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1. A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.
2. An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?
3. I. a^{2} + 8a + 16 = 0, II. b^{2} - 4b + 3 = 0 to solve both the equations to find the values of a and b?
4. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
5. Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
6. 12(13/18) + 16(11/27) - 10(5/9) = ?
7. Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21
8. An amount of Rs.1560 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
9. (3^{-3} * 9^{5/2}) / (27^{2/3} * 3^{-4}) = ?
10. (800 / 64) * (1296 / 36) = ?
11. Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
12. The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
13. The third proportional to 1 and 2 is?
14. Find the one which does not belong to that group ?
15. There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
16. Find the one which does not belong to that group ?
17. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
18. 125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
19. How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
20. A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is:
21. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?
22. Find the one which does not belong to that group ?
23. The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
24. A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
25. In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
26. A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
27. Identify the greatest numbers: 4^{50}, 2^{100}, 16^{25}
28. If one third of 3/4 of a number is 21. Then find the number?
29. How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
30. Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
31. I. a^{2} - 7a + 12 = 0, II. b^{2} - 3b + 2 = 0 to solve both the equations to find the values of a and b?
32. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
33. The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
34. Using all the letters of the word "THURSDAY", how many different words can be formed?
35. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
36. Two numbers have a H.C.F of 16 and a product of two numbers is 2560. Find the L.C.M of the two numbers?
37. A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
38. Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?
39. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
40. After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
41. Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -.
42. By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
43. A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
44. A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
45. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 20 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will raise by nearly?
46. Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
47. 3/20 is what percent of 12/25?
48. A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
49. Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?
50. A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?