Question 1 :
Coordinates of $P$ and $Q$ are $(4, - 3)$ and $(- 1, 7)$. The abscissa of a point $R$ on the line segment $PQ$, such that $\displaystyle \frac { PR }{ PQ } =\frac { 3 }{ 5 } $ is :
Question 2 :
A line has the equation $x =-2y +z$. If $(3, 2)$ is a point on the line, what is $z$?
Question 4 :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. Nuri's age is _____
Question 5 :
Express $y$ in terms of $x$, given $-2x + y - 7 = 0$. Check whether the point $(-3, -2)$ is solution of this equation.<br/>
Question 6 :
In a examination, a student attempted 15 questions correctly and secured 40 marks. If there were two types of questions i.e. of 2 marks and 4 marks, how many questions of 2 marks did he attempt correctly ?
Question 7 :
The ratio of two numbers is $5:4$ and their sum is $54$. The greater of the two numbers is 
Question 8 :
If the numerator of a fraction is increased by $2$ and the denominator is decreased by $4$ then it becomes $2$. If the numerator is decreased by $1$ and the denominator is increased by $2$, then it becomes $\dfrac13$. Find the sum of the numerator and denominator of the fraction.
Question 15 :
Find the value of $q$, if $\sqrt{36x^4+24x^3+16x^2+qx+1}$ is a perfect square.<br/>
Question 16 :
Suppose ${ 4 }^{ a }=5,{ 5 }^{ b }=6,{ 6 }^{ c }=7,{ 7 }^{ d }=8$, then the value of $abcd$ is ?
Question 19 :
<br/>Two supplementary angles are in the ratio $3:2$. The smaller angle measures?
Question 20 :
In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays<br>Then
Question 21 :
In a triangle ABC. The relation which is true for its sides is-
Question 22 :
The area of the triangle formed by the lines $x ^ { 2 } - 3 x y + y ^ { 2 } = 0$ and $x + y + 1 = 0$ is square units. is
Question 23 :
ABC is a right angled at B with $BC = 6$ and $AC = 10\ cm$. Also $\triangle ABC$ and $\triangle BCD$ are on the same base $BC$. Find $ar (\triangle BCD)$.
Question 24 :
Assertion: The area of a parallelogram and a rectangle having a common base and between same parallels are equal.
Reason: Another name of a rectangle is a parallelogram.
Question 25 :
For $3$ parallelograms, $A$, $B$ and $C$, parallelograms $A$ and $B$ shares same base $l$ and lie along same parallels $l$ and $m$. Similarly the parallelograms $B$ and $C$ shares the same base $m$ and between the same parallels. The area of all three parallelograms will be equal.
Question 27 :
If a circle passes through the points of intersection of the lines $x-2y+3=0$ and$\lambda x-y+1=0$ with the axes of reference then the value of$\lambda $ is
Question 28 :
If the lines ${ a }_{ 1 }x+{ b }_{ 1 }y+{ c }_{ 1 }=0$ and ${ a }_{ 2 }x+{ b }_{ 2 }y+{ c }_{ 2 }=0$ cuts the coordinate axes in concyclic points, then
Question 29 :
I. If the points $(\mathrm{a},0)$ , $(\mathrm{b},0)$ , $(0,\mathrm{c})$ , $(0,\mathrm{d})$ are concyclic, then $ab=cd$<br/>II. If the points $(1,-6) , (5,2), (7,0), (-1, \mathrm{k})$ are concyclic then $\mathrm{k}=-3$.<br/>
Question 30 :
If two lines $\displaystyle \displaystyle a_{1}x+b_{1}y+c_{1}=0$ and $\displaystyle a_{2}x+b_{2}y+c_{2}=0$ cut the coordinate axes in concyclic points,then <br>
Question 31 :
A bug travels all the way around a circular path in $30$ minutes travelling at $62.84$ inches per hour. What is the radius of the circular path?
Question 32 : <p>Suppose $2016$ points of the circumference of a circle points are coloured red and the remaining points are coloured blue. Find the minimum possible value of a natural number $n$, for which there exists a regular $n$- sided polygon whose all vertices are blue.</p>
Question 33 :
The construction of $\Delta LMN$ when $MN=6$ $cm$ and $m\angle M=45^\circ$ is not possible when difference between $LM$ and $LN$ is equal to:
Question 34 : There are $40$ students in a class and their results is presented as below :<table class="wysiwyg-table"><tbody><tr><td>Result (Pass/Fail)</td><td>Pass</td><td>Fail</td></tr><tr><td>Number of Students</td><td>$30$</td><td>$10$</td></tr></tbody></table><p></p> If a student chosen at random out of the class, find the probability that the student has passed the examination<br/>
Question 35 :
If a coin is tossed, then the probability that a head turns up is ______.
Question 36 :
A coin is tossed five times, find the probability of getting no head.
Question 38 :
If a coin is tossed twice, find the probability of getting at least one head.
Question 41 :
If the height and radius of a cone are doubled, then the volume of the cone becomes
Question 42 :
The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is 1628 cm$\displaystyle ^{2}$ find the circumference of the base and the volume of the solid
Question 43 :
A rectangular piece of paper is 100 cm x 44 cm A cylinder is formed by rolling the paper along its length then the volume of the cylinder so formed is
Question 44 :
A circular well with a diameter of $2$ metres, is dug to a depth of $14$ metres. What is the volume of the earth dug out?
Question 45 :
The radii of two cylinders are in the ratio $2 : 3$ and their heights are in the ratio $5 : 3$, then the ratio of their volumes is _______.
Question 46 :
A right triangle with its sides $9\space cm, 12\space cm$ and $15\space cm$ is revolved about the side $12\space cm$. Find the volume of the solid so formed.
Question 47 :
The radius of a solid sphere is 'r' cm. It isbisected, then the total surface area of the twopieces obtained is
Question 48 :
Radius and height of a right circular cone and that of a right circular cylinder are respectively, equal. If the volume of the cylinder is $120{cm}^{3}$, then the volume of the cone is equal to
Question 49 :
If two cones have their heights in the ratio 1 : 3 and radii 3 :1 then the ratio of their volumes is
Question 50 :
The radius of a spherical balloon increases from $7cm$ to $14cm$ as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Question 51 :
If a solid right circular cylinder, made of iron is heated to increase its radius and height by $1 \%$ each, then by how much percent is the volume of the solid increased?
Question 52 :
If a solid right circular cylinder  made of iron is heated to  increase its radius and height  by $1 \%$. each, then the volume  of the solid is increased by<br/>
