Question 2 :
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 5 :
If $\alpha$ and $\beta$ are the roots of $x^2-pX +1=0$ and $\gamma$ is a root of $X^2+pX+1=0$, then $(\alpha+\gamma)(\beta+\gamma)$ is
Question 6 :
Workout the following divisions<br/>$36(x + 4) (x^2 + 7x + 10) \div 9(x + 4)$
Question 7 :
If 2 and $-\dfrac {1}{2}$ as the sum and product of its zeros respectively then the quadratic polynomial f(x) is<br/>
Question 8 :
Find the zeros of the quadratic polynomial $f(x) = x^2-3x -28$ and verify the relationships between the zeros and the coefficients.
Question 9 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 13 :
A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.
Question 14 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{15}{1600}$
Question 15 :
Assertion: The denominator of $34.12345$ is of the form $2^n \times 5^m$, where $m, n$ are non-negative integers.
Reason: $34.12345$ is a terminating decimal fraction.
Question 16 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 17 :
Euclids division lemma, the general equation can be represented as .......
Question 18 :
The ........... when multiplied always give a new unique natural number.
Question 20 :
In a question on division if four times the divisor is added to the dividend then how will the new remainder change in comparison with the original remainder?
Question 21 :
Write whether every positive integer can be of the form $4q + 2$, where $q$ is an integer.<br/>
Question 22 :
State whether the given statement is true/false:$\sqrt{p} + \sqrt{q}$, is irrational, where <i>p,q</i> are primes.
Question 23 :
Use Euclid's division lemma to find the HCF of the following<br/>27727 and 53124
Question 25 :
Use Euclid's division lemma to find the HCF of the following<br/>8068 and 12464
Question 26 :
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.<br/>$\dfrac {29}{343}$<br/>
Question 27 :
If any positive' even integer is of the form 4q or 4q + 2, then q belongs to:<br/>
Question 28 :
Find the dividend which when a number is divided by $45$ and the quotient was $21$ and remainder is $14.$
Question 29 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 30 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 31 :
Some students are divided into two groups A & B. If $10$ students are sent from A to B, the number in each is the same. But if $20$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.<br/>
Question 32 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at
Question 34 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 35 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 36 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$
Question 37 :
Solve: $3\left ( 2x+y \right )= 7xy$ and $3\left ( x+3y \right )= 11xy$;  where, $x\neq 0, y\neq 0$
Question 38 :
Solve the following pair of equations:<br/>$\displaystyle \frac{6}{x}+\displaystyle \frac{4}{y}= 20, \displaystyle \frac{9}{x}-\displaystyle \frac{7}{y}= 10.5$
Question 39 :
Solve the set of equations: $3\left ( 2u+v \right )= 7uv$ and $3\left ( u+3v \right )= 11uv$
Question 40 :
In covering a distance of $30$ km, Abhay takes $2$ hours more than Sameer. If Abhay doubles his speed, then he would take $1$ hour less than Sameer. What is Abhay's speed? (in km/hr)
Question 41 :
Solve each of the following system of equations by elimination method. $65x-33y=97, 33x-65y=1$
Question 42 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 43 :
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 44 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 45 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 46 :
ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed in sides AC and AB. Find the ratio between the areas of $\triangle ABE$ and $\triangle ACD$.
Question 47 :
For two triangles, if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. This is called ___ similarity.   
Question 48 :
STATEMENT - 1 : If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.<br>STATEMENT - 2 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.<br>
Question 49 :
Choose and write the correct alternative.<br>Out of the following which is aPythagorean triplet ?<br>
Question 50 :
Given $\Delta ABC-\Delta PQR$. If $\dfrac{AB}{PQ}=\dfrac{1}{3}$, then find $\dfrac{ar\Delta ABC}{ar\Delta PQR'}$.
Question 52 :
The perimeter of two similar triangles is 30 cm and 20 cm. If one altitude of the former triangle is 12 cm, then length of the corresponding altitude of the latter triangle is
Question 53 :
$\Delta ABC \sim \Delta PQR$ and areas of two similar triangles are $64$sq.cm and $121$sq.cm respectively. If $QR=15$cm, then find the value of side BC.
Question 54 :
If $\triangle ABC$ is similar to $\triangle DEF$ such that $BC=3$ cm, $EF=4$ cm and area of $\triangle ABC=54\: \text{cm}^{2}.$ Find the area of $\triangle DEF.$ (in cm$^2$)<br/>
Question 56 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?
Question 57 :
If $\displaystyle x=y\sin \theta \cos \phi ,y=\gamma \sin \theta \sin \phi ,z=\gamma \cos \theta $. Eliminate  $\displaystyle \theta $ and  $\displaystyle \phi $
Question 59 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $
Question 60 :
Find the value of : $\dfrac {\cos 38^{\circ} \csc 52^{\circ}}{\tan 18^{\circ} \tan 35^{\circ} \tan 60^{\circ} \tan 72^{\circ} \tan 55^{\circ}} =$
Question 61 :
The value of$ \displaystyle \tan 1^{\circ}\tan 2^{\circ}\tan 3^{\circ}.....\tan 89^{\circ} $ is
Question 62 :
The value of$\displaystyle \frac { \cos { \left( { 90 }^{ o }-A \right) } }{ 1+\sin { \left( { 90 }^{ o }-A \right) } } +\frac { 1+\sin { \left( { 90 }^{ o }-A \right) } }{ \cos { \left( { 90 }^{ o }-A \right) } }$ is equal to :
Question 63 :
If $\cos A = 0.6$, then the value of $5 \tan A - 4 \sec A$ is equal to 
Question 65 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 66 :
The points $(-2, -1), (1, 0),(4, 3),$ and $(1, 2)$ are the vertices
Question 67 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 68 :
The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are
Question 69 :
The point which is equi-distant from the points $(0,0),(0,8) and (4,6)$ is 
Question 70 :
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 71 :
Find the coordinates of the point which divides the line segment joining $(-3,5)$ and $(4,-9)$ in the ratio $1:6$ internally.
Question 72 :
In what ratio does the point $\begin{pmatrix} \dfrac { 1 }{ 2 },\dfrac { -3 }{ 2 } \end{pmatrix}$ divide the line segment joining the points $(3,5)$ and $(-7,9)$?<br/>
Question 73 :
What will be the value of $y$ if the point $\begin{pmatrix} \dfrac { 23 }{ 5 },y \end{pmatrix}$, divides the line segment joining the points $(5,7)$ and $(4,5)$ in the ratio $2:3$ internally?<br/>
Question 74 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.
Question 75 :
Out of the digits $1$ to $9$, two are selected at random and one is found to be $2$, the probability that their sum is odd is
Question 76 :
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 :
An integer is chosen at random between 1 and 100. Find the probability that it is divisible by 8.<br/>
Question 80 :
$A, B$ are two events of a simple space.Assertion (A):- $A, B$ are mutually exclusive $\Rightarrow P\left ( A \right )\leq P\left ( \bar{B} \right )$Reason (R):- $A, B$ are mutually exclusive  $\Rightarrow P\left ( A \right )+ P\left ( B \right )\leq 1$
Question 81 :
In a single cast with two dice, the odds against drawing $7$ is
Question 82 :
The area of two circles are in the ratio $25 : 36$. Then the ratio of their circumference is _________.
Question 83 :
What is the circumference of a circle whose radius is 8 cm?
Question 84 :
If the circumference of a circle is reduced by 50 % then the area will be reduced by
Question 85 :
A cord in the form of square encloses the area 'S'$ \displaystyle cm^{2} $ If the same cord is bent into the form of a circle then the area of the circle is
Question 86 :
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 87 :
Find the area of a sector in radians whose central angle is $45^o$ and radius is $2$.<br/>
Question 88 :
Ratio of circumference of a circle to its radius is always $2 \pi : 1$
Question 89 :
If the ratio of circumference of two circles is $4 : 9$, then what is the ratio of their areas is?
Question 90 :
If a sector of a circle of diameter 21 cm subtends an angle of $120^{\circ}$ at the centre, then what is its area ? 
