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
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9th Chapter: Probability based on Deck (Card): Question with Solution
1. Find the probability of drawing a black card. Answer: 1/2 2. Find the probability of drawing a red card. Answer: 1/2 3. Find the probability of drawing either a red or black. Answer: 1 4. Find the probability of drawing an ace. Answer: 1/13 5. Find the probability of drawing either a jack or queen or king. Answer: 3/13 6.Find the probability of drawing a black king. Answer: 1/26 7. Find the probability of drawing a white queen. Answer: 0 8. Find the probability of drawing a club. Answer: 1/4 9. Find the probability of drawing a heart. Answer: 1/4 10. Find the probability of drawing either a spade or diamond. Answer: ½ 11.Find the probability of drawing a club and heart. Answer: 1/52 12.Find the probability of drawing either a black card or number 10. Answer:7/13 13.Find the probability of drawing a number more than 5. Answer: 5/13 14.Find the probability of drawing a picture card. (includes jack, queen or king) Answer: 3/13 15. Find the probability of drawing a red ace. Answer: 1/26 16. The probability of selecting neither a jack nor an ace from a well-shuffled pack of 52 playing cards is : Ans: 11/13 17. From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen. Answer: 1/26 18. A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is an Ace. Answer: 1/13 19. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a red face card. Answer: 3/26 20. The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs Ans: (i) 3/49 (ii) 3/49 (iii) 10/49 Further Study Visit: Links 1. Three coins are tossed once, find the probability of getting at least one head (7/8)
2. When three coins are tossed simultaneously, find the probability of getting at least two Tails 3. Three coins are tossed simultaneously 200 times with the following frequencies of different Outcomes Out comes 3 Heads 2 Heads 1 Head No head Frequency 23 72 77 28 Find the probability of getting: a) 2 Heads b) at least 2 Heads 4. A dice is thrown once, find the probability of getting a prime number (1/2) 5. A Pair of dice is thrown once, find the probability of getting a doublet (1/6) 6. A dice is thrown once. Find the probability of getting: a) An even number (1/2) b) A prime number (1/2) c) A number greater than 4 (1/3) 7. A fair die is tossed once. Find the probability of getting: a) a number more than or equal to 3 ( 2/3) b) a multiple of 3 (1/3) 8. A letter of English alphabet is choosen at random. Calculate the probability that the letter choosen is a vowel ( 5/26) 9. A bag contains 15 balls numbered 1 to 15. Find the probability of drawing a prime number, When one ball is drawn from the bag at random (2/5) 10. Marks obtained by 50 students in a class test of 100 marks are given below Marks 0 - 25 25 - 50 50 – 75 75 - 100 No of students 4 12 18 16 Find the probability that a student obtained less than 50% marks 11. in a one day international cricket match, a batsman played 40 balls. The runs scored as Follows Runs scored 0 1 2 3 4 6 No of balls 13 15 5 1 4 2 Find the probability that the batsmen will score: a) 6 runs ( 1/20) b) A four or a six run (3/20) 12. One number is chosen at random from numbers 1 to 100. Find the probability that it is Divisible by 4 or 6 (33/100) 13. In a survey of 80 people, 60 people like apple juice and remaining dislike it. Find the Probability that people dislike apple juice (1/4) 14. 250 families with 2 children are selected randomly and following data were obtained Number of sons in family 2 1 0 Number of families 75 125 50 Find the probability of families having a) 2 sons b) 1 son c) no son 15. 1500 family with 2children were selected randomly and the following data was recorded Number of girls in family 2 1 o Number of family 475 814 211 Compute probability of a family chosen at random having a) At most 1 girl (41/60) b) At least 2 girls (19/60) 16. Probability of an impossible event is always……… a) 0 b) 1 c) 2 d) ½ 17. A die is thrown once. The probability of getting an even prime number is a) ½ b) 1/3 c) 1/6 d) 2/3 18. A coin is tossed once then probability of getting head is a) 2 b) 1 c) ½ d) 3 19. There are 10 bulbs in a bag in which 4 bulbs are good and rest are fused, then the Probability of fused bulbs is a)3/5 b) 2/5 c) 1 d) 2/3 20. Sum of the probability of happening and not happening of an event is a) 1 b) 2 c) 0 d) none of these 21. The probability of winning a game is 0.3. Then, the probability of losing a game is a) 0.3 b) 0.7 c) 0.6 d) 0.1 22. The Probability of a sure event is a) 1 b) – 1 c) 0 d) none of these 23. Out of 35 students participating in a debate 10 are girls. The probability that winner is a boy is : a) 1/7 b) 3/7 c)4/7 d) 5/7 24. Which of the following cannot be the probability of an event a) 1/5 b) 0.3 c) 4% d) 5/4 25. In a cricket match, a batsman hits a sixer 8 times out of32 balls played. The probability that a sixer is not hit in a ball is : a)0.75 b) 0.25 c) – 0.25 d) 0.5 For more Downloads Visit Page: Link For Pdf Download Q.1: Find the surface area of a cuboid which is 16.4 m long , 15.5 m broad and 8.5m high.
Q.2: A chalk box is in the form of a cube of edge 10.5cm.Find its surface area. Q.3: Find the lateral surface area of a right circular cylinder whose height is 13.5cm and radius of the base is 7cm.Find also its whole surface area. Q.4: A roller 150cm long has a diameter of 70 cm.To level a playground it takes 750 complete revolutions .Determine the cost of levelling the playground at the rate of 75 paise per sq. metre. Q.5: Find the diameter of a sphere whose surface is 346.5sq.cm. Q.6: A conical tent is 10m high and the radius of its base is 24m.Find its slant height.Also find the cost of canvas used in making the tent at Rs. 70 per sq.m. Q.7: A hemispherical bowl is made of steel 0.25cm thick .The inner radius of the bowl is 5cm .Find the outer curved surface area of the bowl. Q.8: Find the volume of a cuboid whose length is 16.4m, breadth =15.5m and height =8.5m. Q.9: A river 3m deep and 40m wide is flowing at the rate of 2km per hour .How much water will fall into the sea in a minute? Q.10 The volume of a right circular cylinder is 1100cu cm and the radius of its base is 5cm.Find its curved surface area. Q.11: A cubodal vessel is 10m long and 8 m wide.How high must be made to hold 380 cu m of a liquid. Q.12: Find the capacity in litres of a conical vessel whose diameter is 14 cm and slant height 25cm. Q.13: What are the cubical contents of a well whose diameter is 42 dm and depth 150 dm.? Q.14: The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm .How many litres of water can it hold? [1000cu cm=1litre] Q.15: A heap of wheat in the form of cone whose diameter is 10.5m and height 3m .Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of canvas required. Q.16: The diameter of the moon is approximately one-fourth of the diameter of the earth .What fraction of the earth is the volume of the moon? Q.17: The radius of a sphere is 5cm .f the radius be increased by 20% ,find by how much %age the volume is increased. Q.18: A gowdown measures 40mx25mx10m.Find the maximum number of wooden crates each measuring 1.5m x 1.25m x 0.5m that can be stored in the gowdown. Q.19: Find the length of the longest rod that can be placed in a room 12mx9mx8m. Q.20: A 4cm cube is cut into 1cm cubes .Calculate the total surface area of small cubes. What is the ratio of surface area of small cubes to that of the large cube? Q.21: A field is 60m long and 20m wide.A tank 12m long ,10m broad and 3m deep is dug in the field .The earth taken out of it is spread evenly over the field .How much is the level of the field raised supposing the earth taken out increases by 1/8 of the volume? Q.22: A village having a population of 4000, requires 150 litres of water per head per day . It has a tank measuring 20m x 15m x 6m.For how many days will the water of this tank last ? Q.23: It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10m deep .If the cost of painting is at the rate of Rs. 20 per sq.m, find (i) inner curved surface area of the vessel (ii) radius of the base (iii) capacity of the vessel Q.24: The radius and height of a right circular cone are in the ratio 5:12. If its volume is 314 cu cm, find its slant height. ( take π=3.14) Q.25: A rectangular water reservoir is 7.2m by 2.5m at the base . Water flows into it through a pipe whose cross section is 5cm x 3cm at the rate of 10m per second .Find the height to which the water will rise in the reservoirs in 40 minutes. Let a, b, c are length of the sides and h is height to side of length c of ∆ ABC. We have S = (a + b + c)/2 So, 2s = a + b + c 2(s - a) = - a + b + c 2(s - b) = a - b + c 2(s - c) = a + b – c Let p + q = c as indicated.Then,
h2 = a2 - p2 -------------(1) Also, h2 = b2 - q 2 -------------- (ii) From (i) and (ii) Þ a2 - p2 = b2 - q 2 q2 = - a2 + p2 + b2 Since, q = c - p q2 = (c-p)2 Þ q2 = c2 + p2 -2pc Then, c2 + p2 -2pc = - a2 + p2 + b2 - 2pc = - a2 +b2 – c2 = - ( a2 -b2 + c2) p = ( a2 -b2 + c2)/2cNow, Put this value of p in equation (i) h2 = a2 - p2 h2 = ( a – p ) ( a + p ) h2 = {a – ( a2 -b2 + c2)/2c } {a + ( a2 -b2 + c2)/2c } h2 = {(2ac - a2 + b2 - c2)/2c}x{(2ac+ a2 - b2 + c2)/2c }h2 = {(b2 – (a - c)2 }{(a + c)2 – b2}/4c 2h2 = {(b – a + c) (b + a - c)}{(a + c + b)(a + c – b ) h2 = { 2(s - a) x 2(s - c) x 2s x2(s - b)}/4c2 h2 = { 4 s (s - a) x (s - c) x(s - b)}/c2 h = 2/c √ s (s - a) x (s - b) x(s - c) ½ h c = √ s (s - a) x (s - b) x(s - c) Area of triangle = √ s (s - a) x (s - b) x(s - c) 9th Area of triangles by Heron's formula Test Paper-1 9th Area of triangles by Heron's formula Test Paper-2 9th Area of triangles by Heron's formula Test Paper-3 Assignment for Class IX On : HERONS FORMULA 9th Heron formula proof and test questions Visit and Download Files |
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