Question 1 :
Is it TRUE or FALSE, that the length of tangent from an external point on a circle is always greater than the radius of the circle?
Question 2 :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is
Question 3 :
A line and a circle in the same plane can co-exist in _______ different ways.
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b42273b230584979965.PNG' />
In the above figure, if $\angle AOB = 125^{\circ}$, then $\angle COD$ is equal to
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcf273b230584979a1f.JPG' />
In the above image , XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Then
Question 6 :
Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?
Question 7 :
What is the common point of a tangent to a circle and the circle called?
Question 8 :
A tangent to a circle intersects it in how many point(s)?
Question 9 :
State true or false. A tangent to a circle is a straight line which touches the circle at only one point.
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979967.PNG' />
In the above figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle OTA = 30^{\circ}$. Then AT is equal to
Question 11 :
A tangent to a circle intersects it in _____ point (s)
Question 12 : <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 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4c273b230584979972.PNG' />
In the above figure, The tangent at a point C of a circle and a diameter AB when extended intersect at P. If $\angle PCA=110^{\circ}$ , what is the value of $\angle CBA$?
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcc273b230584979a1b.JPG' />
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see the above image). Find the length TP.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4f273b230584979976.PNG' />
According to the above figure, Is it TRUE or FALSE that BOA is a diameter of a circle and the tangent at a point P meets BA extended at T. If $\angle PBO = 30^{\circ}$, then $\angle PTA$ is equal to $30^{\circ}$?
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcc273b230584979a1a.JPG' />
The above image represents two tangents TP and TQ drawn to a circle with centre O from an external point T . Then
Question 17 :
From a point Q , the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm . The radius of the circle is
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcd273b230584979a1c.JPG' />
The above image shows that a circle and two lines parallel to a given line AB is such that one is a tangent and the other , a secant to a circle , i.e , the line CD is the tangent at point M while the line EF is the secant . Is this statement true ?
Question 19 :
Two circles with centres O and $O ^ { \prime }$ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and $O ^ { \prime }P$ are tangents to the two circles. What is the length of the common chord PQ?
Question 20 :
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, what is the perimeter of the $\triangle ABC$?
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4b273b230584979916.jpg' />
In the above figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. ∠ AOB = ?
Question 22 : <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 23 :
Is it TRUE or FALSE, that AB is a diameter of a circle and AC is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at C intersects AB extended at D, then BC = BD?
Question 24 :
The angle between the two tangents drawn from an external point to a circle is ______ to the angle subtended by the line-segment joining the points of contact at the centre.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4b273b230584979917.JPG' />
In the above figure, a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Question 26 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, find the length of the wire.
Question 27 :
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Question 28 :
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Question 29 :
A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2d273b230584979a8b.JPG' />
In the above image, a juice seller was serving his customers using glasses as shown. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the actual capacity of the glass . (Use $\pi$ = 3.14.)
Question 31 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km /h, in how much time will the tank be filled?
Question 32 :
What is the formulae for total surface area of solid hemisphere?
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c36273b230584979a96.JPG' />
In the above image, an open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see the above image). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the volume of water bucket can hold.Take $\pi$ = $\frac{22}{7}$ .
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3a273b230584979a9a.JPG' />
In the above diagram, a gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm
Question 36 :
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is
Question 37 :
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.
Question 38 :
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
Question 39 :
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $cm^3$ of iron has approximately 8 g mass. (Use $\pi$ = 3.14)
Question 40 :
A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called
Question 41 :
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Question 42 :
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter.A full barrel of ink in the pen is used up on writing 3300 words on an average.How many words can be written in a bottle of ink containing one fifth of a litre?
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c31273b230584979a90.jpg' />
In the above image, a solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take $\pi$ = 3.14)
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b91273b2305849799cc.jpg' />
In the above figure the shape of a glass (tumbler) is usually in the form of
Question 45 :
A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 $cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?
Question 46 :
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
Question 47 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is
Question 48 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 $cm^2$ .
Question 49 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of copper to be 8.88 g per $cm^3$.
Question 50 :
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
