Question 2 :
Find the values of $a$ and $b$ if the following polynomial is perfect square: $x^4-4x^3+10x^2-ax+b$
Question 4 :
The last digit of the value of the number $2003^{2002} + 2001^{2002}$ is ___.
Question 5 :
The product of $\sqrt [ 3 ]{ 2 } $ and $\sqrt { 2 } $ is:
Question 7 :
If $\displaystyle a=\left ( \sqrt{5}+\sqrt{4} \right )^{-3}\: \: and\: \: b=\left ( \sqrt{5}-\sqrt{4} \right )^{-3}$, then the value of $\displaystyle \left ( a+1 \right )^{-1}+\left ( b+1 \right )^{-1}$ is
Question 9 :
For any two non-zero rational numbers $x$ and $y, x^4 \div y^4$ is equal to
Question 10 :
Simplify the square root of the polynomial using factorisation method: $\dfrac{a^3-b^3}{a-b}$<br/>
Question 11 :
$\frac { \sqrt { 5 + 12 i } + \sqrt { 5 - 12 i } } { \sqrt { 5 + 12 i } - \sqrt { 5 - 12 i } } =$
Question 12 :
Find the values of $a$ and $b$ if the following polynomial is perfect square: $4x^4-12x^3+37x^2+ax+b$
Question 13 :
The number of real solutions of the equation (5 + 2$\sqrt6)$ <br> $^{x^2 - 3}$ +(5 - 2$\sqrt6)$ <br> $^{x^2 - 3}$ = 10 is
Question 21 :
Determine the square root of the polynomial using factorisation method: $\sqrt{\dfrac{81(x+y)^2(x-y)^8}{9(x-y)^4}}$ = ?<br/>
Question 23 :
If $a^{m} . a^{n} = a^{mn}$, then $m(n - 2) + n(m - 2)$ is<br>
Question 24 :
What is the value of (X) in the following equation?<br>$x^{0.4}\div 16=32\div x^{2.6}$.<br>
Question 32 :
Which of the following values are equal?<br>(P) $1^{4}$ (Q) $4^{\circ}$ (R) $0^{4}$ (S) $4^{1}$.
Question 33 :
The product of a non-zero rational and an irrational number is<br>
Question 34 :
If $x$ $=$ $5 + 2$ $\sqrt{6}$, find the value of $\sqrt{x} + \displaystyle \frac{1}{\sqrt{x}}$<br/>
Question 35 :
Square root of $\frac { 1 }{ xyz } \left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) +2\left( \frac { 1 }{ x } +\frac { 1 }{ y } +\frac { 1 }{ z } \right) is$
Question 38 :
Simplicity <br>$\left[ \left\{ \left( 625 \right) ^{ -\dfrac { 1 }{ 2 } } \right\} ^{ -\dfrac { 1 }{ 4 } } \right] $
Question 39 :
If ${n}^{k}=64$ and $n$ and $k$ are integers, which of the following cannot be a value of $n$?
Question 40 :
Evaluate: $\displaystyle \left [ \sqrt[3]{\sqrt[6]{5^{9}}} \right ]^{4}\left [ \sqrt[6]{\sqrt[3]{5^{9}}} \right ]^{4}$
Question 41 :
State whether True or False: $\displaystyle \frac{\sqrt{3}+1}{\sqrt{3}-1} = $ <br> $\displaystyle \sqrt{5}+\sqrt{2}$<br/>
Question 42 :
The value of $\frac {1}{\sqrt 3+\sqrt 2-1}$ on simplifying upto 3 decimal places, given that $\sqrt 2=1.4142$ and $\sqrt 6=2.4495$, is
Question 43 :
Simplify and express the result in its simplest form: $\sqrt [ 3 ]{ 4 } \times \sqrt [ 3 ]{ 22 } $
Question 47 :
State whether true or false:Given that $x, y$ and $z$ are integers and $10^x = (4^y) (5^z)$ then, $x$ is even.
Question 48 :
State whether the folloiwng statement is true (T) or false (F):<br>$x^m + x^m = x^{2m}$ where $x$ is a non-zero rational number and $m$ is a positive integer. <br><br>