Question 2 :
The real number $(\sqrt [3]{\sqrt {75} - \sqrt {12}})^{-2}$ when expressed in the simplest form is equal to

Question 3 :
If $a+b+c=6$ and $ ab+bc+ca = 11 $<br/>Find $\left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } \right)$ ?<br/>

Question 4 :
Use Pythagoras theorem to check which of following triplets would make a right triangle.<br/>

Question 5 :
The square root of sum of the digits in the square of $121$ is

Question 7 :
State true or false:The root of the equation $\dfrac{y}{2}+6 = y$ is $\dfrac{1}{\sqrt{2}}$.<br/>

Question 8 :
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 $\displaystyle 1\frac{1}{2} : 2\frac{1}{2}$.&#160;The larger of the numbers is

Question 9 :
A Gym sells two types of memberships. One packages costs $ $325$ for one year of membership with an unlimited number of visits. The second package has a $ $125$ enrolment fee, includes five free visits, and costs an additional $ $8$ per visit after first five. How many visits would a person need to use for each type of membership to cost the same amount over a one-year period?

Question 10 :
$Rs.\,3900.00$ has been distributed among the students (girls/boys) in a class in such a way that the girl student should get $Rs.\,80.00$ and boy should get $Rs.\,30.00$. The number of girl students in the class will be

Question 13 :
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 14 :
By what least number must 3600 be divided to make it a perfect cube?

Question 15 :
Find the value of cube root of the number $2486$. (Round off your number to the nearest whole number)<br/>

Question 18 :
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 19 :
Evaluate: $\displaystyle&#160;\left( 4{ x }^{ 8 }-{ 5x }^{ 6 }+{ 6x }^{ 4 } \right) \div { x }^{ 4 }$

Question 20 :
Find the value of $\displaystyle&#160;\left( { 3x }^{ 3 }+{ 2x }^{ 2 }+x \right) \div 4x$

Question 22 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to

Question 23 :
A sphere of diameter $2 a$ is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is $\displaystyle \frac{8a}{3}$. If the sphere is completely submerged, by how much will the level of water rise ?

Question 24 :
If circle R, of area 4 square inches, radius of circle S is twice of circle R, then the area&#160;of circle S, in square inches, is

Question 25 :
Each side of a square is 5 cm. The perimeterof the equilateral triangle formed on the diagonalof the square would be-

Question 26 :
If the perimeter of an isosceles triangle is $36$ and the altitude to the base is $6$, find the length of the&#160;altitude to one of the legs.

Question 27 :
If the side of a rhombus is $20$ meters and its shorter diagonal is three fourth of its longer diagonal, then the area of the rhombus must be

Question 28 :
If solid cylinder has total surface area&#160;$\displaystyle 1000{ cm }^{ 2 }$ and its curved surface area is&#160;$\displaystyle \frac { 1 }{ 4 }&#160;$ of $d$. What is the volume of cylinder?