Question 3 :
A man sold a bicycle for an amount which was greater than $400$ by half the price he bought it for, and made a profit of Rs. $300$. How much did he buy the bicycle for?

Question 4 :
The values of a so that the equation $\Vert x - 2\vert - 1\vert = a \vert x \vert$ does not contain any solution lying in the interval {2, 3} are

Question 5 :
The length of the diagonals of a rhombus are $16cm$ and $12cm.$ The length of each side of the rhombus is

Question 6 :
A parallelogram has two sides 60 m and 25 m and a diagonal 65 m long.What is the area of a parallelogram ?&#160;<br/>

Question 7 :
Let ABCD be a parallelogram such that AB = q , AB = p, and $\angle BAD $ be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by

Question 8 :
$ABCD$ is a square. A line $AX$ meets the diagonal $BD$ at $X$ and $AX=2018\ cm$ the length of $CX$ (in\ cm) is

Question 10 :
The value of $\dfrac {6}{11} \times \left [\left (\dfrac {-7}{6}\right ) - \left (\dfrac {11}{7}\right )\right ]$ is

Question 11 :
$G$ is a set of all rational numbers except $-1$ and $\ast $ is defined by $a\ast b=a+b+ab$ for all $a,b\in G$, in the group $\left( G,\ast \right) $, the solution of ${ 2 }^{ -1 }\ast x\ast { 3 }^{ -1 }=5$ is

Question 13 :
What is the central angle of the sector (in the above pie chart) representing hormones enzymes and other proteins.

Question 14 :
The diagram used to estimate mode of continuous frequency distribution graphically is _____

Question 15 :
Two cards are drawn simultaneously from a well shuffled pack of $52$ cards. The expected number of aces is?

Question 16 :
The table shows the number of cups of four different beverages sold by a coffee shop. What is the angle of sector representing tea in a pie chart?<br><table class="wysiwyg-table"><tbody><tr><td>Beverage<br></td><td>Number of cups<br></td></tr><tr><td>Coffee</td><td>60<br></td></tr><tr><td>Tea<br></td><td>75<br></td></tr><tr><td>Hot chocolate<br></td><td>25<br></td></tr><tr><td>Milk<br></td><td>40<br></td></tr></tbody></table><br>

Question 19 :
Find the number of digits in the square root of each of the following numbers (without any calculation)<br>$64$<br>$144$<br>$4489$<br>$27225$<br>$390625$

Question 21 :
State true or falseSquare numbers can only have even number of zeros at the end.

Question 23 :
If $3a = 4b = 6c$ and $a + b + c = 27 \displaystyle \sqrt{29}$,&#160;then&#160;$\displaystyle \sqrt{a^{2}+b^{2}+c^{2}}$ is&#160;

Question 25 :
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 26 :
A television set was bought for Rs. $10,500$ and sold at Rs. $9500$. Find the loss.<br/>

Question 27 :
A rectangular plot $85\ m$ long and $60\ m$ broad is to be covered with grass leaving $5\ m$ all around. Find the area to be laid with grass.

Question 28 :
The line $x+y = p$ meets the x-and y-axes at $A$ and $B$, respectively. A triangle $\triangle APQ$ is inscribed in the $\triangle OAB$, $O$ being the origin, with right angle at $Q$. $P$ and $Q$ lie, respectively, on $OB$ and $AB$. If the area of the $\triangle APQ$ is $\dfrac38^{th}$ of the area of the $\triangle OAB$, then $\dfrac{AQ}{BQ}$ is equal to

Question 29 :
Divide $\displaystyle ( 36{ x }^{ 2 }-4 )$ by $\left( 6x-2 \right)&#160;$

Question 30 :
Divide $\displaystyle \left( 9{ x }^{ 2 }-24x+16 \right)&#160;$ by&#160;$\displaystyle \left( 3x-4 \right)&#160;$

Question 31 :
If $n$ and $k$ are positive integers and $8^n=2^k$,&#160;what is the value of $\dfrac{n}{k}$?

Question 33 :
If $5^{k^2}(25^{2k})(625) = 25\sqrt{5}$ and $k &lt; -1$, find the value of $k$.