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1. Simplify the following:
2. I. 9a^{2} + 18a + 5 = 0, II. 2b^{2} + 13b + 20 = 0 to solve both the equations to find the values of a and b?
3. What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?
4. The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
5. Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings.
6. Using all the letters of the word "THURSDAY", how many different words can be formed?
7. A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
8. The base of a right triangle is 8 and hypotenuse is 10. Its area is?
9. Find the average of the series : 312, 162, 132, 142 and 122?
10. 1: 3 = 1 2/3: x. The value of x is?
11. By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
12. The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
13. A library has an average of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
14. Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
15. A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
16. How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together?
17. By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
18. A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
19. H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is:
20. Find the one which does not belong to that group ?
21. A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:
22. How much 60% of 50 is greater than 40% of 30?
23. If x = √11 + √20, y = √15 + √17 and z = √14 + √18, then which of the following holds true?
24. How many figures are required for numbering the pages of a book containing 1000 pages?
25. Find the 37.5% of 976 =
26. How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
27. The fourth proportional to 5, 8, 15 is:
28. In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
29. Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
30. The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
31. 60% of a number is added to 120, the result is the same number. Find the number?
32. Solve for m if 3(√3)^{m+4} = (√3)^{2m+7}
33. A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
34. Find the one which does not belong to that group ?
35. The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
36. The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
37. Express 25 mps in kmph?
38. There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?
39. A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
40. The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
41. A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
42. A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
43. What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
44. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
45. The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm^{3} of metal used in the box weighs 0.5 gms, the weight of the box is?
46. A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
47. What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
48. The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
49. If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
50. The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).