Question 1 :
A vessel is in the form of a frustum of a cone. The area of the ends of the frustum cone are $122$ $cm^2$ and $205$ $cm^2$. If the curved surface area is $305$ $cm^2$. Find the total surface area.
Question 2 :
Identify the volume of largest cone which can be carved out from a cube of edge '$a$' cm.
Question 3 :
During conversion of a solid from one shape to another, the volume of the new shape will<br>
Question 4 :
Given that the volume of a cone is$\displaystyle 2355cm^{3}$ and the area of its base is$\displaystyle 314cm^{2}$ Its height is
Question 5 :
How many bricks, each measuring $25\ cm\times 11.25\ cm\times 6\ cm$, will be needed to build a wall $8\ m$ long, $6\ m$ high and $22.5\ cm$ thick?
Question 6 :
The opposite sides of a quadrilateral circumscribing a circle subtend ________ angles at the centre of the circle.
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b46273b23058497996a.PNG' />
In the above figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and $\angle BQR = 70^{\circ}$, then $\angle AQB$ is equal to
Question 8 :
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^{\circ}$, then $\angle POA$ is equal to
Question 9 :
If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, what is the area of the triangle?
Question 10 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 11 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?
Question 12 :
State true or false. Tangent is perpendicular to the radius through the point of contact.
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979968.PNG' />
In the above figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $50^{\circ}$ with PQ, then $\angle POQ$ is equal to
Question 14 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 15 :
Is it TRUE or FALSE, that if a chord AB subtends an angle of $60^{\circ}$ at the centre of a circle, then angle between the tangents at A and B is also $60^{\circ}$?
Question 16 :
The common point of a tangent to a circle and the circle is called .....
Question 17 :
The tangent to a circle is ..... to the radius through the point of contact.
Question 18 :
If P is a point on a circle with centre C, then the line drawn through P and perpendicular to CP is the tangent to the circle at the point P.
Question 19 :
The point lying on common tangent to the circle $x^2+y^2=4$ and $x^2+y^2+6x+8y-24=0$ is
Question 20 :
Lines are drawn through the point P(-2, -3) to meet the circle ${ x }^{ 2 }+{ y }^{ 2 }-2x-10y+1=0$. The length of the line segment PA.A being the point on the circle where the line meets the circle at coincident points, is
Question 21 :
The lengths of tangent drawn from an external point to a circle are equal.
Question 22 :
If a line intersects a circle in two distinct points then it is known as a
Question 23 :
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is<br><br>
Question 24 :
Write True or False and give reasons for your answer in the following:<br/>A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the center.<br/>
Question 25 :
A tangent to a circle is a line that intersects the circle in only one point.
Question 26 :
The length of the tangents from a point A to a circle of radius $3$ cm is $4$ cm. The distance (in cm) of A from the center of the circle is:<br/>
Question 28 :
There is no tangent to a circle passing through a point lying ..... the circle.
Question 29 :
If the angle between two radii of a circle is $140^{\circ}$, then the angle between the tangents at the ends of the radii is :<br/>
Question 30 :
From a point A which is at a distance of 10 cm from the center O of a circle of radius 6 cm, the pair of tangents AB and AC to the circle are drawn. Then the area of Quadrilateral ABOC is: <br/>
Question 31 :
The number of common tangents to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 4x + 2y - 4 = 0$ is
Question 32 :
Tangents drawn from the origin to the circle $ \displaystyle x^{2}+y^{2}-2px-2qy+q^{2}=0 $ are perpendicular to each other if<br>
Question 33 :
The length of a common tangent to the curves $\displaystyle { 4x }^{ 2 }+{ 25y }^{ 2 }=100$ and$\displaystyle { x }^{ 2 }+{ y }^{ 2 }=16$ intercepted by the coordinate axes is
Question 34 :
A tangent is drawn to the circle $2x^2+2y^2-3x+4y=0$ at the point 'A' and it meets the line $x+y=3$ at B(2, 1), then AB=______<br>
Question 35 :
If from any point on the circle$x^2+ y^2= a^2$tangents are drawn to the circle$x^2+ y^2= a^2 \sin2\alpha $ then the angle between the tangents, is
Question 36 :
The equation of the circle whose radius is $4$, centre lies in the first quadrant and which touches $x$-axis and line $4x-3y = 0$ is<br/>
Question 37 :
The lines $3x -4y + 4 =0$ and $6x -8y -7 = 0$ are tangents to the same circle.
Question 39 :
If tangent and normal to the curve $ y=2 sinx +sin 2x $ are drawn at $ P \left( x= \cfrac { \pi } {3} \right )$<br/>then area of the quadrilateral formed by tangent, the normal at p and coordinate axes is 
Question 40 :
There is ___ tangent to a circle passing through a point lying inside the circle.
Question 41 :
If the points $\left( {0,0} \right)\,,$ and $\left( {2,0} \right)\,,$ are concyclic then K=
Question 42 :
OA, OB are the radii of a circle with 0 as the center, the $\angle AOB = 120^o$. Tangents at A and B are drawn to meet in the point C. If OC intersects the circle in the point D, then D divides OC in the ratio of
Question 43 :
The equation of the circle passing through $(2, 3)$ and touching the lines $x - 2 = 0, 3x - 4y + 1 = 0$ is <br>
Question 44 :
What is the length of shortest path by which one can go from $(-2,0)$ to $(2,0)$ without entering the interior of circle, ${ x }^{ 2 }+{ y }^{ 2 }=1$?
Question 45 :
A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is:
Question 47 :
A tangent drawn from the point (4, 0) to the circle $\displaystyle x^{2}+y^{2}=8 $ touches it at a point A in the first quadrant. The coordinates of another point B on the circle such that $AB$ = 4 are
Question 48 :
The radius of the circle touching the straight lines $x-2y-1=0$ and $3x-6y+7=0$ is
Question 49 :
The square of the length of the tangent from $\left( 3,-4 \right) $ to the circle ${ x }^{ 2 }+{ y }^{ 2 }-4x-6y+3=0$ is
Question 50 :
Tangents PA and PB drawn to $x^2+y^2=9$ from any arbitrary point 'P' on the line $x+y=25$. Locus of midpoint of chord AB is<br>
