{2y}\right)$ is equal to $9x^2-\dfrac{1}{4y^2}$.

Question 47 :
State whether the statement is True or False.Find the square: $(2a-\dfrac{1}{a} )$, then answer is $4a^2-4+\dfrac{1}{a^2} $.

Question 48 :
If $x+y = 9$ and $xy = 16$ , find the value of $(x^2 + y^2)$.

Question 49 :
If $\displaystyle a^{2} + b^{2} = 34$ and $\displaystyle ab = 12$; find $\displaystyle 7 \left (a - b \right )^{2} - 2\left (a + b \right )^{2}$

Question 50 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate: $103\times 97 $

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