Question 1 :
If circumference of a circle is $\displaystyle 3\pi $, then its area is
Question 2 :
Circular dome is a 3D example of which kind of sector of the circle?
Question 3 :
The radius of a circle whose area is equal to the sum of the areas of two circles of radii are  5 cm and 12 cm is
Question 5 :
The radius of a circle whose area is equal to the sum of the areas of two circles of radii 5 cm and 12 cm is
Question 6 :
<span>The circumference of a circular field is $308 m$, Find its </span>Area.
Question 7 :
The cost of fencing a circular field at the rate of $Rs\:.240\: per\: metre$ is $Rs. \: 52,800$ . The field is to be ploughed at the rate of $Rs. 12.50 \: per \: m^{2}$. Find the cost of ploughing the field.
Question 8 :
The area of the sector of a circle whose radius is 6 m when the angle at the centre is $\displaystyle 42^{\circ}$ is
Question 9 :
Circle $C_1$ passes through the centre of circle $C_2$ and is tangential to it. If the area of $C_1$ is $4cm^2$, then the area of $C_2$ is ________.
Question 11 :
A spherical iron ball of radius $9$ cm is melted and recast into three spherical balls. If the radii of two balls are $1$ cm and $8$ cm, find the radius of the third ball.
Question 12 :
Find the volume of the frustum cone whose base and top radius is 11 in and 6 in respectively. The height of the cone is 36 in. (Use $\pi$ = 3.14).
Question 13 :
A cube of side 4 cm is into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes
Question 14 :
A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is
Question 15 :
A bucket is in the shape of the frustum of a right circular cone, whose radii are 5 and 10 mm. The curved surface area is $210$ mm. Find the slant height. (Use $\pi$ = $3$)
Question 16 :
Three solid spheres of radius $1\text{ cm},\;6\text{ cm}$ and $8\text{ cm}$, respectively are melted together and cast into a single sphere. The radius $r$ of this sphere will be 
Question 17 :
A solid sphere of radius $x$ cm is melted and recast into a shape of a solid cone of radius $x$ cm. The height of the cone is:<br/>
Question 18 :
The slant height of the frustrum of a cone is $4$ cm. If the perimeters of its circular bases be $18$ cm and $6$ cm, find the curved surface area of the frustum and also find the cost of painting its total surface at the rate of Rs. $12.50$ per $100 cm^{2}$.
Question 19 :
A rectangular sheet of paper $22$cm long and $12$cm broad can be  curved to form the lateral surface of a right circular cylinder in two ways. Taking $\pi= \dfrac{22}{7}$. Difference in the volumes of the two cylinders thus formed is<br/>
Question 20 :
What length of the solid cylinder that is $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick, and $15$ cm long?
Question 21 :
Find the $31$st term of an AP whose $11$th term is $38$ and $16$th term is $73$ .
Question 22 :
The price of a certain item was $10 in 1990 and it has gone up by $2 per year since 1990. If this trend <span>continues, in what year will the price be $100 ? </span><br>
Question 23 :
If the nth term of an AP is $\dfrac{3+n}{4} $, then its 8th term is<br/>
Question 24 :
If the $9$th term of an A.P is $35$ and $19$th is $75$, then its $20$th term will be
Question 25 :
The sum of the $4th$ and $8th$ terms of an AP is $24$ and the sum of the $6th$ and the $10th$ terms is $44$. Find the first term of the AP
Question 26 :
Find $n$ if the coefficient of $5^{th}, 6^{th}$ & $7^{th}$ terms in the expansion of $(1+x)^{n}$ are in $A.P.$
Question 27 :
An AP consists of $50$ terms of which $3rd$ term is $12$ and the last term is $106$. Find the $29th$ term
Question 28 : <span>Suppose a series of $n$ terms is given by $\displaystyle S_{n}=a_{1}+a_{2}+...+a_{n}$ Then $\displaystyle S_{n-1}=a_{1}+a_{2}+...+a_{n-1}\left ( \forall \ n > 1 \right )$ and then we can write $\displaystyle t_{n}=S_{n}-S_{n-1} \ \forall  n\geq 2$ for $ n=1 $ we have $\displaystyle S_{1}=t_{1}$</span><br/><span>On the basis of above information answer the following questions:</span><div>If sum to $ n$  terms of a series is $\displaystyle an^{2}+bn$ where $a$, $b$ are constants then $ 5^{th} $ term of the series is<br/></div>
Question 29 :
Choose the correct answer from the given four options in the following question:<br/>The 11th term of the A.P. $-5, \dfrac{-5}{2}, 0, \dfrac{5}{2}, ...$ is 
Question 30 :
Let ${T}_{r}$ be the $r$th term of an AP, for $r=1,2,....$ if for some positive integers $m,n$ we have ${T}_{m}=1/n$ and ${T}_{n}=1/m$, then ${T}_{m/n}$ equal to ________
Question 31 :
A ladder '$x$' meters long is laid against a wall making an angle '$\theta$' with the ground. If we want to directly find the distance between the foot of the ladder and the foot of the wall, which trignometrical ratio should be considered?
Question 32 :
A flagstaff stands on the middle of a square tower. A man on the ground, opposite to the middle of one face and distant from it $100$ m, just see the flag ; on his receding another $100$ m, the tangents of the elevation of the top of the tower and the top of the flagstaff are found to be $\dfrac {1}{2}$ and $\dfrac {5}{9}$. Find the height of the flagstaff, the ground being horizontal
Question 33 :
As you ride the Ferris wheel, your distance from the ground varies sinusoidally with time. An equation to model the motion is y=20cos($\frac {\pi}{4} (t-3))+23$. Predict your height above the ground at a time of 1 seconds.<br/>
Question 34 :
The angle of depression of  a boat from the top of a cliff 300 m high is $\displaystyle 60^{\circ}   $  The distance of the boat from the foot of the cliff is 
Question 35 :
Two chimneys 18 m and 13 m high stand upright in the ground. If their feet are 12 m apart, then the distance between <span>their tops is</span>
Question 36 :
The angle of elevation of a cloud from a point $h$ metres above a lake is $\Theta$. The angle of depression of its reflection in lake is $45^{ }$ The height of the cloud is<br>
Question 37 :
The angle of elevation of stationary cloud from a point 25 ml above the lake is $ 15^0$ and the angle of depression of reflection in the lake is $45^0$ .Then the height of the cloud above the level
Question 38 :
A series of steps lead to a temple. The number of steps is 30. The height of each step is 20 cm. Then find the height of the temple from the base.
Question 39 : The angles of elevation of the top of a tower from the top and foot of a pole are respectively $30^o$ and $45^o$. If ${ h }_{ T }$ is the height of the tower and ${ h }_{ p }$ is the height of the pole, then which of the following are correct?<br/>1. $\dfrac { 2{ h }_{ p }{ h }_{ T } }{ 3+\sqrt { 3 }  } ={ h }_{ p }^{ 2 }$<div><br/>2. $\dfrac { { h }_{ T }-{ h }_{ p } }{ \sqrt { 3 } +1 } =\dfrac { { { h }_{ p } } }{ 2 } $</div><div><br/>3. $\dfrac { 2({ h }_{ p }+{ h }_{ T }) }{ { h }_{ p } } =4+\sqrt { 3 } $</div><div><br/>Select the correct answer using the code given below.<br/></div>
Question 40 :
A piece of paper in the shape of a sector of a circle of radius 10cm and of angle $\displaystyle 216^{\circ}$ just covers the lateral surface of a right circular cone of vertical angle$\displaystyle 2\theta$ .Then $\displaystyle \sin\: \theta$ is
Question 42 :
A(3 , 2) and B(5 , 4) are the end points of a line segment . Find the coordinates of the mid-point of the line segment .
Question 43 :
The points A(5, 2), B(3, 4) and C(x, y) are collinear points and AB = BC then find the co-ordinates of C.
Question 44 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 46 :
In the $xy$-plane, the vertices of a triangle are $(-1,3), (6,3)$ and $(-1,-4)$. The area of the triangle is ___ square units.
Question 47 :
$L, M$ and $N$ are the midpoints of the sides $BC, CA$ and $AB$ respectively of triangle $ABC$. If the vertices are $A(3,-4), B(5,-2)$ and $C(1,3)$ the area of $\displaystyle \triangle LMN$ is ____ square units.
Question 48 :
The area of the triangle formed by the points $(2, 6), (10, 0)$ and $(0, k)$ is zero square units. Find the value of $k.$
Question 49 :
Let P and Q be points $(4, 4)$ and $(9, 6)$ of parabola ${y^2} = 4a\left( {x - b} \right)$ If R be a point on the arc of the parabola between P and Q, such that the area of $\Delta PRQ$ is largest, then R is
Question 50 :
If the tangent at (3,-4) to the circle ${ x }^{ 2 }+{ y }^{ 2 }-4x+2y-5=0$ cuts the circle ${ x }^{ 2 }+{ y }^{ 2 }-16x+2y+10=0$ in A and B then the midpoint of AB is
Question 52 :
The value of $ \sin^{2} 30^{\circ} + \cos^{2} 30^{\circ} $ is:
Question 53 :
If ${\rm{sin}}\,{\rm{\theta  + cosec\theta  = 2,}}\,{\rm{then}}\,\,{\rm{si}}{{\rm{n}}^{\rm{2}}}{\rm{\theta  + cose}}{{\rm{c}}^{\rm{2}}}{\rm{\theta }}\,$ is equal to:
Question 56 :
If $\displaystyle x = a\cos ^{3}\theta $ and y = b $\displaystyle \sin ^{3}\theta ,$ then the value of $\displaystyle \left ( \frac{x}{a} \right )^{2/3}+\left ( \frac{y}{b} \right )^{2/3}$ is <br/>
Question 58 :
If $ cosec\Theta -cot\Theta=\dfrac{1}{3}$, then the value of $ \left ( cosec\Theta +cot\Theta  \right )$  is<br/>
Question 59 :
If $'\theta '$ is not an integral multiple of ${ 180 }^{ \circ  }$ , Then ${ sec }^{ 2 }\theta -{ tan }^{ 2 }\theta =$ 
Question 60 :
Consider the following:<br>1. $\cfrac { \cos ^{ 2 }{ \theta } -\sin ^{ 2 }{ \theta } }{ \cos ^{ 2 }{ \theta } +\sin ^{ 2 }{ \theta } } =\cos ^{ 2 }{ \theta } \left( 1+\tan { \theta } \right) \left( 1-\tan { \theta } \right) $<br>2. $\cfrac { 1+\sin { \theta } }{ 1-\sin { \theta } } ={ \left( \tan { \theta } +\sec { \theta } \right) }^{ 2 }$<br>Which of the statements given above is/are correct?
