Become a master of CBSE Grade 10 Math and score high—Part 2.

Name: Become a master of CBSE Grade 10 Math and score high—Part 2.
Rating: 5.0 (1 reviews)

Math for high school CBSE, SSC, and other boards that covers chapters 9–15 in detail with a step-by-step approach.

Created byLakshmi Narayana

Last updated 12/2022

English

What you'll learn

Some Applications of Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

7 sections • 389 lectures • 43h 58m total length

Session 1 - Introduction14:06
Introduction:
Trigonometry is used in our day-to-day life. Here, we shall study the use of trigonometry in measuring the heights and distance of towers, buildings and other objects. Measuring heights and distances is an important application of trigonometry.
Session 1 - Q 13:20
If the length of the shadow of a tower is equal to its height,
then the angle of elevation of the sun is:
A. 300
B. 450
C. 600
D. 750
Session 1 - Q 24:02
If a tower 30m high casts a shadow 10√3m long on the ground, then what is the angle of elevation of the sun?
Session 1 - Q 36:34
An observer 1.5 m tall is 28.5 m away from a tower 30 m high. Find the angle of elevation of the top of the tower from his eye.
Session 1 - Q 43:40
The figure shows the observation of point C from point A. Find the angle of depression from A, if AB = 4 cm and BC = 4√(3 ) cm.
Test your understanding
Home Assignment
Session 2 - Inrtoduction2:02
Problems based on finding one side of right angled triangle when an acute angle and one of the other two sides are known.
Session 2 - Q 15:30
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Session 2 - Q 28:45
An electrician has to repair an electric fault on a pole of height 5 m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work (see Fig.). What should be the length of the ladder that she should use which, when inclined at an angle of 60° to the horizontal, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder? (You may take √3 = 1.73)
Session 2 - Q 38:29
A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30o with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.
Session 2 - Q 43:47
A ladder 15 m long leans against a wall making an angle of 60o with the wall. Find the height of the wall from the point the ladder touches the wall.
Test your understanding
Home Assignment
Session 3 - Introduction2:31
Problems based on two right angled triangle having common base (common horizontal line) or perpendicular (common vertical line)
Session 3 - Q 15:00
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
Session 3 - Q 29:00
From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (You may take √3 = 1.732)
Session 3 - Q 36:47
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.
Session 3 - Q 47:39
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30∘ and that of the top of the flagstaff is 600. Find the height of the tower.
[Use √3 = 1.732.]
Test your understanding
Home Assignment
Session 4 - Introduction1:39
Problems based on use of two right angled triangles when length of one side of each triangle are equal or a relation between them is known:
Session 4 - Q 112:57
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.
Session 4 - Q 210:59
The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 1500√3 m, find the speed of the jet plane.
Session 4 - Q 39:31
The angle of elevation of the top of a vertical tower from a point on the ground is 600. From another point 10m vertically above the first, its angle of elevation is 300. Find the height of the tower.
Test your understanding
Home Assignment
Session 5 - Introduction1:20
Problems based on right angled triangle formed by the angle of depression.
Session 5 - Q 15:44
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Session 5 - Q 27:57
A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 300. The peacock catches the serpent in 12 s with the speed of 300 m/min. what is the height of the tree?
Session 5 - Q 39:51
The angle of elevation of a cloud from a point 120 m above a lake is 300 and the angle of depression of its reflection in the lake is 600. Find the height of the cloud.
Session 5 - Q 49:07
Two ships are approaching a light house from opposite directions. The angle of depression of two ships from top of the light house are 300 and 450. If the distance between two ships is 100 m. Find the height of light-house.
Test your understanding
Home Assignment
Exercise 9.1 - Q 14:25
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°
(see Fig. 9.11).
Exercise 9.1 - Q 28:18
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Exercise 9.1 - Q 39:06
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Exercise 9.1 - Q 44:37
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Exercise 9.1 - Q 55:15
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
Exercise 9.1 - Q 611:23
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
Exercise 9.1 - Q 78:34
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Exercise 9.1 - Q 810:46
Compute pedestal height from the 45° and 60° elevations with the statue at 1.6 m, yielding about 2.19 m.
Exercise 9.1 - Q 98:00
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
Exercise 9.1 - Q 1011:50
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
Exercise 9.1 - Q 1110:38
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.
Exercise 9.1 - Q 128:19
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Exercise 9.1 - Q 1310:53
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Exercise 9.1 - Q 1411:16
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

Session 1 - Introduction11:23
Introduction:
In earlier class, we studied circle and various related terms like chord, segment, sector, are, etc. in this chapter, we will examine different situations that can be arise when a circle and a line are given in a plane.
Session 1 - Theorem 15:28
The TANGENTat any point of a circle is perpendicular to the radius through the point of contact.
Session 1 - Q 13:05
From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
Session 1 - Q 23:37
In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle
Test your understanding
Home Assignment
Session 2 - Introduction6:53
Number of Tangents from a Point on a Circle:
Session 2 - Theorem 23:35
The lengths of two tangents drawn from an external point to a circle are equal.
Session 2 - Q 13:00
Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Session 2 - Q 26:04
In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then find the radius of the smaller circle.
Session 2 - Q 33:59
Two concentric circles are of radii 7 cm and r cm respectively where r > 7. A chord of the larger circle of the length 48 cm, touches the smaller circle. Find the value of r.
Session 2 - Q 47:12
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 Figure). Find the length TP.
Test your understanding
Home Assignment
Session 3 - Introduction2:44
Number of Tangents from a Point on a Circle :
Problems based on length of the tangent from an external point to a circle.
Session 3 - Q 18:06
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ.
Session 3 - Q 25:33
From P, tangents PA and PB are equal and form a 60-degree angle. Radii OA and OB are perpendicular to tangents, making triangle APB equilateral, so AB equals 10 cm.
Session 3 - Q 33:33
If two tangents inclined at an angle of 600 are drawn to a circle of a radius 3 cm, then find the length of each tangent.
Session 3 - Q 44:38
In two concentric circles, prove that all chord of the outer circle which touch the inner circle are of equal length.
Test your understanding
Home Assignment
Session 4 - Introduction2:27
Miscellaneous problems related to circles.
Session 4 - Q 18:29
In fig. the radius of the in circle of △ABC of area 84 cm2 and the lengths of the segments AP and BP into which side AB is divided by the point of contact are 6 cm and 8 cm. Find the lengths of the sides AC and BC
Session 4 - Q 27:10
If a, b and c are the sides of a right angled triangle, where c is hypotenuse, then prove that the radius of the circle which touches the sides of the triangle is given by r = (a+b-c)/2
Session 4 - Q 35:30
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA.
Session 4 - Q 46:48
In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, P and S respectively. If AB = 29 cm, AD = 23 cm, ZB = 90o and DS = 5 cm, then find the radius of the circle (in cm.).
Test your understanding
Home Assignment
Exercise 10.1 - Q 11:20
How many tangents can a circle have?
Exercise 10.1 - Q 22:32
Fill in the blanks :
(i) A tangent to a circle intersects it in ___________ point (s).
(ii) A line intersecting a circle in two points is called a _____________.
(iii) A circle can have ___________ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called __________.
Exercise 10.1 - Q 33:19
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 :
(A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm.
Exercise 10.1 - Q 41:44
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
Exercise 10.2 - Q 14:41
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
(A) 7 cm (B) 12 cm
(C) 15 cm (D) 24.5 cm
Exercise 10.2 - Q 23:17
In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that
∠POQ = 110°, then ∠PTQ is equal to
(A) 60° (B) 70° (C) 80° (D) 90°
Exercise 10.2 - Q 39:10
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to
(A) 50° (B) 60° (C) 70° (D) 80°
Exercise 10.2 - Q 46:03
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Exercise 10.2 - Q 57:16
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Exercise 10.2 - Q 64:59
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Exercise 10.2 - Q 77:03
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Exercise 10.2 - Q 87:17
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that
AB + CD = AD + BC
Exercise 10.2 - Q 910:15
In Fig. 10.13, 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. Prove that ∠AOB = 90°.
Exercise 10.2 - Q 105:34
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Exercise 10.2 - Q 116:57
Prove that the parallelogram circumscribing a circle is a rhombus.
Exercise 10.2 - Q 1217:00
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 (see Fig. 10.14). Find the sides AB and AC.
Exercise 10.2 - Q 139:40
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Session 1 - Introduction10:51
Introduction
Session 1 - Q 18:13
Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that AP/AB = 3/5
Session 1 - Q 27:39
Draw a line segment of length 5 cm and divide it in the ratio 3: 7.
Session 1 - Q 38:21
Draw a line segment of length 8 cm and divide it internally in the ratio 4: 5.
Test your understanding
Home Assignment
Session 2 - Introduction6:29
Construction of a Triangle Similar to Given Triangle when m/n< 1 or m < n
Session 2 - Q 110:59
Construct a triangle similar to a given triangle ABC with its sides equal to 3/4 of the corresponding sides of the triangle ABC (i.e., of scale factor 3/4).
Session 2 - Q 210:29
Construct an isosceles triangle ABC with base BC = 6 cm, AB = AC and ∠A = 900. Draw another similar triangle whose sides are 4/5 times of the sides of △ABC. Justify your construction.
Session 2 - Q 37:02
Construct a triangle with BC = 7cm, ∠B = 450 and ∠C = 600.Then, construct a similar triangle to its whose sides are 3/5 times of the corresponding sides of the given triangle.
Test your understanding
Home Assignment
Session 3 - Introduction6:10
Construction of a Triangle Similar to Given Triangle when m/n> 1 or m > n
Session 3 - Q 110:45
Construct a triangle similar to a given triangle ABC with its sides equal to 5/3 of the corresponding sides of the triangle ABC (i.e., of scale factor 5/3).
Session 3 - Q 28:12
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
Session 3 - Q 39:29
Draw a triangle ABC with side BC = 7 cm, ∠B = 450, ∠A = 1050. Then construct a triangle whose sides are 4/3 times the corresponding sides of ∆ABC.
Test your understanding
Home Assignment
Session 4 - Introduction2:06
Construction of Tangents to a Circle:
Session 4 - Q 14:30
Draw a circle of diameter AB = 6 cm with centre O and then draw a tangent to the circle at point A or B.
Session 4 - Q 26:02
Draw a circle of radius 4cm from a point P, 7cm from the centre of the circle, draw a pair of tangents to the circle measure the length of each tangent segment.
Session 4 - Q 35:25
Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle.
Session 4 - Q 47:11
Draw a circle of radius 4 cm. Take two points P and Q on one of its extended diameters, each at a distance of 9 cm from its centre. Draw tangents to the circle from these two points P and Q.
Session 4 - Q 57:27
Draw a pair of tangents to a circle of radius 3 cm which are inclined to each other at angle of 60°.
Test your understanding
Home Assignment
Session 5 - Introduction2:36
Construction of a Quadrilateral Similar to a Given Quadrilateral:
Session 5 - Q 110:04
Constructa quadrilateral AB = 3 cm, BC = 4 cm , AC = 5 cm, CD = 2 cm and ∠A = 700. And construct a quadrilateral similar to the given quadrilateral with scale factor 3/5.
Test your understanding
Home Assignment
Exercise 11.1 - Q 112:29
Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure the two parts.
Exercise 11.1 - Q 214:13
Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
Exercise 11.1 - Q 316:05
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.
Exercise 11.1 - Q 413:57
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 11/2 times the corresponding sides of the isosceles triangle.
Exercise 11.1 - Q 516:09
Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.
Exercise 11.1 - Q 615:58
Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a
triangle whose sides are 4/3 times the corresponding sides of D ABC.
Exercise 11.1 - Q 715:08
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
Exercise 11.2 - Q 110:31
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Exercise 11.2 - Q 211:58
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Exercise 11.2 - Q 311:30
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Exercise 11.2 - Q 411:13
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
Exercise 11.2 - Q 58:47
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Exercise 11.2 - Q 610:52
Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the
perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
Exercise 11.2 - Q 79:31
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Session 1 - Introduction10:22
Introduction
Session 1 - Q 15:03
An athlete runs on a circular track of radius 49 m and covers a distance of 3080 m along its boundary. How many rounds has he taken to cover this distance? [Take π=22/7].
Session 1 - Q 27:41
The cost of fencing a circular field at the rate of ₹24 per metre is ₹5280. The field is to be ploughed at the rate of ₹0.50 per m2. Find the cost of ploughing the field[Take π =22/7].
Session 1 - Q 33:25
If the ratio of the circumferences of two circles is 3 : 1, then find the ratio of their areas.
Session 1 - Q 44:24
If the perimeter of a protractor is 72 cm, then calculate its area.
Test your understanding
Home Assignment
Session 2 - Introduction5:53
Sector and Areas of Sector
Session 2 - Q 12:29
In a circle of radius 21 cm, an arc subtends an angle of 600 at the centre.
Find the area of sector formed by the arc. (Use π = (22 )/7)
Session 2 - Q 25:20
Find the area of the sector of a circle with radius 4 cm and of angle 30°.
Also, find the area of the corresponding major sector (Use π = 3.14).
Session 2 - Q 33:21
What is the perimeter of a sector of a circle whose central angle is 900 and radius is 7 cm?
Session 2 - Q 44:40
Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.
Test your understanding
Home Assignment
Session 3 - Introduction4:23
Area of Segment of a Circle
Session 3 - Q 19:25
Find the area of the segment AYB shown in Fig., if radiusof the circle is 21 cm and ∠AOB = 120°. (Use π = 22/7)
Session 3 - Q 25:50
In a circle with centre O and radius 5 cm, AB is a chord of length 5√3 cm. Find the area of sector AOB.
Session 3 - Q 35:52
A round table cover has six equal designs as shown in the given figure.
If the radius of the cover is 35 cm then find the total area of the design. [Use √3 =1.732 and π= 3.14.]
Test your understanding
Home Assignment
Session 4 - Introduction2:21
Areas of Combinations of Plane Figures:
When combination of circle(or)semi-circle and square (or) rectangle are given:
Session 4 - Q 18:18
In figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.
Session 4 - Q 24:22
Find the area of the shaded region in figure, where ABCD is a square of side 14 cm.
Session 4 - Q 37:00
Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π = 3.14)
Session 4 - Q 46:55
In the given figure, ABCD is a trapezium with AB‖DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then, find the area of the shaded region of the figure.
(Use π = 22/7).
Test your understanding
Home Assignment
Session 5 - Introduction1:31
Areas of Combinations of Plane Figures:
When combination of two concentric circles are given
Session 5 - Q 13:44
In the given figure, the area of the shaded region between two concentric circles is 286 cm2. If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
Session 5 - Q 24:35
In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.
Session 5 - Q 38:26
In the given figure, two concentric circles with centre O have radii 21 cm
and 42 cm. If ∠AOB = 600, find the area of the shaded region. (Use π = 22/7)
Session 5 - Q 43:35
Nitika has a circular plot of radius 105 m. he donates a 7 m wide track along its boundary for community track.Find the area of the track. [Take,π=22/7]
Test your understanding
Home Assignment
Session 6 - Introduction1:16
Areas of Combinations of Plane Figures:
When combination of circle and triangle are given
Session 6 - Q 16:50
Find the area of the shaded region in figure, if AC = 20 cm, AB = 15 cm and O is the centre of the circle.
Session 6 - Q 27:32
In the given figure, AOB is a sector of angle 600 of a circle with centre O and radius 17 cm. If AP ⊥ OB and AP = 15 cm, find the area of the shaded region.
Session 6 - Q 36:43
Find the area of the shaded region in figure, if BC = BD = 8 cm, AC = AD = 15 cm and O is the centre of the circle. (Take π = 3.14)
Session 6 - Q 43:51
A memento is made as shown in the figure. Its base PBCR is silver plated from the front side. Find the area which is silver plated.(π =(22 )/7)
Test your understanding
Home Assignment
Session 7 - Introduction1:21
Areas of Combinations of Plane Figures :
When combination of quadrant of circle and triangle (or) square is given
Session 7 - Q 14:47
A square OABC is inscribed in a quadrant OPBQ of a circle as shown in the adjoining figure. If OA = 14 cm, find the area of the shaded region.
Session 7 - Q 28:35
In figure, ABC is a right-angled triangle at A. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
Session 7 - Q 34:04
In figure, APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region.
Session 7 - Q 48:39
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in a given figure. Find the area of the shaded region.
Test your understanding
Home Assignment
Exercise 12.1 - Q 15:12
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Exercise 12.1 - Q 26:46
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Exercise 12.1 - Q 319:46
Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
Exercise 12.1 - Q 410:30
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Exercise 12.1 - Q 51:49
Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units (B) p units (C) 4 units (D) 7 units
Exercise 12.2 - Q 12:42
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Exercise 12.2 - Q 23:47
Find the area of a quadrant of a circle whose circumference is 22 cm.
Exercise 12.2 - Q 34:44
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Exercise 12.2 - Q 412:41
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use = 3.14)
Exercise 12.2 - Q 512:22
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(i) the length of the arc (ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Exercise 12.2 - Q 611:12
A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use π = 3.14 and √3 = 1.73)
Exercise 12.2 - Q 78:40
A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.
(Use π = 3.14 and √3 = 1.73)
Exercise 12.2 - Q 89:47
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
Exercise 12.2 - Q 98:53
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 12.12. Find :
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Exercise 12.2 - Q 106:19
An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Exercise 12.2 - Q 116:58
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Exercise 12.2 - Q 124:47
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)
Exercise 12.2 - Q 1311:14
A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2. (Use √3 = 1.7)
Exercise 12.2 - Q 142:12
Tick the correct answer in the following :
Area of a sector of angle p (in degrees) of a circle with radius R is
(A) p/180 × 2πR (B) p/180 × πR2 (C) p/360 × 2πR (D) p/720 × 2πR2
Exercise 12.3 - Q 19:56
Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
Exercise 12.3 - Q 27:15
Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.
Exercise 12.3 - Q 35:59
Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Exercise 12.3 - Q 48:32
Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
Exercise 12.3 - Q 57:27
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.
Exercise 12.3 - Q 611:45
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral
triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.
Exercise 12.3 - Q 76:47
In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
Exercise 12.3 - Q 810:51
Fig. 12.26 depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find :
(i) the distance around the track along its inner edge
(ii) the area of the track.
Exercise 12.3 - Q 98:37
In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Exercise 12.3 - Q 1014:39
The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region.
(Use π = 3.14 and √3 = 1.73205)
Exercise 12.3 - Q 117:04
On a square handkerchief, nine circular designs each of radius 7 cm are made
(see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
Exercise 12.3 - Q 127:53
In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If
OD = 2 cm, find the area of the
(i) quadrant OACB, (ii) shaded region.
Exercise 12.3 - Q 139:21
In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
Exercise 12.3 - Q 146:36
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.
Exercise 12.3 - Q 1512:29
In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
Exercise 12.3 - Q 168:20
Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each.

Session 1 - Introduction15:31
Introduction:
In earlier classes, we have learnt to find the surface area and volume of solid figures, like; sphere, cylinder, cones, etc. there are some solid figures which are the combination of two or more different or similar solid figures. In this chapter, we will learn to find the surface area and volume of combination of solid figures.
Session 1 - Q 12:40
Find the number of cubes of side 2 cm which can be cut from a cube of side 4 cm.
Session 1 - Q 23:49
The surface areas of two spheres are in the ratio 16: 9. Find the ratio of their volumes?
Session 1 - Q 33:06
A rectangular sheet of paper 40cm × 22 cm is rolled to form a hollow cylinder of height 40 cm. Find the radius of the cylinder.
Test your understanding
Home Assignment
Session 2 - Introduction1:55
Surface Area of a Combination of Solids: When combination of any two figures like - cone (or) sphere (or) hemisphere (or) cylinder (or) cube (or) cuboid is given
Session 2 - Q 15:53
Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take π = 22/7)
Session 2 - Q 29:03
A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take π = 3.14)
Session 2 - Q 34:39
The decorative block shown in Fig. is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π = 22/7)
Session 2 - Q 44:55
In given fig., from a cuboidal solid metallic block of dimensions 15 cm × 10 cm × 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block. [ Use π = 22/7]
Test your understanding
Home Assignment
Session 3 - Introduction2:18
Surface Area of a Combination of Solids:
When combination of cylinder or half cylinder and sphere (or) hemisphere (or) cube (or) cuboid is given.
When combination of two or more than two figures of same type is given.
Session 3 - Q 14:30
Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end (see Fig.). The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
(Take π = 22/7)
Session 3 - Q 22:57
Two cubes of 5 cm each are kept together joining edge to edge to form a cuboid. Find the surface area of the cuboid so formed.
Session 3 - Q 32:22
The radius of sphere is r cm. It is divided into two equal parts. Find the whole surface of two parts.
Session 3 - Q 43:40
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Test your understanding
Home Assignment
Session 4 - Introduction0:50
Volume of a Combination of Solids :
When combination of cone and sphere (or) hemisphere(or) cylinder is given.
When combination of sphere (or)hemisphere and cube (or) cuboid is given.
Session 4 - Q 17:30
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. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take π = 3.14)
Session 4 - Q 24:09
50 circular plates, each of radius 7 cm and thickness 1/2 cm, are placed one above another to form a solid right circular cylinder. Find the total surface area and the volume of the cylinder so formed.
Session 4 - Q 37:15
A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.
Test your understanding
Home Assignment
Session 5 - Introduction0:46
Volume of a Combination of Solids :
1. When combination of cylinder (or) half cylinder and sphere (or) hemisphere (or) cube (or) cuboid is given.
2. When combination of two or more than two figures of same type is given.
Session 5 - Q 15:50
Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see figure). If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of 300 m3, and there are 20 workers, each of whom occupy about 0.08 m3 space on an average. Then, how much air is in the shed? (Take π =22/7)
Session 5 - Q 23:29
A juice seller was serving his customers using glasses as shown in figure. 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 apparent capacity of the glass and its actual capacity. (Use π = 3.14.)
Session 5 - Q 33:13
A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. [Use π = 22/7]
Test your understanding
Home Assignment
Session 6 - Introduction3:45
Conversion of Solid from One Shape to Another.
Session 6 - Q 13:09
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
Session 6 - Q 25:17
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Session 6 - Q 36:30
A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Test your understanding
Home Assignment
Session 7 - Introduction1:27
Conversion of Solid from One Shape to Another :
water and canal related problems
Session 7 - Q 16:14
Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use = 3.14)
Session 7 - Q 24:03
A hemispherical tank full of water is emptied by a pipe at the rate of 3 4/7 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take π = 22/7)
Session 7 - Q 34:31
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
Test your understanding
Home Assignment
Session 8 - Introduction3:44
Frustum of a Cone.
Session 8 - Q 18:11
The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm (see figure). Find its volume, the curved surface area and the total surface area(Take π = 22/7).
Session 8 - Q 23:17
Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see figure). If each cm3 of molasses has mass about 1.2 g, find the mass of the molasses that can be poured into each mould. [Take π = 22/7]
Session 8 - Q 34:45
An open metal bucket is in the shape of a frustum of a cone, mounted on ahollow cylindrical base made of the same metallic sheet (see figure). 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 area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. [Take π = 22/7 ]
Session 8 - Q 44:54
A cone is cut by a plane parallel to the base and upper part is removed. If the curved surface area of upper cone is 1/9 times the curved surface of original cone. Find the ratio of line segment to which the cone's height is divided by the plane.
Test your understanding
Home Assignment
Exercise 13.1 - Q 15:46
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Exercise 13.1 - Q 27:04
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Exercise 13.1 - Q 312:00
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Exercise 13.1 - Q 49:23
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Exercise 13.1 - Q 58:55
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.
Exercise 13.1 - Q 68:50
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Exercise 13.1 - Q 79:31
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹ 500 per m2. (Note that the base of the tent will not be covered with canvas.)
Exercise 13.1 - Q 811:02
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
Exercise 13.1 - Q 96:05
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Exercise 13.2 - Q 15:20
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
Exercise 13.2 - Q 29:41
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Exercise 13.2 - Q 312:58
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 (see Fig. 13.15).
Exercise 13.2 - Q 411:43
A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by
3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 13.16).
Exercise 13.2 - Q 58:06
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.
Exercise 13.2 - Q 611:13
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 cm3 of iron has approximately 8g mass. (Use π = 3.14)
Exercise 13.2 - Q 710:46
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Exercise 13.2 - Q 89:20
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π = 3.14.
Exercise 13.3 - Q 15:56
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Exercise 13.3 - Q 27:38
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Exercise 13.3 - Q 38:22
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.
Exercise 13.3 - Q 412:14
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Exercise 13.3 - Q 512:04
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Exercise 13.3 - Q 68:27
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
Exercise 13.3 - Q 711:26
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Exercise 13.3 - Q 811:56
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Exercise 13.3 - Q 99:49
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?
Exercise 13.4 - Q 15:13
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
Exercise 13.4 - Q 25:59
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
Exercise 13.4 - Q 36:10
A fez, the cap used by the Turks, is shaped like the frustum of a cone (see Fig. 13.24). If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.
Exercise 13.4 - Q 411:48
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 the milk which can completely fill the container, at the rate of ₹ 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 8 per 100 cm2. (Take π = 3.14)
Exercise 13.4 - Q 513:10
A metallic right circular cone 20 cm high and whose vertical angle is 60° 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 1/16 cm, find the length of the wire.
Exercise 13.5 - Q 111:11
determine the length of a 3 mm copper wire needed to wrap a 12 cm by 10 cm cylinder in 40 rounds and compute its mass using 8.88 g/cm³ density.
Exercise 13.5 - Q 213:52
Revolve a 3-4-5 right triangle about its hypotenuse to form a double cone; radius 12/5 cm, heights 9/5 and 16/5 cm, volume 30.14 cm^3 and surface area 52.75 cm^2.
Exercise 13.5 - Q 311:37
Compute the number of porous bricks that can be added to a cuboid cistern without overflow, considering 1/17 water absorption per brick, yielding 1792 bricks.
Exercise 13.5 - Q 46:44
Compute rainfall volume over a 7280 km² valley with 10 cm rainfall, convert to km³, and show it nearly matches the combined volume of three rivers.
Exercise 13.5 - Q 57:25
Calculate tin sheet area for a funnel made of a 10 cm cylinder and a frustum with diameter 18 cm using curved surface areas and a 13 cm slant height.
Exercise 13.5 - Q 616:54
Derive the curved and total surface areas of a frustum of a cone using similar triangles and Pythagoras, with slant height L = sqrt(h^2+(r1−r2)^2) and TSA = pi L(r1+r2)+pi(r1^2+r2^2).
Exercise 13.5 - Q 711:46
Derive the frustum volume by subtracting the smaller cone from the larger cone, using similar triangles to relate heights and radii, yielding V = (1/3)πh(r1^2 + r2^2 + r1 r2).

Session 1 - Introduction8:13
Introduction:
Session 1 - Q 12:58
Find the mean of first five odd multiples of 5.
Session 1 - Q 22:21
If the mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, find the value of x.
Session 1 - Q 33:36
If the mean of 25 observations is 27 and each observation is decreased by 7, what will be the new mean?
Session 1 - Q 43:50
The mean of the marks secured by 15 students of section A of class X is 40, that of 25 students of section B is 50 and that of 20 students of section C is 60. Find the combined mean of the marks of students of three sections of class X.
Test your understanding
Home Assignment
Session 2 - Introduction4:14
Method of Calculating Mean of Grouped Data by Direct Method
Session 2 - Q 14:27
The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students
Session 2 - Q 26:19
The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by Direct method.
Session 2 - Q 35:10
If the mean of the following frequency distribution is 24, find the value of p.
Test your understanding
Home Assignment
Session 3 - Introduction3:51
Mean of Grouped Data by Assumed Mean Method
Session 3 - Q 18:02
The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all the three methods discussed in this section.
Percentages of female teacher 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85
Number of states/U.T. 6 11 7 4 4 2 1
Session 3 - Q 24:39
For the following distribution, calculate mean by using direct assumed mean method.
Class interval 1 – 4 4 – 9 9 – 16 16 – 27
Frequency 6 12 26 20
Session 3 - Q 34:42
Find the mean of the following frequency distribution using a suitable method:
Class 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency 25 40 42 33 10
Test your understanding
Home Assignment
Session 4 - Introduction4:40
Mean of Grouped Data by Step Deviation Method
Session 4 - Q 16:55
The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by Step Deviation Method.

Percentages of female teacher 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85
Number of states/U.T. 6 11 7 4 4 2 1
Session 4 - Q 27:04
The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?
Number of wickets 20 - 60 60 - 100 100 - 150 150 – 250 250 – 350 350 - 450
Number of bowlers 7 5 16 12 2 3
Session 4 - Q 36:38
The mean of the following distribution is 31.4. Determine the missing frequency x.
Class 0 - 10 10 -20 20 -30 30 -40 40 -50 50 - 60
Frequency 5 x 10 12 7 8
Test your understanding
Home Assignment
Session 5 - Introduction7:22
Mode of Grouped Data
Session 5 - Q 11:33
The wickets taken by a bowler in 10 cricket matches are as follows:
2 6 4 5 0 2 1 3 2 3
Find the mode of the data.
Session 5 - Q 23:53
A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in ahousehold:
Family size 1 – 3 3 – 5 5 – 7 7 - 9 9 - 11
Number of families 7 8 2 2 1
Find the mode of this data.
Session 5 - Q 34:13
Following frequency distribution shows the daily expenditure on milk of 30 households in a locality:
Daily expenditure on milk (in Rs) 0 - 30 30 -60 60 -90 90 -120 120-150
Number of households 5 6 9 6 4
Find the mode for the above data
Session 5 - Q 45:16
On Sports Day of a school, agewise participation of students is shown in the following distribution:
Age(in years) 5-7 7-9 9-11 11-13 13-15 15-17 17-19
Number of students x 15 18 30 50 48 x
Find the mode of the data. Also, find the missing frequencies when sum of frequencies is 181.
Session 5 - Q 54:10
The mode of the following data is 36. Find the missing frequency x in it.
Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 8 10 x 16 12 6 7
Test your understanding
Home Assignment
Session 6 - Introduction7:29
Median of ungrouped &Grouped Data
Session 6 - Q 12:10
Find the median of the first ten prime numbers.
Session 6 - Q 22:17
The median of the observations 21, 24, 27, 30, (x – 1), (x + 1), 35, 38, 48 and 50 arranged in ascending order is 33. Then, find the value of x.
Session 6 - Q 32:06
Find the median of the following data.
Marks obtained 20 29 28 42 19 35 51
Number of students 3 4 5 7 9 2 3
Session 6 - Q 41:52
Find the unknown values in the following table :
Class Interval Frequency Cumulative Frequency
0 - 10 5 5
10 - 20 7 x1
20 - 30 x2 18
30 - 40 5 x3
40 - 50 x4 30
Test your understanding
Home Assignment
Session 7 - Introduction2:19
Median for Grouped Data&Missing frequency
Session 7 - Q 15:44
The weekly expenditure of 500 families is tabulated below:
Session 7 - Q 26:35
A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data was obtained:
Session 7 - Q 34:56
Find the median of the following data :
Session 7 - Q 45:20
The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
Test your understanding
Home Assignment
Session 8 - Introduction2:21
Relationship between Mean, Median and Mode
Session 8 - Q 12:41
Find the mean of the data using an empirical formula when it is given that mode is 50.5 and median is 45.5.
Session 8 - Q 22:21
If the median of a series exceeds the mean by 3, find by what number the mode exceeds its mean?
Session 8 - Q 32:16
If the median of a series exceeds the mean by 3, find by what number the mode exceeds its mean?
Session 8 - Q 46:30
Recently the half-yearly examination was conducted in DAV public school. The mathematics teacher maintains a record of the marks of 100 students. On the basis of the recorded data of the marks obtained in Mathematics, the histogram is given below:
On the basis of the above histogram, answer the following questions:
1. Identify the modal class from the given graph.
2. Find the mode of the following distribution of marks obtained by the students in an examination.
Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.
Test your understanding
Home Assignment
Session 9 - Introduction5:43
Graphical Representation of Cumulative Frequency Distribution:
Less than Type O give
Session 9 - Q 16:57
The marks scored by 750 students in an examination are given in the form of a frequency distribution table:
Prepare a cumulative frequency table of less than type and draw an ogive
Session 9 - Q 27:10
For an ogive graph, we have to prepare the cumulative frequency table of less than type which is given below
Now, we make the upper class limits along X-axis on a suitable scale and cumulative frequency along Y-axis on a suitable scale on the graph paper. Then, plot the points (640, 16), (680, 61), (720, 217), (760, 501), (800, 673), (840, 732) and (880, 750).
On joining these points by a smooth curve we get an ogive of less than type.
GRAPH
Session 9 - Q 36:05
The following distribution gives the daily income of 50 workers of a factory
Convert the distribution to a 'less than type' cumulative frequency distribution and draw its ogive. Hence obtain the median of daily income
Test your understanding
Home Assignment
Session 10 - Introduction3:44
Graphical Representation of Cumulative Frequency Distribution:
More than Type Ogive
Session 10 - Q 14:47
Graphical Representation of Cumulative Frequency Distribution:
More than Type Ogive
Session 10 - Q 25:19
In an orchard, the numbers of apples on trees are given below :
Draw a 'more than type' ogive and hence obtain median from the curve.
Session 10 - Q 38:50
The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution :
Draw both ogives for the data above. Hence obtain the median profit
Test your understanding
Home Assignment
Exercise 14.1 - Q 110:39
A survey was conducted by a group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Which method did you use for finding the mean, and why?
Exercise 14.1 - Q 212:13
Consider the following distribution of daily wages of 50 workers of a factory.

Find the mean daily wages of the workers of the factory by using an appropriate method.
Exercise 14.1 - Q 312:59
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs18. Find the missing frequency f.
Exercise 14.1 - Q 411:44
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.
Exercise 14.1 - Q 511:46
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Exercise 14.1 - Q 610:35
The table below shows the daily expenditure on food of 25 households in a locality.
Daily expenditure
(in ₹) 100 – 150 150 – 200 200 – 250 250 - 300 300 - 350
Number of households 4 5 12 2 2

Find the mean daily expenditure on food by a suitable method.
Exercise 14.1 - Q 710:09
To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
Concentration of SO2 (in ppm)
frequency
0.00 – 0.04
0.04 – 0.08
0.08 – 0.12
0.12 – 0.16
0.16 – 0.20
0.20 – 0.24
4
9
9
2
4
2

Find the mean concentration of SO2 in the air.
Exercise 14.1 - Q 89:43
A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Exercise 14.1 - Q 97:50
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Exercise 14.2 - Q 114:58
The following table shows the ages of the patients admitted in a hospital during a year:
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency
Exercise 14.2 - Q 27:12
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :
Determine the modal lifetimes of the components.
Exercise 14.2 - Q 316:09
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure :
Exercise 14.2 - Q 413:11
The following distribution gives the state-wise teacher-student ratio in higher
secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
Exercise 14.2 - Q 55:50
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
Find the mode of the data
Exercise 14.2 - Q 66:01
A student noted the number of cars passing through a spot on a road for 100
periods each of 3 minutes and summarised it in the table given below. Find the mode of the data :
Exercise 14.3 - Q 121:26
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
Exercise 14.3 - Q 211:11
If the median of the distribution given below is 28.5, find the values of x and y.
Exercise 14.3 - Q 311:44
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
Exercise 14.3 - Q 47:17
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :
Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)
Exercise 14.3 - Q 57:59
The following table gives the distribution of the life time of 400 neon lamps
Find the median life time of a lamp.
Exercise 14.3 - Q 620:45
100 surnames were randomly picked up from a local telephone directory and the
frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames
Exercise 14.3 - Q 76:05
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Exercise 14.4 - Q 114:05
The following distribution gives the daily income of 50 workers of a factory.
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive
Exercise 14.4 - Q 218:57
During the medical check-up of 35 students of a class, their weights were recorded as follows:
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula
Exercise 14.4 - Q 314:00
The following table gives production yield per hectare of wheat of 100 farms of a village.
Change the distribution to a more than type distribution, and draw its ogive

Session 1 - Introduction14:25
Introduction
Session 1 - Q 11:40
Find the probability that a number selected at random from the numbers 1, 2, 3,....., 15 is a multiple of 4.
Session 1 - Q 21:44
A single letter is selected at random from the word "PROBABILITY". Find the probability that it is vowel.
Session 1 - Q 31:54
The probability of guessing the correct answer to certain question is p/12. If the probability of not guessing the correct answer to same question is 34, find the value of p.
Test your understanding
Home Assignment
Session 2 - Introduction2:37
Probability—A Theoretical Approach : Problems is based on tossing a coin(s)
Session 2 - Q 11:38
Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.
Session 2 - Q 21:37
Harpreet tosses two different coins simultaneously (say, one is of ₹1 and other of ₹2). What is the probability that she gets at least one head?
Session 2 - Q 32:28
A game consists of tossing a one-rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.
Session 2 - Q 42:09
Three different coins are tossed together. Find the probability of getting
1. Exactly two heads.
2. at least two heads
3. at least two tails
Test your understanding
Home Assignment
Session 3 - Introduction2:43
Probability—A Theoretical Approach : Problems is based on throwing a die(s)
Session 3 - Q 12:47
Suppose we throw a die once.
(i) What is the probability of getting a number greater than 4?
(ii) What is the probability of getting a number less than or equal to 4?
Session 3 - Q 24:52
Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is
(i) 8? (ii) 13? (iii) Less than or equal to 12?
Session 3 - Q 32:14
A pair of dice is thrown once. Find the probability of getting
1. even number on each dice
2. a total of 9.
Session 3 - Q 41:12
Two dice are thrown together. The probability of getting the same number on both dice is
Test your understanding
Home Assignment
Session 4 - Introduction2:46
Probability—A Theoretical Approach : Problems is based on playing cards
Session 4 - Q 12:49
One card is drawn from a well-shuffled deck of 52 cards. Calculate theprobability that the card will
(i) be an ace,
(ii) Not be an ace.
Session 4 - Q 21:41
A card is drawn at random from a well shuffled pack of 52 cards. Find the probability of getting a black face card.
Session 4 - Q 32:14
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king.
Session 4 - Q 44:11
The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card
1. of spade
2. of black king
3. of club
4. of jacks
Test your understanding
Home Assignment
Session 5 - Introduction2:02
Probability—A Theoretical Approach : Problems is based on selection of an object (or) thing from a box(or) bag.
Session 5 - Q 12:26
A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the:
(i) Yellow ball? (ii) Red ball? (iii) Blue ball?
Session 5 - Q 22:18
A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be
(i) White? (ii) Blue? (iii) Red?
Session 5 - Q 32:12
A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that
(i) It is acceptable to Jimmy?
(ii) It is acceptable to Sujatha?
Session 5 - Q 43:17
A bag contains 18 balls out of which x balls are red. If two more red balls are put in the bag, the probability of drawing a red ball will be 9/8times the probability of drawing first case. Find the value of x.
Session 5 - Q 53:56
A piggy bank contains hundred 50-p coins, fifty ₹1 coins, twenty ₹2 and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability the coin falling out will be (i) a 50-p coin, (ii) of value more than ₹1, (iii) of value less than ₹5 (iv) a ₹1 or ₹2 coin.
Test your understanding
Home Assignment
Session 6 - Introduction2:50
Probability—A Theoretical Approach : Problems is based on geometry& Spinning wheel
Session 6 - Q 13:05
A missing helicopter is reported to have crashed somewhere in the rectangular region shown in Fig. 15.2. What is the probability that it crashed inside the lake shown in the figure?
Session 6 - Q 22:50
Figure shows the top view of an open square box that is divided into 6 compartments with walls of equal height. Each of the rectangles D, E, F has twice the area of each of the square A, B and C. when a marble is dropped into the box at random, it falls into one of the compartments. What is the probability that it will fall into compartment F?
Session 6 - Q 34:20
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3, ..., 12 as shown in the figure. What is the probability that it will point to

1. 6
2. An even number?
3. A prime number?
4. A number which is a multiple of 5?
Session 6 - Q 41:30
A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2, or 3) see figure. Are the outcomes 1, 2 and 3 equally likely to occur? Give reason.
Test your understanding
Home Assignment
Session 7 - Introduction1:16
Probability: Miscellaneous problems
Session 7 - Q 11:54
Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match?
Session 7 - Q 23:34
Savita and Hamida are friends. What is the probability that both will have
(i) Different birthdays?
(ii) The same birthday? (Ignoring a leap year).
Session 7 - Q 31:35
What is the probability that a non-leap year has 53 Mondays?
Session 7 - Q 42:36
There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of
(i) A girl?
(ii) A boy?
Session 7 - Q 52:49
In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?
Session 7 - Q 62:40
A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.
Test your understanding
Home Assignment
Exercise 15.1 - Q 18:02
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ = _________.
(ii) The probability of an event that cannot happen is _________. Such an event is called _________.
(iii) The probability of an event that is certain to happen is ___________. Such an event is called ________.
(iv) The sum of the probabilities of all the elementary events of an experiment is __________.
(v) The probability of an event is greater than or equal to and less than or equal to __________.
Exercise 15.1 - Q 24:25
Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iii) A trial is made to answer a true-false question. The answer is right or wrong.
(iv) A baby is born. It is a boy or a girl.
Exercise 15.1 - Q 31:53
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?
Exercise 15.1 - Q 42:13
Which of the following cannot be the probability of an event?
(A) 2/3 (B) –1.5 (C) 15% (D) 0.7
Exercise 15.1 - Q 53:04
If P (E) = 0.05, what is the probability of ‘not E’?
Exercise 15.1 - Q 62:31
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
(i) An orange flavoured candy?
(ii) A lemon flavoured candy?
Exercise 15.1 - Q 72:53
It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
Exercise 15.1 - Q 84:36
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is
(i) Red? (ii) Not red?
Exercise 15.1 - Q 94:27
A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
(i) Red? (ii) White? (iii) Not green?
Exercise 15.1 - Q 106:03
A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin
(i) Will be a 50 p coin? (ii) Will not be a ₹5 coin?
Exercise 15.1 - Q 112:53
Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see
Fig. 15.4). What is the probability that the fish taken out is a male fish?
Exercise 15.1 - Q 127:35
A game of chance consists of spinning an arrow
which comes to rest pointing at one of the numbers
1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 15.5), and these are equally likely outcomes. What is the probability that it will point at
(i) 8?
(ii) An odd number?
(iii) A number greater than 2?
(iv) A number less than 9?
Exercise 15.1 - Q 134:31
A die is thrown once. Find the probability of getting
(i) A prime number; (ii) a number lying between 2 and 6; (iii) an odd number.
Exercise 15.1 - Q 149:34
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour (ii) a face card (iii) a red face card
(iv) the jack of hearts (v) a spade (vi) the queen of diamonds
Exercise 15.1 - Q 155:49
Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is the queen?
(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) An ace? (b) A queen?
Exercise 15.1 - Q 163:58
12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
Exercise 15.1 - Q 178:01
(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot.
What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
Exercise 15.1 - Q 1810:02
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears
(i) A two-digit number (ii) A perfect square number (iii) A number divisible by 5.
Exercise 15.1 - Q 193:05
A child has a die whose six faces show the letters as given below:

The die is thrown once. What is the probability of getting (i) A? (ii) D?
Exercise 15.1 - Q 205:44
Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?
Exercise 15.1 - Q 216:01
A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it? (ii) She will not buy it?
Exercise 15.1 - Q 2216:57
Refer to Example 13. (i) Complete the following table:

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability1/11. Do you agree with this argument?
Justify your answer.
Exercise 15.1 - Q 236:30
A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Exercise 15.1 - Q 245:16
A die is thrown twice. What is the probability that
(i) 5 will not come up either time? (ii) 5 will come up at least once?
[Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]
Exercise 15.1 - Q 254:59
Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3.
(ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.
Exercise 15.2 - Q 113:52
Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on
(i) The same day? (ii) Consecutive days? (iii) Different days?
Exercise 15.2 - Q 211:42
A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

What is the probability that the total score is
(i) Even? (ii) 6? (iii) At least 6?
Exercise 15.2 - Q 36:00
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.
Exercise 15.2 - Q 48:18
A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.
Exercise 15.2 - Q 55:21
A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue balls in the jar.

Requirements

Basic knowledge of fundamental operations - addition, subtraction, product, and division.
Basic elementary math knowledge.
Each chapter includes prerequisite knowledge classes in which the child gains extensive knowledge and a thorough understanding of the chapters.

Description

This course is carefully designed to explain various chapters of CBSE Grade 10 Math with video lectures of fully solved exercises and optional exercises.
It has 389 lectures spanning around 44 hours of on-demand videos that are divided into 7 sections, and each chapter is a section and further divided into simple sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key. The students are encouraged to solve practise questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand it very well.
It covers 100% video solutions of the NCERT exercises, NCERT optional exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning math and never feel that math is troublesome.

Topics covered in the course:

Some Applications of Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

With this course you'll also get:

Perfect your mathematical skills on CBSE, SSC, and other board exam preparations.

A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations as well as job aspirants.
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the solving different real life situations as well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.
These are the people whose jobs require them to solve basic daily math-related problems.

Become a master of CBSE Grade 10 Math and score high—Part 2.

What you'll learn

Explore related topics

Course content

Some Applications of Trigonometry38 lectures • 4hr 44min

Circles37 lectures • 3hr 37min

Constructions34 lectures • 5hr 28min

Areas Related to Circles69 lectures • 7hr 56min

Surface Areas and Volumes73 lectures • 8hr 48min

Statistics71 lectures • 8hr 34min

Probability67 lectures • 4hr 51min

Requirements

Description

Who this course is for: