Question 1 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 2 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.
Question 3 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.
Question 4 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 5 :
The perimeter of two similar triangles $\triangle ABC$ and $\triangle DEF$ are $36$ cm and $24$ cm respectively. If $DE=10 $ cm, then $AB$ is :
Question 6 :
State true or false:<br/>Triangle $ABC$ is similar to triangle $PQR$. If $AD$ and $PM$ are altitudes of the two triangles, then<br/>$\displaystyle \dfrac{AB}{PQ}=\dfrac{AD}{PM}.$<br/>
Question 7 :
In $\Delta ABC$, $D$ is a point on $BC$ such that $3BD = BC$. If each side of the triangle is $12 cm$, then $AD$ equals:
Question 8 :
If in$\displaystyle \triangle ABC$ and$\displaystyle\triangle DEF$,$\displaystyle \frac{AB}{DE}=\frac{BC}{FD}$ then they will be similar if
Question 9 :
Two isosceles triangles have equal vertical angles and their areas are in the ratio $9:16$. Find the ratio of their corresponding heights.
Question 10 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 11 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 12 :
We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .
Question 15 :
State whether the given statement is True or False :If $p,  q $ are prime positive integers, then $\sqrt { p } +\sqrt { q } $ is an irrational number.<br/>
Question 18 :
What must be subtracted from $4x^4 - 2x^3 - 6x^2 + x - 5$, so that the result is exactly divisible by $2x^2 + x - 1$?
Question 19 :
The remainder when$4{a^3} - 12{a^2} + 14a - 3$ is divided by $2a-1$, is
Question 20 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$
Question 21 :
If one factor of the polynomial $x ^ { 3 } + 4 x ^ { 2 } - 3 x - 18$ is $x + 3,$ then the other factor is
Question 23 :
If $\alpha, \beta$ be the zeros of the quadratic polynomial $2x^2+5x+1$, then the value of $\alpha+\beta+\alpha \beta=$<br>
Question 24 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is
Question 25 :
The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two. 
Question 26 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 27 :
Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is
Question 30 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: $8x + 5y = 9$, $3x + 2y = 4$
Question 32 :
Solve the following pair of simultaneous equations:$\displaystyle\, y\, -\, \frac{3}{x}\, =\, 8\, ;\, 2y\, +\, \frac{7}{x}\, =\, 3$
Question 33 :
Find the value of x and y using elimination method:<br/>$\dfrac{-1}{x} + \dfrac{2}{y} = 0$ and $\dfrac{x}{2}+  \dfrac{y}{3} = 1$<br/>
Question 35 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 36 :
The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :
Question 38 :
A(2,6) and B(1,7) are two vertices of a triangle ABC and the centroid is (5,7) The coordinates of C are
Question 40 :
State whether the following statements are true or false . Justify your answer.<br>Point $ A(-6 , 10) , B(-4 , 6) $ and $ C(3 , -8) $ are collinear such that $ AB = \dfrac{2}{9} AC $ .
Question 41 :
If the line joining A(2, 3) and B(-5, 7) is cut by X - axis at P, then find AP : PB.
Question 42 :
The line segment joining the points $(3, -4)$ and $(1, 2) $ is trisected at the points P and Q. If the and co-ordinates of P and Q are $(p, -2)$ and $(\frac{5}{3}, q)$ respectively, find the value of p and q.
Question 43 :
If X-axis divides the line joining $(3,-4)$ and $(5,6)$ in the ratio $a:b $, then what is the value of $\dfrac{a}{b}$?
Question 44 : <p>x-axis divides line segment joining points (2, -3) and (5,6) in the ratio</p>
Question 45 :
The straight line $3x+y=9$ divides the line segment joining the points $(1,\,3)$ and $(2,\,7)$ in the ratio
Question 46 :
The mid-point of line segment joining thepoints (3, 0) and (-1, 4) is :
Question 47 :
Select the correct option.<br>The value of $p$, for which the points $A(3,1) , B (5, p)$ and $C (7, -5)$ are collinear, is
Question 48 :
The coordinates of one end of a diameter of a circle are $(5, -7)$. If the coordinates of the centre be $(7, 3)$, the co ordinates of the other end of the diameter are
Question 49 :
The ratio by which the line $2x + 5y - 7 = 0$ divides the straight line joining the points $(-4, 7) $ and $(6, -5)$ is
Question 50 :
The point which is equi-distant from the points $(0,0),(0,8) and (4,6)$ is 
Question 51 :
Point $P$ divide a line segment $AB$ in the ratio $5:6$ where $A(0,0)$ and $B(11,0)$. Find the coordinate of the point $P$:
Question 52 :
If P(x, y) is any point on the line joining thepoints (a, 0) and (0, b) then the value of$\displaystyle \frac{x}{a} + \frac{y}{b}$
Question 53 :
If $P(2, 2), Q(-2, 4)$ and $R(3, 4)$ are the vertices of $\Delta PQR$ then the equation of the median through vertex R is _______.
Question 54 :
If $\displaystyle 5\tan \theta =4$, then find the value of $\displaystyle \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$. 
Question 55 :
The value of $[\dfrac{\tan 30^{o}.\sin 60^{o}.\csc 30^{o}}{\sec 0^{o}.\cot 60^{o}.\cos 30^{o}}]^{4}$ is equal to
Question 56 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 61 :
The value of $\displaystyle { \left( \frac { \sin { { 47 }^{ o } }  }{ \cos { { 43 }^{ o } }  }  \right)  }^{ 2 }+{ \left( \frac { \cos { { 43 }^{ o } }  }{ \sin { { 47 }^{ o } }  }  \right)  }^{ 2 }-4{ \cos }^{ 2 }{ 45 }^{ o }$ is :
Question 62 :
If $\cos\theta = \dfrac{14}{4}$ and $\sin\theta$ $=$ $\dfrac{8}{3}$, what is the value of $\cot\theta$?<br/>
Question 63 :
If the number of units in the circumference of a circle is same is same as the number of units in the area then the radius of the circle will be
Question 64 :
The ratio of areas of square and circle is givenn : 1 where n is a natural number. If the ratio of side of square and radius of circle is k :1, where k is a natural number, then n will be multiple of
Question 65 :
The area of two circles are in the ratio $25 : 36$. Then the ratio of their circumference is _________.
Question 66 :
A wire of length $36$ cm is bent in the form of a semicircle. What is the radius of the semicircle?
Question 67 :
The area of a sector formed by two mutually perpendicular radii in $\odot \left( 0,5cm \right) $ is ............... ${cm}^{2}$.
Question 68 :
The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long is
Question 69 :
If the area of a circle is $346.5 \displaystyle cm^{2}$. Its circumference is
Question 70 :
If an arc of a circle subtends an angle of<b></b>$ \displaystyle x^{\circ} $ at the centre then the length of the arc will be equal to - (Given radius of the circle=r)
Question 71 :
The area of a circle is 616 cm$^2$. Find its circumference.
Question 72 :
A man runs with the speed of $15.84\ km/hr$. He completes $12$ rounds of a circular ground in one hour, find the area of the ground in $sq. m$.
Question 73 :
The radii of two circles are in the ratio $3 : 8$. If the difference between their areas is$2695\pi \: cm^{2}$ ,find the area of the smaller circle.
Question 74 :
If a sector of a circle of diameter 21 cm subtends an angle of $120^{\circ}$ at the centre, then what is its area ? 
Question 75 : <p>If the circumference of a circle is $8$ units and arc length of major sector is $5$ units then find the length of minor sector.</p>
Question 76 :
When the circumference and area of a circle are numerically equal then the diameter is numerically equal to
Question 77 :
A circular ground whose diameter is $140$meters is to be fenced by wire three times around its circumference. Find the length of wire needed.<br><br>$[$use $\displaystyle \pi = \frac {22}{7}$ <br> $]$
Question 78 :
A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.
Question 79 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is
Question 80 :
A fair dice has faces numbered $0, 1, 7, 3, 5$ and $9$. If it is thrown, the probability of getting an odd number is
Question 81 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.
Question 82 :
One hundred identical coins each with probability p as showing up heads are tossed. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is
Question 84 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:
Question 85 :
The probability expressed as a percentage of a particular occurrence can never be
Question 86 :
Vineeta said that probability of impossible events is $1$. Dhanalakshmi said that probability of sure events is $0$ and Sireesha said that the probability of any event lies between $0$ and $1$.<br>in the above, with whom will you agree?
Question 87 :
$(a)$ The probability that it will rain tomorrow is $0.85$. What is the probability that it will not rain tomorrow?<br><br>$(b)$ If the probability of winning a game is $0.6$, what is the probability of losing it?
Question 88 :
Odds $8$ to $5$ against a person who is $40$yr old living till he is $70$ and $4$ to $3$ against another person now $50$ till he will be living $80$. Probability that one of them will be alive next $30$yr.
Question 89 :
A coin is tossed $100$ times with following frequency:<br/>Head: $25$, Tail: $75$<br/>Find the probability of not getting a head.
Question 90 :
A missile target may be at a point P with probability$\displaystyle \frac{9}{10}$ or at a point Q with probability$\displaystyle \frac{1}{10}$ we have 20 shells each of which can be fired either at point P or Q Each shell may hit the target independently of the other shoot with probability$\displaystyle \frac{2}{3}$ Then number of shells must be fired at point P to hit any target with maximum probability is
Question 91 :
A die is rolled three times. The probability that the sum of three numbers obtained is $15,$ is equal to :
