Question 1 :
If $S\equiv { x }^{ 2 }+{ y }^{ 2 }+2gx+2fy+c=0$ is a given circle, then the locus of the foot of the perpendicular drawn from origin upon any chord of $S$ which subtends a right angle at the origin, is

Question 2 :
In a circle of radius $7$ cm, an arc subtends an angle of $\displaystyle 108^{\circ} $ at the centre. The area of the sector is $\displaystyle \left ( \pi =\frac{22}{7} \right )$

Question 3 :
If PQ is a chord of a circle whose centre is 0 and PR is the tangent to the circle at the point P, then $\angle POQ$ is equal to

Question 4 :
The construction of a $\Delta ABC$ in which $BC=6$ $cm$ and $\angle B=50^\circ$, is not possible when $(AB-AC)$ is equal to:

Question 5 :
The construction of $\Delta EFG$ when $FG=3$ $cm$ and m$\angle G=60^\circ$ is possible when difference of $EF$ and $EG$ is equal to:

Question 7 :
The construction of $\Delta LMN$ when $MN=7$ $cm$ and $m\angle M=45^\circ$ is not possible when difference of $LM$ and $LN$ is equal to:

Question 8 :
$PQRS$ is the smallest square whose vertices are on the respective sides of the square $ABCD$. The ratio of the areas of $\square PQRS$ to $\square ABCD$ is

Question 11 :
Find the total surface area of a hemisphere of radius $10$ cm. (Use $\pi =3.14$)

Question 12 :
There are two vessels - one is in the shape of a cylinder and the other in the shape of a right circular cone. Both the vessels have the same height and the same base radius. The cylindrical vessel and the conical vessel are filled with milk and water respectively and are both filled to half of their maximum heights. The cone is standing on its vertex. The contents of the conical vessel are emptied into the cylindrical vessel. What is the ratio of water to milk in the cylindrical vessel now -<br>

Question 13 :
A kite with $x$ cm, $x$ cm, $y$ cm and $y$ cm is inscribed in a circle. The area of the kite is

Question 14 :
ABCD is a parallelogram with AB $=$ 8.3 cm and its perimeter is 25 cm. Then BC equals

Question 15 :
In parallelogram ABCD, AB $=$ (x+8) cm and CD $=$ (3x-2) Then AB equals

Question 16 :
Assertion: Consider an event for which probability of success is 1/2.<br>Probability that in n trials,there are r success where r-4K and k is an integer is $\dfrac{1}{4}+\dfrac{1}{2^{n/2+1}}cos (\dfrac{n\pi}{4})$ Reason: $^nC_0+^nC_4+^nC_7+.......=2^{n/2} sin (\dfrac{n \pi}{4})$

Question 17 :
A die is thrown $400$ times, the frequency of the outcomes of the events are given as under.<br/><table class="wysiwyg-table"><tbody><tr><td>outcome<br/></td><td>$1$<br/></td><td>$2$<br/></td><td>$3$<br/></td><td>$4$<br/></td><td>$5$<br/></td><td>$6$<br/></td></tr><tr><td>Frequency<br/></td><td>$70$<br/></td><td>$65$<br/></td><td>$60$<br/></td><td>$75$<br/></td><td>$63$<br/></td><td>$67$<br/></td></tr></tbody></table>Find the probability of occurrence of an odd number.<br/>

Question 18 :
Mean of $50$ observations was found to be $80.4$. But later on, it was discovered that $96$ was misread as$ 69$ at one place. Find the correct mean.<br>

Question 19 :
The mean age of a combined group of men and women is $25$ years. If the mean age of the group of men is $26$ and that of the group of women is $21$, then the percentage of men and women in the group is