Question 1 :
State whether the statement is True or False.$\left(3x-\dfrac{1}{2y}\right)\left(3x+\dfrac{1}{2y}\right)$ is equal to $9x^2-\dfrac{1}{4y^2}$.<br/>
Question 2 :
State whether the statement is True or False.Expand: $(2a+b)^2 $ is equal to $4a^2+4ab+b^2$.<br/>
Question 3 :
State whether the statement is True or False.Expand: $(2x-\dfrac{1}{2x})^2 $ is equal to $4x^2-2+\dfrac{1}{4x^2} $.<br/>
Question 4 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br>$21\times 19 $
Question 5 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.<br/>
Question 6 :
State whether the statement is True or False.Expand: $(a-2b)^2 $ is equal to $a^2-4ab+4b^2$.<br/>
Question 7 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br/>$103\times 97 $
Question 8 :
State whether the statement is True or False.Evaluate: $(a+bc)(a-bc)(a^2+b^2c^2)$ is equal to $a^4-b^4c^4$.<br/>
Question 9 :
State whether the statement is True or False.Evaluate: $(1.6x+0.7y)(1.6x-0.7y)$ is equal to $2.56x^2-0.49y^2$.<br/>
Question 10 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 11 :
State whether the statement is True or False.Find the square: $(a+\dfrac{1}{5a})$, then answer is $a^2+1+\dfrac{1}{4a^2}$.<br/>
Question 13 :
State whether the statement is True or False.The square of $(x+3y)$ is equal to $x^2+6xy+9y^2$.<br/>
Question 15 :
State whether the statement is True or False.Evaluate: $(4x^2-5y^2)(4x^2+5y^2)$ is equal to $16x^4-25y^4$.<br/>
Question 16 :
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} $.<br/>
Question 17 :
State whether the statement is True or False.Evaluate: $(2x-\dfrac{3}{5})(2x+\dfrac{3}{5})$ is equal to $4x^2-\dfrac{9}{25}$.<br/>
Question 20 :
If $\displaystyle a+b=7 \ and \ ab=6 \, ,find \ a^{2}-b^{2}$<br/>
Question 21 :
$\displaystyle \left ( x-y-z \right )^{2}-\left ( x+y+z \right )^{2}$ is equal to
Question 25 :
If $x + \displaystyle \frac{1}{x} = a+ b$ and $x - \displaystyle \frac{1}{x} = a - b$, then
Question 29 :
If $x+\dfrac { 1 }{ x } =3$, then ${ x }^{ 4 }+\dfrac { 1 }{ x^{ 4 } }$=
Question 30 :
If $x+y = 9$ and $xy = 16$ , find the value of $(x^2 + y^2)$.
Question 34 :
If $\displaystyle a^{2} + b^{2} = 34$ and $\displaystyle ab = 12$; find $\displaystyle 7 \left (a - b \right )^{2} - 2\left (a + b \right )^{2}$<br/>
Question 36 :
If $\displaystyle \left (x - \frac{1}{x} \right ) = 5$  find the value of $\displaystyle \left (x^4 + \frac{1}{x^4} \right )$.
Question 39 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$
Question 46 :
Simplify the following: <br/>$(\sqrt{3}-\sqrt{2})^{2}$ is equal to $5-2\sqrt{6}$<br/> If true then enter $1$ and if false then enter $0$<br/>
Question 47 :
The product of $(2x^2 -3x + 1)$ and (x -3) is.equal to
Question 48 :
If $a-b=3$ and $ \displaystyle a^{3}-b^{3}=117 $ then $a+b$ is equal to 
Question 50 :
$(2x + 3y)^{2} = 4x^{2} + 9y^{2} + M$, find M.<br/>
Question 52 :
Add the following :<br>i) $5y^3 , 26y^3, 10y^3, -3y^3$<br>ii) $3x^2, -10x^2, 4x^2$<br>iii) $4x^2y, -3xy^2, -5xy^2, 5x^2y$
Question 53 :
The number to be added to make $x^2-\frac {1}{2}$ x a perfect square is
Question 54 :
A two digit number is such that the product of its digit is $18$. When $63$ is subtracted from the number, the digits interchange their places. Find the number.
Question 55 :
What is the missing term in the following product<br>$\displaystyle \left ( 2a^{3}-3 \right )\left ( 5a^{3}-2 \right )=10a^{6}+$_____+6<br>
Question 56 :
Find the product :$\displaystyle \left ( a^{2}+b^{2} \right )\left ( a^{4}+b^{4} \right )\left ( a+b \right )\left ( a-b \right )$
Question 57 :
Which of the following expressions are exactly equal in value?<br>$1. {(3x-y)}^{2}-({5x}^{2}-2xy)$<br>$2. {(2x-y)}^{2}$<br>$3. {(2x+y)}^{2}-2xy$<br>$4. {(2x+3y)}^{2}-8y(2x+y)$<br>
Question 58 :
Find the difference between the values of $5m^3-4m$ and $2m^2+9$, when $m=-2$.
Question 70 :
If $3x-7y = 10$ and $xy = -1$, then the value of $9x^2\, +\, 49y^2$ is equal to
Question 71 :
The value of $\displaystyle \left ( 5x-3y \right )^{2}-\left ( 5x+3y \right )^{2}$, when $\displaystyle x=-1$ and $y=\sqrt{\cfrac{1}{25}}$ is
Question 76 :
If $2x - \dfrac{1}{2x} = 3$, find the value of $16x^4 + \dfrac{1}{16x^4} $
Question 77 :
If $\left(y + \dfrac{1}{y}\right) = 12$, then $\left(y^3 + \dfrac{1}{y^3}\right)$ is equal to:-
Question 79 :
If $\displaystyle P=3x-4y-8z,\:Q=-10y+7x+11z$ and $\displaystyle R=19z-6y+4x$, then $P - Q + R$ is equal to
Question 89 :
If $\displaystyle a + \dfrac{1}{a} = 4$ and $\displaystyle a \neq 0$, find :<br/>$\displaystyle a^{4} + \dfrac{1}{a^{4}}$
Question 90 :
If $x + \dfrac {1}{x} = 2$, what is the value of $x^{2} + \dfrac {1}{x^{2}}$?
Question 92 :
What must be added to the sum of $\displaystyle 2a^{2}-3a+7,-5a^{2}-2a-11$ and $\displaystyle 3a^{2}+5a-8$ to get $0$?
Question 95 :
Given that $a(a + b) =36$ and $b(a +b) = 64$, where $a$ and $b$ are positive, $(a -b)$ equals:
Question 98 :
The value of $0.645 \times 0.645 + 2 \times 0.645 \times 0.355 + 0.355 \times 0.355$ is
Question 100 :
How many pairs of natural numbers are there so that difference of the square of the first tois 60 ?<br>(Note : If (a,b) is a pair satisfying , we will not consider (b,a) as a pair)
Question 101 :
If $x+y=a $ and $xy=b$, then the value of $\displaystyle \frac{1}{x^{3}}+\frac{1}{y^{3}} $ is
Question 102 :
Given the polynomial $a_{0}x^{n} + a_{1}x^{n - 1} + ... + a_{n - 1}x + a_{n}$, where $n$ is a positive integer or zero, and $a_{0}$ is a positive integer. The remaining $a's$ are integers or zero. Set$h = n + a_{0} + |a_{1}| + |a_{2}| + .... + |a_{n}|$. The number of polynomials with $h = 3$ is
Question 106 :
Two numbers are such that their sum multiplied by the sum of their squares is $5500$ and their difference multiplied by the difference of the squares is $352$. Then the numbers are ?<br/>
Question 107 :
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
Question 110 :
If $\displaystyle 27={ a }^{ 3 }$, find the value of $a$.
Question 113 :
Find the cube root of each of the following numbers by prime factorisation method 512
Question 116 :
Evaluate: $\sqrt [ 3 ]{ \cfrac { 216 }{ 2197 }  } $<br/>
Question 117 :
Find the cube root of the following number by prime factorization method:$27000$
Question 118 :
Find the cube root of the following number by prime factorization method: $15625$
Question 120 :
Find the cube root of the following number by prime factorization method: $175616$
Question 121 :
Find the cube root of the following number by prime factorization method: $46656$
Question 122 :
Find the cube root of the following number by prime factorization method: $110592$
Question 129 :
Find the cube root of the following number by prime factorization method: $91125$
Question 131 :
If the cube root of a number , which is $8$ more than a number $n$ equals $-0.5$, find the value of $n$.
Question 132 :
If the square root of the cube root of $x$ is $3$, find the value of $x$.
Question 134 :
The number of zeros in the cube root of $1000$ is
Question 142 :
The value of $3\displaystyle \sqrt[3]{2} \times\, 7\displaystyle \sqrt[3]{6}\,\times\, 5\displaystyle \sqrt[3]{18}$ is
Question 146 :
The number whose cube and cube root both are equal is ..............
Question 148 :
The digit at units place of the cube root of $2197$is
Question 151 :
$\dfrac { 625 } { x } = \dfrac { x } { 1156 }$ then what will be the value of $x$
Question 152 :
Evaluate the cube root of : $\displaystyle \sqrt[3]{\left (\dfrac{125}{216} \right )}$
Question 155 :
If $x = \sqrt [3]{a + \sqrt {a^{2} - b^{3}}} + \sqrt [3]{a - \sqrt {a^{2} - b^{3}}}$ then $x^{3} + 3bx = $ ____________.
Question 159 :
What is the value cube root of ${ 4913 }$? Use estimation method to find the cube root.
Question 160 :
Find the smallest number by which $243$ must be multiplied to make it a perfect cube.<br/>
Question 161 :
From which of the following options  perfect cube cannot end with
Question 163 :
What is the value of $\displaystyle \sqrt [ 3 ]{ 125 } +\sqrt [ 3 ]{ 125 } $ ?<br/>Use estimation method to find the cube root.
Question 165 :
By what number $4320$ must be multiplied to obtain a number which is a perfect cube?
Question 167 :
The smallest number by which $392$ must be multiplied so that the product is a perfect cube, is ____________.
Question 169 :
By what least number $4320$ be multiplied to become a perfect cube?
Question 170 :
Find the smallest number by which $26244$ is divided to get the quotient as a perfect cube. 
Question 171 :
Which of the following number has same unit digit as its cube?
Question 172 :
If $\displaystyle x={ 2 }^{ 3 }\times { 4 }^{ 2 }\times { 17 }^{ 3 }$, then which number should be divided  by $x$ to get a perfect cube.
Question 173 :
Find the cube root of $13824$ by the method of prime factorization.
Question 174 :
If $\displaystyle { a }^{ 3 }={ b }^{ 21 }$, find the value of $a$.
Question 175 :
Find the value of $\displaystyle { 9 }^{ 3 }-{ 8 }^{ 3 }$
Question 176 :
What is the approximate value of the cube root of the number $12?$<br/>
Question 179 :
If $\displaystyle x={ 2 }^{ 3 }\times { 4 }^{ 2 }\times { 17 }^{ 3 }$, then which number should be divided  by $x$ to get a perfect cube.
Question 182 :
What is the smallest positive number greater than $1$ which is a cube as well as a square ?
Question 183 :
If $\displaystyle \sqrt [ 3 ]{ 675+a } =15$ ,then find the cube root of $\displaystyle \frac { a }{ 100 }. $  <br/>
Question 184 :
Find the smallest number by which $128$ must be divided, so that the quotient is a perfect cube.
Question 186 :
The number of positive integers with the property that they can be expressed as the sum of cubes of $2$ positive integers in two different way is?
Question 187 :
State whether true or false:<br/>If $x^3 = 11$, then $x=\sqrt[3] {11}$
Question 188 :
What is the smallest number by which $2560$ must be multiplied so that the product is a perfect cube?
Question 190 :
What is the value of $\displaystyle \sqrt [ 3 ]{ -8 } -\sqrt [ 3 ]{ -216 } $?
Question 191 :
Find the smallest number by which $4232$ must be multiplied to make it a perfect cube.
Question 192 :
In the five digit number $1b6a3$, a is the greatest single digit perfect cube and twice of it exceeds by $7$. Then the sum of the number and its cube root is __________.
Question 193 :
Find the smallest number by which $500$ should be multiplied to make it a perfect cube.
Question 195 :
If the cube of $n$ is $729$. Find the square root of $n$.
Question 197 :
Write true $(T)$ or false $(F)$ for the following statements:<br>If $a$ divides $b$, then $a^{3}$ divides $b^{3}$.
Question 198 :
Find the smallest number by which $256$ must be multiplied, so that the product is a perfect cube.
Question 199 :
The cube root of any multiple of $8$ is always divisible by:
Question 200 :
What is the approximate value of the cube root of the number $9?$<br/>
Question 201 :
How many consecutive odd numbers will be needed to obtain the sum of $6^3$?<br>
Question 202 :
What is the smallest number by which $3645$ be multiplied so that the product becomes a perfect cube?
Question 204 :
Find the cube root of the following number by prime factorization method: $13824$
Question 205 :
Find the smallest number by which $4232$ must be multiplied to make it a perfect cube.
Question 206 :
By what number $4320$ must be multiplied to obtain a number which is a perfect cube?
Question 207 :
Find the smallest number by which $26244$ is divided to get the quotient as a perfect cube. 
Question 208 :
Find the smallest numbers by which $11979$ must be multiplied so that the product is a perfect cube
Question 209 :
Find the value of cube root of the number $1290$. (Round off your number to the nearest whole number)<br/>
Question 210 :
Find the value of cube root of the number $6860$. (Round off your number to the nearest hundredth)<br/>
Question 212 :
Find the value of cube root of the number $45$. (Round off your number to the nearest whole number)<br/>
Question 214 :
Find the value of cube root of the number $2486$. (Round off your number to the nearest whole number)<br/>
Question 215 :
Choose the correct answer from the alternatives given.<br>If $x \, = \, 2^{\frac{1}{3}} \, + \,2^{\frac{-1}{3}}$ then the value of $2x^3 \, - \, 6x$ will be
Question 217 :
By what least number must 3600 be divided to make it a perfect cube?
Question 219 :
Find the value of cube root of the number $823$. (Round off your number to the nearest whole number)<br/>
Question 221 :
By what least number must 3600 be divided to make it a perfect cube?
