Category: Class 9 Maths

Important Questions CBSE  Class 9 Mathematics Chapter 4 Circles

The topics and sub-topics in NCERT Class 9 Maths Textbook Chapter 10 Circles:

• Circles
• Introduction
• Circles And Its Related Terms: A Review
• Angle Subtended By A Chord At A Point
• Perpendicular From The Centre To A Chord
• Circle Through Three Points
• Equal Chords And Their Distances From The Centre
• Angle Subtended By An Arc Of A Circle
• Cyclic Quadrilaterals
• Summary

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS
1. In the given figure, O is the centre of the circle with chords AP and BP being produced to R and Q respectively. If ∠QPR = 35°, find the measure of ∠AOB. [CBSE-14-17DIG1U]

Answer.

2. In the given figure, what is the measure of angle x ?

Answer. We know that exterior angle of a cyclic quadrilateral is equal to interior opposite angle.
.-. ∠CBE = ∠ADC
=> x = 120°

More Resources for CBSE Class 9

• NCERT Solutions
• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

3. In the given figure, if O is the centre of circle and ∠POQ = 110°, then find ∠PRQ

Answer. We know that angle subtended by an arc at the centre is double the angle subtended by it at the remaining part of the circle.
∠PRQ =1/2 ∠POQ
= 1/2 x 110°
= 55°

4. In the given figure, ΔABC is an equilateral triangle and ABDC is a cyclic quadrilateral, then find the measure of ∠BDC.

Answer.

5. In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If ∠PRQ = l and ∠OPQ = m, then find l + m.

Answer.

6. The given figure shows a circle with centre O in which a diameter AB bisects the chord PQ at the point R. If PR = RQ = 8 cm and RB = 4 cm, then find the radius of the circle.

Answer.

7. In the given figure, ABCD is a cyclic quadrilateral such that ∠ADB= 40° and ∠DCA = 70°, then find the measure of ∠DAB .

Answer.

8. In the figure, ‘O’ is the centre of the circle, ∠ABO= 20° and ∠ACO= 30°, where A, B, C are points on the circle. What is the value of x ?

Answer.

9. In the given figure, if O is the centre of circle. Chord AB is equal to radius of the circle, then find ∠ACB.

Answer.

10. In the given figure, if ∠OAB = 40°, then find the measure of ∠ACB. [NCERT Exemplar Problem]

Answer.

11. In the given figure, O is the centre of the circle. If∠BOC= 120°, then find the value of x.

Answer.

12. In the given figure, O is the centre of the circle, then compare the chords.

Answer. In chords AB and CD, AB is passing through the centre of the circle. AB is the diameter of circle. Thus, AB>CD [v diameter is the largest chord]

13. In the given figure, ∠ACP = 40° and ∠BPD = 120°, then find ∠CBD .

Answer.

14. In the given figure, if ∠SEC = 120°, ∠DCE = 25°, then find ∠BAC.

Answer.

15. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, then find the distance of AB from the centre of the circle. [CBSE March 2012]

Answer.

16. In the given figure, if ∠DAB = 60°, ∠ABD= 50°, then find ∠ACB. [NCERT Exemplar Problem]

Answer.

17. In the given figure, AB || DC. If ∠A = 50°, then find the measure of ∠ABC. [NCERT Exemplar Problem]

Answer.

SHORT ANSWER QUESTIONS TYPE-I
18. Equal chords of a circle subtend equal angles at the centre. [CBSE March 2012]
Answer.

19. If the angles subtended by the chords of a circle at the centre are equal, then chords are equal. [CBSE March 2012]
Answer.

20. In the figure, O is the centre of the circle and ∠ABC= 45°. Show that OA⊥OC[/latex]. [CBSE March 2013]

Answer. Since angle subtended by an arc at the centre of the circle is double the angle subtended it at any point on the remaining part of the circle.

21. In the given figure, ∠PQR= 100°, where P,Q and R are points on a circle with centre O. Find ∠OPR. [CBSE March 2012]

Answer.

22. In figure, ABCD is a cyclic quadrilateral in which AB is extended till F and BE || DC. If ∠FBE= 20° and ∠DAB = 95°, then find∠ADC. [CBSE March 2012]

Answer.

23. In the figure, chord AB of circle with centre O, is produced to C such that BC = OB. CO is joined and produced to meet the circle in D. If ∠ACD = y and ∠AOD= x, show that x = 3y. [CBSE March 2011 ]

Answer.

24. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see fig.). [CBSE March 2013]

Answer. Draw OM⊥ l
Since perpendicular from the centre of a circle to a chord of the circle bisects the chord.
BM = CM …(i)
and AM = DM …(ii)
Subtracting (i) from (ii), we have
AM – BM = DM – CM
AB = CD

25. In the given figure, P is the centre of the circle. Prove that : ∠ XPZ = 2(∠ XZY +∠  YXZ)

Answer.

26. Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see fig.). Prove that ∠ ACP =∠ QCD.

Answer.

27. If the diagonals of a cyclic quadrilateral are diameters of the circle through the opposite vertices of the quadrilateral. Prove that the quadrilateral is a rectangle. [CBSE-14-GDQNI3W]
Answer.

SHORT ANSWER QUESTIONS TYPE-II
28. If the non-parallel sides of a trapezium are equal, prove that it is cyclic. [CBSE March 2013]
Answer.

29. ABCD is a parallelogram. The circle through A, B and C intersects (produce if necessary) at E. Prove that AE = AD.
Answer.

30. ABCD is a cyclic quadrilateral in which AB and CD when produced meet in E and EA = ED. Prove that : (i) AD\\BC (ii) EB = EC
Answer.

31. If two equal chords of a circle intersect within a circle, prove that the line segment joining the point of intersection to the centre makes equal angles with the chords. [CBSE-15-NS72LP7]
Answer.

32. Two circles whose centres are O and O’ intersect at P. Through P, a line parallel to OO’, intersecting the circles at C and D is drawn as shown in the figure. Prove the CD = 200′. [CBSE-15-6DWMW5A] [CBSE-14-ERFKZ8H]

Answer.

33. If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC . [NCERT Exemplar Problem]
Answer.

34. In the given figure, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively. If ∠ POQ  = 120°, find ∠APQ . [CBSE-14-ERFKZ8H]

Answer.

LONG ANSWER TYPE QUESTIONS
35. Show that the quadrilateral formed by angle bisectors of a cyclic quadrilateral, is also cyclic. [CBSE March 2012]

Answer.

36. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. [CBSE March 2012]
Answer.

37. Prove that the angle bisectors of the angle formed by producing opposite sides of a cyclic quadrilateral (provided they are not parallel) intersect at right angle.
Answer.

38. Bisectors of angles A, B and C of triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the ΔDEF are 90° -∠ A/2 ,90° – ∠ B/2 and 90°- ∠ C/2 respectively.
Answer.

39. In the given figure, O is the centre of a circle of radius r cm, OP and OQ are perpendiculars to AB and CD respectively and PQ = 1 cm. If AB II CD, AB = 6cm and CD = 8cm, determiner. [ CBSE-15-6DWMW5A]

Answer. Since the perpendicular drawn from the centre of the circle to a chord bisects the chord. Therefore, P and Q are mid-points of AB and CD respectively.

40. If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see fig.), prove that arc CXA + arc DZB = arc AYD + arc BWC = semicircle. [NCERT Exemplar Problem]

Answer. Given two chords AB and CD of a circle intersect at right angle. Let P be the point of intersection of the chord and O be the centre of circle AYDZBWCX.

41. In the given figure, AC is a diameter of the circle with centre O. Chord BD is perpendicular to AC. Write down the measures of angles a, b, c and d in terms of x. [CBSE-15-NS72LP7]

Answer.

42. The bisector of \(\angle B\) of an isosceles triangle ABC with AB = AC meets the circumcircle of ΔABC at P as shown in the given figure. If AP and BC produced meet at Q, prove that CQ = CA. [CBSE-14-GDQNI3W]

Answer.

Value Based Questions
1. A small cottage industry employing people from a nearby slum area prepares round table cloths having six equal designs in the six segment formed by equal chords AB, BC, CD, DE, EF and FA. If O is the centre of round table cloth (see figure). Find \(\angle AOB\), \(\angle AEB \) and \(\angle AFB\).What value is depicted through this question ? [CBSE-14-17DJG1U]

Answer.

Value depicted : By employing people from a slum area to prepare round table cloths realize their social responsibility to work for helping the ones in need.

2. Three students Priyanka, Sania and David are protesting against killing innocent animals for commercial purposes in a circular park of radius 20 m. They are standing at equal distances on its boundary by holding banners in their hands.
(i) Find the distance between each of them.
(ii) Which mathematical concept is used in it ?
(iii) How does an act like this reflects their attitude towards society ?
Answer.

3. A circular park of radius 10 m is situated in a colony. Three students Ashok, Raman and Kanaihya are standing at equal distances on its circumference each having a toy telephone in his hands to talk each other about Honesty, Peace and Discipline.
(i) Find the length of the string of each phone.
(ii) Write the role of discipline in students’ life.
Answer. Let us assume, A, B and C be the position of three students Ashok, Raman and Kanaihya respectively on the circumference of the circular park with centre O and radius 10 m. Since the centre of circle coincides with the centroid of the equilateral ΔABC.

4. Three scouts Rajat, Rohit and Ramit in the cultural show holded three stringed balloons with a message ‘Stop Child Labour’. Keeping themselves on the boundary of a circle of radius 25 cm, each scout holded the string tightly. Find the distance between Rajat and Ramit, when distance between Rajat and Rohit and Rohit and Ramit is 30 cm. What message was given by scouts and why ?
Answer.

Important Questions for CBSE Class 9 Mathematics Chapter 5 Constructions

The topics and sub-topics in NCERT Class 9 Maths Text Book Chapter 11 Constructions:

• Constructions
• Introduction
• Basic Constructions
• Some Constructions Of Triangles
• Summary

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS
1. Construct an angle of 90° at the initial point of the given ray. [CBSE-15-6DWMW5A]
Answer.

2. Draw a line segment PQ = 8.4 cm. Divide PQ into four equal parts using ruler and compass. [CBSE-14-ERFKZ8H], [CBSE – 14-GDQNI3W], [CBSE-14-17DIG1U]
Answer. Steps of construction :

1. Draw a line segment PQ = 8.4 cm.
2. With P and Q as centres, draw arcs of radius little more than half of PQ. Let his line intersects PQ in M.
3. With M and Q as centres, draw arcs of radius little more than half of MQ. Let this line intersects PQ in N.
4. With P and M as centres, draw arcs of radius little more than half of PM. Let this line intersects PQ in L. Thus, L, M and N divide the line segment PQ in four equal parts.
   

More Resources for CBSE Class 9

• NCERT Solutions
• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

3. Draw any reflex angle. Bisect it using compass. Name the angles so obtained. [CBSE-15-NS72LP7]
Answer.

4. Why we cannot construct a ΔABC, if ∠A=60°, AB — 6 cm, AC + BC = 5 cm but construction of A ABC is possible if ∠A=60°, AB = 6 cm and AC – BC = 5 cm. [CBSE-14-GDQNI3W]
Answer. We know that, by triangle inequality property, construction of triangle is possible if sum of two sides of a triangle is greater than the third side.
Here, AC + BC = 5 cm which is less than AB ( 6 cm)
Thus, ΔABC is not possible.
Also, by triangle inequality property, construction of triangle is possible, if difference of two
sides of a triangle is less than the third side
Here, AC – BC = 5 cm, which is less than AB (6 cm)
Thus, ΔABC is possible.

5. Construct angle of \({{\left[ 52\frac{1}{2} \right]}^{0}}\) using compass only. [CBSE-14-17DIG1U]
Answer.

SHORT ANSWER QUESTIONS TYPE-I
6. Using ruler and compass, construct 4∠XYZ, if ∠XYZ= 20° [CBSE-14-ERFKZ8H]
Answer.

7. Construct an equilateral triangle LMN, one of whose side is 5 cm. Bisect ∠ M of the triangle. [CBSE March 2012]
Answer. Steps of construction :

1.  Draw a line segment LM = 5 cm.
2. Taking L as centre and radius 5 cm draw an arc.
3. Taking M as centre and radius draw an other arc intersecting previous arc at N.
4. Join LN and MN. Thus, ΔLMN is the required equilateral triangle.
5. Taking M as centre and any suitable radius, draw an arc intersecting LM at P and MN at Q.
6. Taking P and Q as centres and same radii, draw arcs intersecting at S.
7. Join MS and produce it meet LN at R. Thus, MSR is the required bisector of ∠M.
   

SHORT ANSWER QUESTIONS TYPE-II
8. Construct a A ABC with BC = 8 cm, ∠B= 45° and AB – AC = 3.1 cm. [CBSE-15-NS72LP7]
Answer.

9. Construct an isosceles triangle whose two equal sides measure 6 cm each and whose base is 5 cm. Draw the perpendicular bisector of its base and show that it passes through the opposite vertex [CBSE-15-6DWMW5A]
Answer. Steps of construction :

1. Draw a line segment AB = 5 cm.
2. With A and B as centres, draw two arcs of radius 6 cm and let they intersect each other in C.
3.  Join AC and BC to get ΔABC.
4. With A and B as centres, draw two arcs of radius little more than half of AB. Let they intersect each other in P and Q. Join PQ and produce, to pass through C.
   

10. Construct a right triangle whose base is 8 cm and sum of the hypotenuse and other side is 16 cm.
Answer. Given : In ΔABC, BC = 8 cm, ∠B= 90° and AB + AC = 16 cm.
Required : To construct ΔABC.
Steps of construction:

1. Draw a line segment BC = 8 cm.
2. At B, Draw ∠CBX = 90°.
3. From ray BX, cut off BE = 16 cm.
4.  Join CE .
5. Draw the perpendicular bisector of EC meeting BE at A.
6. Join AC to obtain the required ΔABC.
   

11. To construct an isosceles ΔABC in which base BC = 4 cm, sum of the perpendicular from A to BC and side AB = 6.5 cm.
Answer. Given : In  ΔABC, BC = 4 cm and sum of the perpendicular from A to BC and side AB = 6.5 cm.
Required : To construct ΔABC.
Steps of construction :

1. Draw any line segment BC = 4 cm.
2. Draw ‘p’ the perpendicular bisector of BC and let it intersect BC in R
3. Cut off PQ = 6.5 cm.
4. Join QB.
5. Draw the perpendicular bisector of BQ and let it intersect PQ in A.
6. Join AB and AC. Thus, ΔABC is the required triangle.
   

12. Construct an  equilateral triangle of altitude 6 cm. [CBSE-15-6DWMW5A]
Answer. Steps of construction :

1. Draw any line l.
2. Take any point M on it and draw  a line p perpendicular to l.
3. With M as centre, cut off MC = 6 cm
4. At C, with initial line CM construct angles of measures 30° on both sides and let these lines intersect line l in A and B. Thus, ΔABC is the required triangle.
   

13. Draw a line segment QR = 5 cm. Construct perpendiculars at point Q and R to it. Name them as QX and RY respectively. Are they both parallel ? [CBSE-15-NS72LP7] [CBSE-14-ERFKZ8H]
Answer. Steps of construction :

1. Draw a line segment QR = 5 cm.
2. With Q as centre, construct an angle of 90° and let this line through Q is QX.
3. With R as centre, construct an angle of 90° and let this line through R is RY. Yes, the perpendicular lines QX and- RY are parallel.
   

LONG ANSWER TYPE QUESTIONS
14. Construct a triangle ABC in which BC = 4.7 cm, AB + AC = 8.2 cm and ∠C = 60°. [CBSE March 2012]
Answer. Given : In ΔABC, BC= 4.7 cm, AB + AC = 8.2 cm and ∠C= 60°.
Required : To construct ΔABC.

15. To construct a triangle, given its perimeter and its two base angles, e.g., construct a triangle with perimeter 10 cm and base angles 60° and 45°. [CBSE March 2012]
Answer.

16. Construct ΔXYZ, if its perimeter is 14 cm, one side of length 5 cm and ∠X= 45°. [CBSE-14-ERFKZ8H]
Answer. Here, perimeter of ΔXYZ = 14 cm and one side XY = 5 cm
.-. YZ + XZ = 14 – 5 = 9 cm and ∠X = 45°.
Steps of construction :

1. Draw a line segment XY = 5 cm.
2. Construct an ∠YXA = 45° with the help of compass and ruler.
3. From ray XA, cut off XB – 9 cm.
4. Join BY.
5. Draw perpendicular bisector of BY and let it intersect XB in Z.
6. Join ZY. Thus, ΔXYZ is the required triangle.
   

Important Questions for CBSE  Class 9 Mathematics Chapter 6 Surface Areas and Volumes

NCERT Solutions for Class 9 Maths Chapter 13  – Surface Areas and Volumes Topics and Sub Topics

• Surface Areas And Volumes
• Introduction
• Surface Area of a Cuboid and a Cube
• Surface Area of a Right Circular Cylinder
• Surface Area of a Right Circular Cone
• Surface Area of a Sphere
• Volume of a Cuboid
• Volume of a Cylinder
• Volume of a Right Circular Cone
• Volume of a Sphere
• Summary

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS
1. How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm ? [CBSE-14-GDQNI3W]
Answer.

2. The total surface area of a cube is 726 cm². Find the length of its edge. [CBSE-14-ERFKZ8H]
Answer.

More Resources for CBSE Class 9

• NCERT Solutions
• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

3. If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions 8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be carried in the wooden box. [CBSE-14-GDQNI3W]
Answer.

4. Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area of the cuboid. [CBSE-15-NS72LP7]
Answer. When two cubes are joined end to end, then
Length of the cuboid = 6 + 6 = 12 cm
Breadth of the cuboid = 6 cm
Height of the cuboid = 6 cm
Total surface area of the cuboid = 2 (lb + bh + hi)
= 2(12 x6 + 6×6 + 6×12)
= 2(72 + 36 + 72) = 2(180) = 360 cm²

5. Calculate the edge of the cube if its volume is 1331 cm³. [CBSE-15-6DWMW5A]
Answer.

6. If in a cylinder, radius is doubled and height is halved, then find its curved surface area.
Answer.

7. The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.
Answer.

8. Find the area of the sheet required to make closed cylindrical vessel of height 1 m and diameter 140 cm.
Answer.

9. Find the volume of cone of radius r/2 and height ‘2h’.
Answer.

10. How many balls, each of radius 2 cm can be made from a solid sphere of lead of radius 8 cm ? [CBSE-14-17DIG1U]
Answer.

11. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of the sphere.[NCERT Exemplar Problem]
Answer.

12. If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere.
Answer.

13. The radius of a spherical balloon increases from 6 cm to 12 cm as air is being pumped into it. Then what will be the ratio of surface areas of the original balloon to the resulting new balloon ?
Answer.

14. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume. [CBSE-14-17DIG1U]
Answer. Inner radius of hollow sphere (r) = 10 cm Outer radius of hollow sphere (R) = 12 cm

15. In a cylinder, if radius is halved and height is doubled, then find the volume with respect to original volume. [NCERT Exemplar Problem]
Answer.

SHORT ANSWER QUESTIONS TYPE-I
16. A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball. [use π = 3.14] [CBSE-14-GDQNI3W]
Answer.

17. Find the length of the longest pole that can be put in a room of dimensions 10 m x 10 m x 5 m. [NCERT Exemplar Problem]
Answer. Here, we have a cuboid with dimensions
l= length = 10 m, b = breadth = 10 m and h = height = 5 m
Now, length of longest pole = diagonal of cuboid

18. Find the capacity in litres of a conical vessel having height 8 cm and slant height 10 cm. [CBSE-15-6DWMW5A]
Answer.

19. Calculate the surface area of a hemispherical dome of a temple with radius 14 m to be whitewashed from outside. [CBSE -15-NS72LP7]
Answer.

20. A school provides milk to the students daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk up to a height of 12 cm, find how many litres of milk is needed to serve 1600 students. [CBSE March 2011]
Answer.

21. A rectangular piece of paper is 22 cm long and 10 cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder. [CBSE-14-ERFKZ8H]
Answer.

22. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find it volume. If 1cm³ wheat cost is Rs 10, then find total cost. [CBSE-14-GDQNI3W]
Answer.

23. A shot-put is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g/cm³. Find the mass of the shot-put. [CBSE March 2012]
Answer.

24. A cylindrical vessel can hold 154 g of water. If the radius of its base is 3.5 cm, and 1 cm³ of water weighs lg,find the depth of water. [CBSE-14-17DIG1U]
Answer.

SHORT ANSWER QUESTIONS TYPE-II
25. A wall of length 10 m is to be built across an open ground. The height of the wall is 5 m and thickness of the wall is 42 cm. If this wall is to be built with bricks of dimensions 42 cm x 12 cm x 10 cm, then how many bricks would be required ? [CBSE-14-ERFKZ8H] [CBSE-15-NS72LP7]
Answer.

26. The curved surface area of a cylinder is 176 cm² and its area of the base is 38.5 cm². Find the volume of the cylinder. (Take π = 22/7) [CBSE March 2012]
Answer.

27. The diameter of a roller is 42 cm and its length is 120 cm. It takes 500 complete revolutions to move once to land a playground. Find the area of the playground in m². [CBSE March 2012]
Answer.

28. Rinku has built a cuboidal water tank in his house. The top of the water tank is covered with an iron lid. He wants to cover the inner surface of the tank including the base with tiles of size 10 cm by 8 cm. If the dimensions of the water tank are 180 cm x 120 cm x 60 cm and cost of tiles is f 480 per dozen, then find the total amount required for tiles. [CBSE March 2012]
Answer.

29. The diameter of moon is approximately 1/4 th of the diameter of earth. What fraction of volume of earth is the volume of moon ? [CBSE March 2012]
Answer.

30. The curved surface area of a cylinder is 154 cm². The total surface area of the cylinder is three times its curved surface area. Find the volume of the cylinder. [CBSE-14-GDQNI3W]
Answer.

31. A right angled A ABC with sides 3 cm, 4 cm and 5 cm is revolved about the fixed side of 4 cm. Find the volume of the solid generated. Also, find the total surface area of the solid. [CBSE-14-17DIG1U]
Answer.

32. Curved surface area of cylindrical reservoir 12 m deep is plastered from inside with concrete mixture at the rate of Rs 15 per m². If the total payment made is of Rs 5652, then find the capacity of this reservoir in litres. [CBSE-14-GDQNI3W]
Answer.

33. How many metres of 5 m wide cloth will be required to make a conical tent, the radius of whose base is 3.5 m and height is 12 m ? [CBSE March 2011 ]
Answer.

34. A shopkeeper has one spherical laddoo of radius 5 cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made ? [NCERT Exemplar Problem]
Answer.

35. A semicircular sheet of metal of radius 14 cm is bent to form an open conical cup. Find the capacity of the cup.
Answer.

LONG ANSWER TYPE QUESTIONS
36. A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height ?[NCERT Exemplar Problem]
Answer. Let ‘r’ be the radius of sphere and right circular cylinder with height ‘h’. According to the statement of question, we have

37. A cube and a cuboid have the same volume. The dimensions of the cuboid are in the ratio 1:2: 4. If the difference between the cost of painting the cuboid and cube (whole surface area) at the rate of Rs 5 per m² is Rs 80. Find their volumes. [CBSE March 2012]
Answer.

38. Ajay has built a cubical witter tank in his house. The top of the water tank is covered with lid. He wants to cover the inner surface of the tank including the lid with square tiles of side 25 cm. If each inner edge of the water tank is 2 m long and tiles costs Rs 360 per dozen, then find the total amount required for tiles. [CBSE March 2012]
Answer.

39. A tent is in shape of a right circular cylinder up to a height of 3 m and a cone above it. The maximum height of the tent above ground is 13.5 m. Calculate the cost of painting the inner side of the tent at the rate of Rs 3 per sq. m, if the radius of the base is 14 m. [CBSE March 2011]
Answer.

40. Manoj Sweets placed an order of making 30 cm x 20 cm x 6 cm cardboard boxes for packing their sweets. For all overlaps, 5 % of total area is required extra. If cost of the cardboard is Rs 2 for 1000 cm² , find the cost of the cardboard used for making 500 boxes. [CBSE-14-17DIG1U]
Answer.

41. A cylindrical bucket 32 cm high and with base diameter 36 cm is filled with wheat. This bucket is emptied on the ground and a conical heap is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.[CBSE-14-ERFKZ8H]
Answer.

42. Using clay, Anant made a right circular cone of height 48 cm and base radius 12 cm. Versha reshapes it in the form of a sphere. Find the radius and curved sutface area of the sphere so formed. [CBSE-15-6DWMW5A]
Answer.

43. A metallic right circular cylinder is 15 cm high and the diameter of its base is 14 cm. It is melted and recasted into another cylinder with radius 4 cm. Find its height and curved surface area of the new cylinder. [CBSE-14-17DIG1U]
Answer.

44. A spherical metallic shell with 10 cm external diameter weighs 1789 1/2 g. Find the thickness of the shell, if the density of the metal is 7g/cm³. [CBSE-15-6DWMW5A], [CBSE-15-NS72LP7]
Answer. External radius of metallic shell (R) = 5 cm
Let internal radius of metallic shell be r.

45. A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs 498.96. If the rate of whitewashing is Rs 4 per square metre, find the :
(i) Inside surface area of the dome
(ii) Volume of the air inside the dome [CBSE-15-6DWMW5A]
Answer. Here, dome of building is a hemisphere.
Total cost of white washing inside the dome = Rs 498.96
Rate of whitewashing = Rs 4 per m²

Value Based Questions
1. A residential house society is built is 4000 sq. m area. It has an underground tank to collect the rain water, the length, breadth and height of which are 50 m, 40 m and 4 m respectively. If it rains at the rate of 2 mm per minute for 5 hours, then calculate the depth of water in the tank. What value is depicted in this problem ? [CBSE-15-6DWMW5A]
Answer.

2. A village having a population of 4000 requires 150 litres of water per head per day. Due to lack of sources of water, they collect the water into a tank measuring 20 m x 15 m x 6 m from a river using a long pipe.
(i) For how many days will the water of this tank last ?
(ii) Which message is conveyed by the people of village ?
Answer.

3. Arihant builds a room measuring roof 22 m by 20 m. He also builds a cylindrical tank having diameter of base 2 m and height 3.5 m adjoining the room to collect the rainwater of roof for harvesting. If the tank is just filled with rainwater, find the rainfall in cm. What values are depicted in Arihant’s plan ?
Answer.

4. Naresh, a juice seller has set up his juice shop. He has three types of glasses (see figure) of inner diameter 5 cm to serve the customers. The height of the glasses is 10 cm.

He decided to serve the customer in ‘A’ type of glasses. (Take π = 3.14)
(i) Find the volume of each type of glass.
(ii) Which glass has the minimum capacity ?
(iii) Which mathematical concept is used in above problem ?
(iv) By choosing a glass of type A, which value is depicted by juice seller Naresh?
Answer.

Important Questions for CBSE  Class 9 Mathematics Chapter 7 Statistics

The topics and sub-topics in NCERT Class 9 Maths Text Book Chapter 14 Statistics:

• Statistics
• Introduction
• Collection Of Data
• Presentation Of Data
• Graphical Representation Of Data
• Measures Of Central Tendency
• Summary

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS
1. Mean of 20 observations is 17. If in the observations, observation 40 is replaced by 12, find the new mean. [CBSE-14-ERFKZ8H]
Answer. Since mean of 20 observations is 17
Sum of the 20 observations = 17 x 20 = 340
New sum of 20 observations = 340 – 40 + 12 = 312
Newmean=312 / 20 =15.6

2. If the mean of the data x₁,x_2,x₃…………….x_n is \( \bar { x }\) ,then find the mean of αx₁, αx_2, αx₃…………….αx_n.
Answer.

More Resources for CBSE Class 9

• NCERT Solutions
• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

3. Mean of 36 observations is 12. One observation 47 was misread as 74. Find the correct mean. [CBSE-14-17DIG1U]
Answer. Mean of 36 observations = 12
Total of 36 observations = 36 x 12 = 432
Correct sum of 36 observations = 432 – 74 + 47 = 405
Correct mean of 36 observations =  405/ 36 =11.25

4. If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 11, then write the value of x.
Answer.

5. Determine the mean of first 10 natural numbers.
Answer. First ten natural numbers are 1, 2, 3. 4, 5, 6, 7, 8, 9 and 10

6. Find the mean of x, x + 2, x + 4, x + 6, x + 8.
Answer.

7. Write the class mark of an interval 90 – 120.
Answer. Classmark= (90+120 )/ 2  = 210 / 2 =105

8. The mean of 8 observations is 40. If 5 is added to each observation, then what will be the new mean ?
Answer.

9. Find the range of the given data : 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20
Answer. Here, the minimum and maximum values of given data are 6 and 32 respectively.
Range = 32 – 6 = 26

10. There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be – 3.5. Find the mean of the given numbers.
Answer.

11. Find the median of the values 37, 31, 42, 43, 46, 25, 39, 45, 32.
Answer. Arranging the data in ascending order, we have 25, 31, 32, 37, 39, 42, 43, 45, 46 Here, number of observations = 9 (odd)

12. If the median of data (arranged in ascending order) 31, 33, 35, x, x+10, 48, 48, 50 is 40, then find value of x.
Answer.

13. Find the mode of the following scores : 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
Answer. 14 repeat maximum number of times (4 times) in the given data.
Mode = 14

14.To draw a histogram to represent the following frequency distribution :

Find the adjusted frequency for the class 25-45.
Answer.

15. The median of the data 26,56,32,33,60,17,34,29,45 is 33. If 26 is replaced by 62, then find the new median.
Answer. Here, the given data in ascending order is 17, 29, 32, 33, 34, 45, 56, 60, 62

Hence, new median is 34.

SHORT ANSWER QUESTIONS TYPE-I
16. For a particular year, following is the distribution of ages (in years) of primary school teachers in a district:

1. Write the lower limit of first class interval.
2. Determine the class limits of the fourth class interval.
3. Find the class mark of the class 45 – 50.
4. Determine the class size. [CBSE March 2012]

Answer.

1. First class interval is 15 – 20 and its lower limit is 15.
2. Fourth class interval is 30 – 35 Lower limit is 30 and upper limit is 35.
3. Class  mark  of the class 45 – 50 =( 45+50 )/ 2  =95 / 2  =47.5
4.  Class size = Upper limit of each class interval – Lower limit of each class interval
   .•. Here, class size = 20 – 15 = 5

17. The class marks of a frequency distribution are 104, 114, 124, 134, 144, 154, 164. Find the class size and class intervals. [CBSE March 2012]
Answer. Since the class marks are equally spaced.
.•. Class size = 114 – 104 = 10

18. Find  the mean of the following distribution : [CBSE-14-GDQNI3W]

Answer.

19. The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them in kg are 52, 54, 55, 53, 56, 54. Find the weight of the seventh student. [CBSE March 2012]
Answer.

20. Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. The median of the data is 24. Find the value of x. [NCERT Exemplar Problem]
Answer. Here, the arranged data is 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43
Total number of observations = 10

21. In figure, there is a histogram depicting daily wages of workers in d factory. Construct the frequency distribution table. (CBSE March 2013)

Answer.

22. Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows :
1 6 2 3 5 12 5 8 4 8 10 3 4 12 2
8 15 1 17 6 3 2 5 9 6 8 7 14 12
(i) Make a frequency distribution table for this data, taking class width 5 and one of the class as 5-10.
(ii) How many children watched television for 15 or more than 15 hours a week? [CBSE March 2012]
Answer. (i) Frequency distribution table :

(ii) From the above frequency distribution table, we observe that number of children in the class- interval 15 – 20 is 2.
So, 2 children view television for 15 hours or more than 15 hours a week.

SHORT ANSWER QUESTIONS TYPE-II
23. Given are the scores (out of 25) of 9 students in a Monday test :
14, 25, 17, 22, 20, 19, 10, 8 and 23
Find the mean score and median score of the data. [CBSE-14-GDQNI3W]
Answer.

24. The scores of an English test out of 100 of 20 students are given below :
75, 69, 88, 55, 95, 88, 73, 64, 75, 98, 88, 95, 90, 95, 88, 44, 59, 67, 88, 99.
Find the median and mode of the data [CBSE-14-17DIG1U]
Answer. Ascending order of given data is as given below :
44, 55, 59, 64, 67, 69, 73, 75, 75, 88, 88, 88, 88, 88, 90, 95, 95, 95, 98, 99

25. Obtain the mean of the following distribution and also find the mode. [CBSE-14-ERFKZ8H]

Answer.

LONG ANSWER TYPE QUESTIONS
26. A random survey of the number of children of various age groups playing in a park was found as follows :

Draw a histogram to represent the data above.
Answer. In this question, the class sizes are different. So, calculate the adjusted frequency for each class by using the following formula :

Let us represent the class intervals along X-axis and corresponding adjusted frequencies on Y-axis on a suitable scale.
Now, draw rectangles with the class intervals as bases and the corresponding adjusted frequencies as the heights.
Therefore, the required histogram is as given below :

27. In a mathematics test given to 15 students, the following marks (out of 100) are recorded :
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60.
Find the mean, median and mode of this data. [CBSE March 2013]
Answer.

28. The following two tables gives the distribution of students of two sections according to the marks obtained by them : [CBSE March 2011, 2013]

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Answer. The class marks are as under :

Let us take class marks on X-axis and frequencies on Y-axis.
To plot frequency polygon of Section-A, we plot the points (5, 3), (15,9), (25,17), (35,12), (45,9) and join these points by line segments.

To plot frequency polygon of Section-B, we plot the points (5,5), (15,19), (25,15), (35,10), (45,1) on the same scale and join these points by dotted line segments.
From the above two polygons, clearly the performance of Section-A is better.

29. The following data given the weight (in grams) of 30 oranges picked from a basket:
106 107 76 109 187 95 125 92 70
139 128 100 88 84 99 113 204 141
136 123 90 115 110 97 90 107 75
80 118 82
Construct a grouped frequency distribution table taking class width equal to 20 in such a way that the mid-value of first class in 70.
From the frequency table, find the number of oranges
(i) weighing more than 180 g.
(ii) less than 100 g. [CBSE-14-GDQNI3W]
Answer. Here , class width = 20
class mark = 70
Half of the class width =20 /2  =10
Upper limit of first class interval = 70 + 10 = 80
Lower limit of  first class interval = 70 – 10 = 60
Thus, class interval becomes 60 – 80
So, frequency distribution table becomes :

(a) Number of oranges weights more than 180 g = 1 + 1 = 2
(b) Number of oranges weights less than 100 g = 3 + 10 = 13

30. The following table gives the pocket money (in Rs) given to children  per day by their parents : Represent the data in the form of a histogram. [CBSE-14-ERFKZ8H]

Answer. The required histogram is as below :

31. In a school marks obtained by 80 students are  given in the table. Draw a histogram. Also, make frequency polygon. [CBSE-14-17DIG1U]

Answer.

32. Draw a histogram and frequency polygon for the following distribution :

Answer. We represent class limits along x-axis and number of students along y-axis on a suitable Scale.

33. Following is the frequency distribution of total marks obtained by the students of different section of class-IX.

Draw a histogram for the distribution.
Answer. Since class intervals of the given frequency distribution are not of equal width.
We would make modifications in the lengths of the rectangles in the histogram, so that the areas of rectangles are proportional to the frequencies.

Now, we draw rectangles with lengths as given in the last column. The histogram of the data is given below :

34. Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.

Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe ?
Answer.

Value Based Questions
1. A survey conducted by an organisation for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %) :

(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
(iii) Try to find out , with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
Answer. (i) The bar graph of the data is as given below :
In the graph, drawn causes of illness and death among women between the ages 15-44 (in years) worldwide is denoted on X-axis and female fatality rate (%) is denoted on the Y-axis.
(ii) The major cause of women’s ill health and death worldwide is reproductive  health condition.
(iii) Two other factors which play a major role in the cause in (ii) above are neuro-psychiatric conditions and other causes.

2. The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the Indian society is given below :

(i) Represent the information above by a bar graph.
(ii) In the classroom, discuss what conclusions can be arrived at from the graph.
(iii) What steps should be taken to improve the situation ?
Answer. (i) The required graph is given alongside :
In the graph, different sections of the society is taken on X-axis and number of girls per thousand boys is I taken on the Y-axis. [Scale : 1 cm = 10 girls.]
(ii) From the graph, the number of girls to the nearest ten per i thousand boys are maximum in scheduled tribes  whereas they are minimum in urban.
(iii) Prenatal sex determination should strictly banned in urban.

3. Shimpi, a class IX student received cash award of Rs 10000 (Ten thousand) in the singing competition. Her father advised her to make a budget plan for spending this amount. She made the following plan :

Make a bar graph for the above data.
From above answer the following questions :
(i) Which mathematical concepts have been covered in this ?
(ii) How will you rate her budget plan ? In your opinion which head has been given (a) more than deserved and (b) less than it deserved ?
(iii) Which values are depicted in her plan ?
Answer. The bar graph of given data is given below :

In the graph, head is taken on X-axis and amount is taken on Y-axis.
(i) Representation of data using bar graph.
(ii) Very good
(a) Picnic for family
(b) Tuition fee for needy child
(iii) Help the needy people and respect the elders.

4. In a year, the number of deaths due to habit of smoking for different age group is given below :

(i) Represent the given information with the help of a histogram.
(ii) What lesson do you learn from this information ?
Answer. (i) The histogram of given information is as given below :

(ii) Smoking is injurious to health

5. Find the mean of children per family from the data given below :

What values are depicted from this data?
Answer.

Important Questions for CBSE  Class 9 Mathematics Chapter 8 Probability

The topics and sub-topics in NCERT Solutions for Class 9 Maths Chapter 15 Probability are:

• Probability
• Introduction
• Probability – An Experimental Approach
• Summary

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS
1. A box contains 50 bolts and 150 nuts. On checking the box, it was found that half of the bolts and half of the nuts are rusted. If one item is chosen at random, find the probability that it is rusted. [CBSE-15-NS72LP7]
Answer.

2. A dice is rolled number of times and its outcomes are recorded as below :

Find the probability of getting an odd number. [CBSE-15-NS72LP7]
Answer. Total number of outcomes = 250
Total number of outcomes of getting odd numbers = 35 + 50 + 53 = 138
.-. P(getting an odd number) = 138/250=69/125

More Resources for CBSE Class 9

• NCERT Solutions
• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

3. IfP (event E) = 0.47, then find P(not E).
Answer. P(not E) = 1 – P(E)
=> 1 – 0.47 = 0.53

4. The probability of guessing the correct answer to a certain question is x/ 2.If probability of not guessing the correct answer is 2 /3 then find x. [CBSE-14-ERFKZ8H], [CBSE-14-17DIG1U]
Answer.

5. A die is thrown six times and number on it is noted as given below :

Compute the probability of getting a prime number. [NCERT Exemplar Problem]
Answer. Here, in 6 trials, each number occur once and total prime numbers i.e., 2, 3, 5 occur one time each
Hence, the number of prime occur = 3
Probability of getting a prime = 3/6 =1/2

6. In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, compute the probability that he/she does not like to eat potato chips. [NCERT Exemplar Problem]
Answer. Total children = 364
Number of children like potato chips = 91
.-. Number of children do not like potato chips = 364 – 91 = 273 273
Required probability = 273 / 364 =0.75

7. In a medical examination of students of a class, the following blood groups are recorded :

A student is selected at random from the class. Find the probability that he/she has blood group B. [NCERT Exemplar Problem]
Answer. Total number of students = 10 + 13 + 12 + 5 = 40
Number of students having blood group ‘B’ = 12
Required probability =12 / 40 = 3 / 10

8. Two coins are tossed 1000 times and the outcomes are recorded as below :

Based on this information, find the probability for at most one head.
Answer. Required probability = P(0 heads) + P(1 head)
= 250/1000 + 550 / 1000  = 800/ 1000  =4 / 5 =0.8

9. A bag contains x white, y red and z blue balls. A ball is drawn at the random, then what is the probability of drawing a blue ball.
Answer. Number of blue balls = z
Total balls = x + y + z
therefore P(ablueball)= z /(x+y+z )

10. In a throw of a die, find the probability of not getting 4 or 5.
Answer. Required probability = 1 – P(4) – P(5)
\(\)=1- 1 / 6  – 1 / 6  = 4 / 6 = 2 / 3

11. In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, find the probability that the person has a high school certificate.
Answer. Total number of persons = 642
Number of persons with high school certificate = 514
therefore Required probability=514 /642 =0.80

12. In a class, there are x girls and y boys, a student is selected at random, then find the probability of selecting a boy.
Answer. Number of boys = y
Total students = (x + y)
Thus,P(aboy)= y/(x+y)

13. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes ;

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up. [CBSE March 2012]
Answer. Total number of chances = 23 + 72 + 77 + 28 = 200
Number of chances of coming 2 heads = 72
therefore P( coming 2 heads)= 514 / 642 = 9/ 25

SHORT ANSWER QUESTIONS TYPE-I
14. 750 families with 3 children were selected randomly and the following data recorded
If a family member is chosen at random, compute the probability that it has :

(i) no boy child
(ii) no girl child [CBSE-15-6DWMW5A]
Answer. (i) P(no boy child) =100 / 750  = 2/15
(ii) P (no girl child) = 120 /750  =4 /25

15.If the probability of winning a race of an athlete is 1 / 6 less than the twice the probability of losing the race. Find the probability of winning the race. [CBSE-15-6DWMW5A]
Answer. Let probability of winning the race be p Probability of losing the race = 1 – p According to the statement of question, we have
p = 2 (1 – p) – 1/6
=>6p=12-12p-1
=>18p=11
=>p=11 / 18
Hence, probability of winning the race is  11 / 18  .

16. Two coins are tossed simultaneously for 360 times. The number of times ‘2 Tails’ appeared was three times ‘No Tail’ appeared and number of times ‘1 tail’ appeared is double the number of times ‘No Tail’ appeared. Find the probabiliy of getting ‘Two tails’. [CBSE-14-ERFKZ8H], [CBSE-14-17DIG1U]
Answer. Total number of outcomes = 360
Let the number of times ‘No Tail’ appeared be x
Then, number of times ‘2 Tails’ appeared =3x
Number of times ‘1 Tail’ appeared =2x
Now, x + 2x + 3x =360
=>6x=360
=>x=60
P(of getting two tails)=(3 x 60)/360 =1 /2

17. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes :

If the three coins are simultaneously tossed again, compute the probability of getting less than 3 tails. [NCERT Exemplar Problem].
Answer. It is given that coin is tossed 200 times Total number of trials = 200
Number of events for getting less than three tails = 68 + 82 + 30 = 180
Probability of getting less than 3 tails =180 / 200 =9 / 10

18. A die was rolled 100 times and the number of times, 6 came up was noted. If the experimental probability calculated from this information is 2 /5 then how many times 6 came up ? Justify your answer. [CBSE March 2013]
Answer.

SHORT ANSWER QUESTIONS TYPE-II
19. The table shows the marks obtained by a student in unit tests out of 50 :

Find the probability that the student get 70% or more in the next unit test. Also, the probability that student get less than 70%. [CBSE-14-GDQNI3W]
Answer.

20. Books are packed in piles each containing 20 books. Thirty five piles were examined for defective books and the results are given in the following table :

One pile was selected at random. What is the probability that it has :
(i) no defective books ?
(ii) more than 0 but less than 4 defective books ?
(iii) more than 4 defective books ? [CBSE-15-NS72LP7]
Answer.

21. The given table shows the month of birth of 40 students of class IX of a particular section in a school.

If one student is chosen at random, find the probability that the student is born :
(a) in the later half of the year
(b) in the month having 31 days
(c) in the month having 30 days [CBSE-14-17DIG1U]
Answer.

22. Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on them is noted and recorded in the following table :

From the above data, what is the probability of getting a sum :
(i) more than 10 (ii) between 8 and 12. [NCERT Exemplar Problem]
Answer.

LONG ANSWER TYPE QUESTIONS
23. The daily cost of milk (in Rs) supplied to 25 houses in a locality are given below :

If one house is chosen at random, find the probability that ;
(a) the milk bill of the house lies between Rs 60 and Rs 80.
(b) house is paying at the most Rs 69, for the milk bill.
(c) the milk bill of the house is below Rs 50. [CBSE-14-ERFKZ8H]
Answer.

24. A travel company has 100 drivers for driving buses to various tourist destination. Given below is a table showing the resting time of the drivers after covering a certain distance (in km).

What is the probability that the driver chosen at random
(a) takes a halt after covering 80 km ?
(b) takes a halt after covering 115 km ?
(c) takes a halt after covering 155 km ?
(d) takes a halt after crossing 200 km ? [CBSE-15-6DWMW5A]
Answer.

25. A survey of 2000 people of different age groups was conducted to find out their preference in watching different types of movies :
Type I —> Family
Type II —> Comedy and Family
Type III —> Romantic, Comedy and Family
Type IV —> Action, Romantic, Comedy and Family

Find the probability that a person chosen at random is :
(a) in 18-29 years of age and likes type II movies
(b) above 50 years of age and likes all types of movies
(c) in 30-50 years and likes type I movies. [CBSE-14-GDQNI3W]
Answer.

Value Based Questions
1. An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table :

Find the probability of the following events for a driver selected at random from the city:
(i) being 18-29 years of age and having exactly 3 accidents in one year.
(ii) being 30-50 years of age and having one or more accidents in a year.
(iii) having no accident in one year.
(iv) Which value would you like to remember from this data ?
Answer.

(iv) Most number of people in India died or injured due to accidents as compared to any other country. So, we should obey the traffic rules as life is very precious.

2.There is a group of 130 people who are patriotic, 50 people believe in violence. What is the probability of people who believe in non-violence 7 Which value you will develop in your character ?
Answer.

In order to have a peaceful environment both values are required patriotism and non-violence. Only patriotism with violence is very dangerous.

3. 100 plants were sown in six different colonies A, B, C, D, E, and E After 31 days, the number of plants survived as follows ;

What is the probability of:
(i) more than 80 plants survived in a colony ?
(ii) less than 82 plants survived in a colony ?
(iii) which value are depicted from above data ?
Answer.

4. For travelling, different mode of transport used by 1500 people are as follows:
Find the probability of number of people :

(i) used car and scooter only ?
(ii) used only cycle ?
(iii) used at least one kind of mode of transport ?
(iv) which value would you learn from above data ?
Answer.

5. There is a group of 75 people who are patriotic, 35 people believe in violence. What is the probability of people who believe in non-violence ? Which value you will develop in your character ?
Answer.

In order, to have a peaceful environment both values are required patriotism and non¬violence. Only patriotism with violence is very dangerous.