Question 1 :
Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.
Question 2 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 3 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 5 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 6 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 8 :
The value of $m$ for which the equation $\dfrac { a }{ x+a+m } +\dfrac { b }{ x+b+m } =1$ has roots equal in magnitude but opposite in sign is<br>
Question 9 :
If ${(5{x}^{2}+14x+2)}^{2}-{(4{x}^{2}-5x+7)}^{2}$ is divided by ${x}^{2}+x+1$, then the quotient $q$ and the remainder $r$ are given by:
Question 10 :
If $\displaystyle \alpha ,\beta$are the roots of the quadratic equation$\displaystyle { x }^{ 2 }-8x+p=0$, find the value of p if$\displaystyle { \alpha }^{ 2 }+{ \beta }^{ 2 }=40$.
Question 11 :
If the roots of the equation $ a x^{2}+b x+c=0 $are of the form $(k+1) / k $and $(k+2) /(k+1), $then $(a+b+c)^{2} $is equal to
Question 12 :
Evaluate :$\displaystyle \frac { 50xyz\left( x+y \right) \left( y+z \right) \left( z+x \right) }{ 100xy\left( x+y \right) \left( y+z \right) }$
Question 13 :
Solve the following equations:<br/>$y + \sqrt {x^{2} - 1} = 2$<br/>$\sqrt {x + 1} - \sqrt {x - 1} = \sqrt {y}$.
Question 14 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {10}{(x+y)}+\dfrac {2}{(x-y)}=4, \dfrac {15}{(x+y)}-\dfrac {5}{(x-y)}=-2$<br/>
Question 15 :
Solve the following pair of equations by reducing them to a pair of linear equations:$6x + 3y = 6xy, 2x + 4y = 5xy$<br/>
Question 16 :
From the following figure, we can say: $\displaystyle \frac{2x}{3}+\frac{3y}{2}=8\frac{1}{3}; \, \, \frac{3x}{2}+\frac{2y}{3}=13\frac{1}{3}$
Question 17 :
Solve the following pair of equations by cross multiplication rule.$x + y = a + b, ax - by = a^2-b^2$<br/>
Question 18 :
Find the value of $x$ and $y$ using cross multiplication method: <br/>$6x + y = 18$ and $5x + 2y = 22$
Question 19 :
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 21 :
The ratio of areas of two similar triangles is $81 : 49$. If the median of the smaller triangle is $4.9\ cm$, what is the median of the other?
Question 22 :
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 23 :
$ABCD$ is parallelogram and $P$ isthe mid point of the side $AD$. The line $BP$ meets the diagonal $AC$ in $Q$. Then the ratio $AQ:QC=$
Question 24 :
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 25 :
Check whether the statement is true/false <br/>$\sec ^ { 2 } \theta + cosec ^ { 2 } \theta = \sec ^ { 2 } \theta \cdot \sin ^ { 2 } \theta$
Question 26 :
If $\sec 4A = cosec (A-20^{\small\circ})$, where $4A$ is an acute angle, find the value of $A$.
Question 27 :
The value of $\cos { \dfrac { \pi }{ 7 } } +\cos { \dfrac { 2\pi }{ 7 } } +\cos { \dfrac { 3\pi }{ 7 } } +\cos { \dfrac { 4\pi }{ 7 } } +\cos { \dfrac { 5\pi }{ 7 } } +\cos { \dfrac { 6\pi }{ 7 } } +\cos { \dfrac { 7\pi }{ 7 } } $ is
Question 29 :
The value of $\displaystyle \frac { 2\cos { { 67 }^{ o } }  }{ \sin { { 23 }^{ o } }  } -\frac { \tan { { 40 }^{ o } }  }{ \cot { { 50 }^{ o } }  } $ is :
Question 30 :
The probability that a person will hit a target in shooting practice is $0.3$. If he shoots $10$ times, then the probability of his shooting the target is
Question 31 :
$P(A\cap B) = \dfrac{1}{2}, P(\overline{A} \cap \overline{B})=\dfrac{1}{2}$ and $2P(A)=P(B)=p$, then the value of $p$ is equal to
Question 32 :
A coin tossed $100$ times. The no. of times head comes up is $54$.What is the probability of head coming up?
Question 33 :
A family is going to choose two pets at random from among a group of four animals: a cat, a dog, a bird, and a lizard. Find the probability that the pets that the family chooses will include the lizard.
Question 34 :
$H$ is one of the $6$ horses entered for a race and is to be ridden by one of the two jokeys A and B. It is $2$ to $1$ that $A$ rides $H$ in which case all the horses are likely to win. If $B$ rides $H$, his chance is trebled. Then the odds against H winning is
Question 35 :
If the odds in favour of winning a race by three horses are $1 : 4, 1 : 5$ and $1 : 6$, find the probability that exactly one of these horses will win.
Question 36 :
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 37 :
State whether the following statements are true or false . Justify your answer.<br>The points $ (0 , 5) , (0 , -9) $ and $ (3 , 6) $ are collinear .
Question 38 :
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 39 :
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 40 :
If the point $(x_1 + t (x_2 -x_1), y_1+t (y_2-y_1))$ divides the join of $(x_1, y_1)$ and $(x_2, y_2)$ internally, then
Question 41 :
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 42 :
If the radius of a circle is $\displaystyle \frac{7}{\sqrt{\pi}}$ cm, then the area of the circle is equal to
Question 43 :
The area of a circle is$\displaystyle 2464\:m^{2}$, then the diameter is
Question 44 :
The diameter of two circles are $32 cm$ and $24 cm$. Find the radius of the circle having its area equal to sum of the area of the two given circle.
Question 45 :
A wire in the shape of an  equilateral triangle encloses  an area of $s$ $cm^2$. If the same  wire is bent to form a circle,  then the area of the circle will  be<br/>
Question 46 :
The length of minute hand of a clock is $14cm$. Find the area swept by the minute hand in one minute.<br/> [Use $\pi=\dfrac{22}{7}$]
Question 47 :
The circumference of a circle exceeds its diameter by $15 cm$ then, the circumference of the circle is
Question 48 :
The radius of a circle is increased by 1 cmthen the ratio of the new circumference to the new diameter is
Question 49 :
Points $A$ and $B$ lie on circle $O$ (not shown). $AO=3$ and $\angle AOB ={120}^{o}$. Find the area of minor sector $AOB$.
Question 50 : <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>
