Question 1 :
Two numbers are in the ratio $\displaystyle 1\frac {1}{2} : 2\frac{2}{3}$.When each one of these is increased by $15$, their ratio becomes $\displaystyle 1\frac{1}{2} : 2\frac{1}{2}$. The larger of the numbers is

Question 2 :
If $\left| x+4 \right| +\left| x-4 \right| =2\left| x \right| $ and $\left| x+1 \right| +\left| 5-x \right| =6$, then x belongs to:

Question 3 :
Sameera covers a distance of $85.075$ km. She travelled $32.125$ km by bus, $45.5$ km by train and rest by rickshaw. How much distance did she travel by rickshaw?

Question 4 :
A solid cylinder of iron, the radius of whose base is $2$ cm and height $9$ cm, is melted and turned into sphere. The radius of the sphere so formed is  

Question 5 :
If one side of rhombus has end points $(4, 5)$ and $(1, 1)$ then the maximum area of the rhombus is:

Question 6 :
The area of a parallelogram formed by the lines $ax \pm by \pm c= 0$ is

Question 7 :
If $5^{k^2}(25^{2k})(625) = 25\sqrt{5}$ and $k < -1$, find the value of $k$.

Question 9 :
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 10 :
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 12 :
Consider a three-digit number with the following properties.<br>I. If its digits in units place and tens place are interchanged, the number increases by $36$;<br>II. If its digits in units place and hundreds place are interchanged, the number decreases by $198$.<br>Now suppose that the digits in tens place and hundreds place are interchanged. Then the number.<br>

Question 14 :
&#160; &#160; &#160; $\bigcirc \ \ \Diamond$ <br> $\times$ &#160;&#160;$\Box\ \ \ &#160;\Diamond$__________&#160; &#160; $ &#160; \triangle\ &#160;\Box\ \Diamond$&#160; &#160; &#160;<br/>In the multiplication above, each symbol represents a different unknown digit, and $\bigcirc&#160; \times&#160;\Box \times&#160;\Diamond = 36$.&#160;What is the three-digit integer&#160;$\bigcirc &#160;\Box &#160;\Diamond$?

Question 15 :
Consider the number $N=8\ 7\ a\ 2\ 7\ 9\ 3\ 1\ b$, where $b$ is a digit at unit's place and $a$ is a digit at ten lakh's place. Answer the following questions.&#160;<br/>The least value of $a$ for which $N$ is divisible by $12$ is

Question 16 :
The number of Four digit number formed by using the digits0,2,4,5and which are not divisible by 5,is

Question 18 :
Divide:$\displaystyle\left( -16{ x }^{ 6 }-24{ x }^{ 4 } \right)$ by$\displaystyle\left( -{ 8x }^{ 3 } \right)$

Question 19 :
Simplify: $\displaystyle&#160;\left( { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } \right) \div { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }$

Question 20 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to