Question Text
Question 1 :
The pair of irrational numbers whose product is rational are $\displaystyle 2\sqrt{3}-3\sqrt{2}$ and $\displaystyle 2\sqrt{3}+4\sqrt{2}$ <br/><br/>
Question 6 :
If $2^{m} + 2^{1 + m} = 24$, then what is value of $m$?
Question 9 :
The value of $\dfrac { { 2 }^{ m+3 }\times { 3 }^{ 2m-n }\times { 5 }^{ m+n+3 }\times { 6 }^{ n+1 } }{ { 6 }^{ m+1 }\times { 10 }^{ n+3 }\times { 15 }^{ m } }$ is equal to
Question 14 :
The product of a non-zero rational and an irrational number is<br>
Question 18 :
Find the value of: $\left [\dfrac {1}{5^{-2}} + \dfrac {1}{3^{-3}} + \dfrac {1}{2^{-4}}\right ]$
Question 20 :
If ${n}^{k}=64$ and $n$ and $k$ are integers, which of the following cannot be a value of $n$?
Question 22 :
If $a = \displaystyle \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $b  = \displaystyle \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, find the value $a^2+b^2-5ab$.
Question 23 :
If $\cfrac { \sqrt { 7 } -1 }{ \sqrt { 7 } +1 } -\cfrac { \sqrt { 7 } +1 }{ \sqrt { 7 } -1 } =a+b\sqrt { 7 } $, then find the values of $a$ and $b$