Class 8th mensuration

 1. If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true? 

(a) Volume of the cylinder will be doubled. 

(b) Volume of the cylinder will remain unchanged. 

(c) Volume of the cylinder will be halved. 

(d) Volume of the cylinder will be1/4 of the original volume 

2. The surface area of the three coterminous faces of a cuboid are 6, 15 and 10 cm2, respectively. The volume of the cuboid is

 (a) 30 cm3 (b) 40 cm3 (c) 20 cm3 (d) 35 cm3 

3. The volume of a cube is 64 cm3 . Its surface area is 

(a) 16 cm2 (b) 64 cm2 (c) 96 cm2 (d) 128 cm2 

4. What is the area of the rhombus ABCD below if AC = 6 cm, and BE = 4cm?

 (a) 36 cm2 (b) 16 cm2 (c) 24 cm2 (d) 13 cm2 

5. The perimeter of a trapezium is 52 cm, and its each non-parallel side is equal to 10 cm with a height 8 cm. Its area is 

(a) 124 cm2 (b) 118 cm2 (c) 128 cm2 (d) 112 cm2

 6. The volume of a cylinder whose radius r is equal to its height is 

(a) 1/4 πr3 (b) πr3 /32 (c) πr3 (d) πr3  

Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box covered with coloured paper with picture of Santa Claus on it (see the below figure). She must know the exact quantity of paper to buy for this purpose. The box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively and she wants to use square sheets of paper of side 40 cm for the decoration.

 7. Find the total surface area of the box. 

(a) 11200 cm2 (b) 12000 cm2 (c) 12100 cm2 (d) none of these

 8. Find the area of each sheet of the paper. 

(a) 1600 cm2 (b) 1620 cm2 (c) 1610 cm2 (d) none of these

 9. Find the number of sheets required. 

(a) 6 (b) 8 (c) 7 (d) 9 

10. Find the volume of the box. 

(a) 640 cm3 (b) 6400 cm3 (c) 64000 cm3 (d) none of these

 11. Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of the diagonals is 8 cm long, find the length of the other diagonal. 

12.A carpenter makes a box which has a volume of 13,400 cm3 . The base has an area of 670 cm2 . What is the height of the box? 

13.A cuboidal tin box opened at the top has dimensions 20 cm × 16 cm × 14 cm. What is the total area of metal sheet required to make 10 such boxes?

14 .A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases? 

15.A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in figure). If the label is placed 2 cm from top and bottom, what is the area of the label?

16 .Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC. 

17.A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank. 

 18.Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of reservoir is 108 m^3, find the number of hours it will take to fill the reservoir.

 19 .Diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area. 

20 .Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.

Class 6th Maths Ratio and Proportion

class 8th Maths Factorization

class 10th Maths Exempler ( Trigo, Real, Stats and Probability)

Question 1  The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A) 13 (B) 65

(C) 875 (D) 1750

Question 2. If cos A = 45 , then the value of tanA is

Question 3 If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is
(A) 1
(B) 12
(C) 2
(D) 3

Question 4. lf 4tanθ = 3, then (4sinθ−cosθ4sinθ+4cosθ) is equal to

Question 5. A pole 6m high casts a shadow 2√3 m long on the ground, then the Sun’s elevation is
(A) 600
(B) 45°
(C) 30°
(D) 90°

Question 6. If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is
(A) xy
(B) xy2
(C) x3y3
(D) x2y2

Question 7  If two positive integers p and q can be expressed as p = ab2, and q = ab; a, b being prime numbers, then LCM (p, q) is

(A) ab
(B) a2b2
(C) a3b2
(D) a3b3

Question 8. Prove that √3 + √5 is irrational.

Question 9. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

Question 10. Consider the following frequency distribution

Question 11. The upper limit of the median class is
(a) 7                                (b) 17.5                      (c) 18                                 (d) 18.5

Question 12. While computing mean of grouped data, we assume that the frequencies are
(a) evenly distributed over all the classes
(b) centred at the class marks of the classes
(c) centred at the upper limits of the classes
(d) centred at the lower limits of the classe

Question 13.

Question 14. For the following distribution,

the modal class is
(a) 10-20                             (b) 20-30            (c) 30-40                           (d) 30-40

Question 15. If an event cannot occur, then its probability is
(a) 1                          (b) 34                          (c) 12                 (d) 0

Question 16. The probability expressed as a percentage of a particular occurrence can never be
(a) less than 100                                        (b) less than 0
(c) greater than 1                                       (d) anything but a whole number

Question 17. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
(a) 4                           (b) 13                        (c) 48                       (d) 51

Question 18. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7                           (b) 14                        (c) 21                       (d) 28

Question 19.

Question 20.If tanA = 34 , then sinA cosA = 1225 .

Question 21. (√3 +1)(3 – cot 30°) = tan3 60° – 2 sin 60°

Question 22. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

Question 23. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Question 24. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Question 25. If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or 12 .

Question 26. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β , respectively. Prove that the height of the tower is ( htanαtanβ−tanα)

Question 27. If a sinθ + b cosθ = c, then prove that acosθ – bsinθ = a2+b2+c2−−−−−−−−−√.

Question 28. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower.

Question 29. A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h (1 + tan α cot β) metres.

Question 30. The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30°, respectively. Find the height of the balloon above the ground.

Question 31. I toss three coins together. The possible outcomes are no heads, 1 head,2 head and 3 heads. So, I say that probability of no heads is 14. What is wrong with this conclusion?

Question 32. Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

Question 33. Calculate the mean of the following data

Question 34. The daily income of a sample of 50 employees are tabulated as follows.

Find the mean daily income of employees.

Question 35. Size of agricultural holdings in a survey of 200 families is given in the following
Compute median and mode size of the holdings.

Question 36. The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90.

Question 37. Find the mean marks of students for the following distribution

Question 38. Box A contains 25 slips of which 19 are marked  ₹ 1 and other are marked  ₹ 5 each. Box B contains 50 slips of which 45 are marked  ₹ 1 each and others are marked  ₹ 13 each. Slips of both boxes are poured into a third box and resuffled. A slip is drawn at random. What is the probability that it is marked other than  ₹ 1?

Question 39. the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value.
(i) 7                              (ii) greater than 7                                      (iii) Less than 7

Question 40. A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since, this situation has only two possible outcomes, so the 1 probability of each is 

12. Justify.