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1. A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
2. How many of the following numbers are divisible by 132?
3. If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
4. If the sum of a number and its square is 182, what is the number?
5. Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
6. The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is __________ .
7. Ratio of the ages of Mahesh and Nilesh is 5:x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
8. (98 / 7 / 2) / ? = 14
9. A contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose. After 120 days, he finds that only 240 meters of the tunnel is complete. How many more men should be employ in order to complete the work in time?
10. Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
11. In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?
12. A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
13. Find the least number by which (5^{9})(3^{6})(17) has to be multiplied to obtain a perfect square?
14. The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
15. Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
16. Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
17. The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
18. Simplify : 1 - {1 + (a^{2} - 1)^{-1}}^{-1}
19. An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
20. A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
21. (27^{2}/4^{-3})^{-5/6} = ?
22. Find the one which does not belong to that group ?
23. The average of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?
24. Subtracting 30 from a number, the remainder is one fourth of the number. Find the number?
25. Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
26. Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21.
27. The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
28. In each of the following numbers, what should be the missing digit in the indicated place such that the number is a multiple of 11?
29. The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
30. A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
31. A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?
32. The edge of a cube is 2a cm. Find its surface?
33. A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
34. The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
35. What is the sum of all the composite numbers up to 20?
36. The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
37. Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?
38. √3584 * 52.034 = ?
39. At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
40. Three men start together to travel the same way around a circular track of 11 kilometers in circumference. Their speeds are 4, 5 and 8 kilometers per hour respectively. When will they meet at a starting point?
41. A and B can do a work in 12 days and 36 days respectively. If they work on alternate days beginning with B, in how many days will the work be completed?
42. A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
43. The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid.
44. The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?
45. Find the greatest number which divides 83, 125 and 209 leaving the same remainder in each case.
46. Find the least square number which is divisible by 10, 12, 15 and 18?
47. A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
48. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
49. The sides of a cube are in the ratio 1:2 the ratio of their volume is?
50. The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?