Partnership, Mixture and Alligation, Mensuration, Probability, Permutation and Combination - Question Bank
1. The area of a circle is 154 sq cm. What is its radius? (Use pi = 22/7)
2. How many 4-letter words can be formed using the letters of the word 'DATING' if repetition of letters is not allowed?
3. What is the probability of selecting a consonant from the word 'EQUATION'?
4. A mixture contains milk and water in the ratio 7:5. If 15 liters of water are removed, the ratio becomes 7:3. What is the quantity of milk in the original mixture?
5. A and B invest Rs. 40,000 and Rs. 60,000 respectively in a business. A invests for 12 months and B for 8 months. If the total profit is Rs. 52,000, what is B's share?
6. The length of a rectangle is twice its width. If the area of the rectangle is 200 sq cm, what is its perimeter?
7. In how many ways can 5 people be arranged in a circle?
8. What is the probability of getting a sum of 5 when two dice are rolled?
9. What is the perimeter of a triangle with sides 5 cm, 12 cm, and 13 cm?
10. A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water are added to the mixture, the ratio becomes 4:5. What is the quantity of alcohol in the original mixture?
11. A and B enter into partnership investing Rs. 16,000 and Rs. 12,000 respectively. A invests for 8 months and B for 6 months. If the total profit is Rs. 38,000, what is A's share?
12. The radius of a circle is increased by 50%. By what percentage does its area increase?
13. A shopkeeper mixes two types of tea, one at Rs. 80/kg and another at Rs. 120/kg. In what ratio should he mix them to obtain a mixture worth Rs. 90/kg?
14. How many ways are there to arrange the letters in the word 'BANANA'?
15. What is the probability of selecting a vowel from the word 'COMPUTER'?
16. A committee of 5 members is to be formed from 6 men and 4 women. What is the probability that the committee has exactly 3 men?
17. What is the probability that a randomly chosen 3-digit number is divisible by 5?
18. In how many ways can the letters of the word 'ENGINEERING' be arranged?
19. How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?
20. A father and son, along with 4 other people, are to be seated in a row. In how many ways can they be seated if the father and son must sit together?
21. In how many ways can the letters of the word 'MADAM' be arranged?
22. How many ways can 4 different books be arranged on a shelf?
23. In how many ways can a committee of 3 people be selected from a group of 5 people?
24. How many different permutations of the letters of the word 'SUCCESS' are there?
25. In how many ways can the letters of the word 'APPLE' be arranged?
26. What is the probability of getting exactly 2 heads when a coin is tossed 3 times?
27. A card is drawn from a pack of 52 cards. What is the probability of drawing an ace?
28. Two dice are rolled simultaneously. What is the probability of getting a sum of 7?
29. In a bag, there are 5 red balls and 7 blue balls. If one ball is drawn at random, what is the probability that it is a blue ball?
30. A die is rolled. What is the probability of getting an even number?
31. If a coin is tossed twice, what is the probability of getting at least one head?
32. A cone has a radius of 3 cm and a height of 4 cm. What is its slant height?
33. What is the volume of a cylinder with a radius of 7 cm and a height of 10 cm? (Use pi = 22/7)
34. A cuboid has dimensions 10 cm x 5 cm x 4 cm. What is its surface area?
35. What is the volume of a cube with a side length of 5 cm?
36. The perimeter of a square is 36 cm. What is the length of its side?
37. A square has a side length of 9 meters. What is its area?
38. What is the area of a rectangle with a length of 15 cm and a width of 10 cm?
39. A rectangle has a length of 12 cm and a width of 8 cm. What is its perimeter?
40. What is the area of a circle with a diameter of 14 cm?
41. The radius of a circle is 7 cm. What is its circumference?
42. A vessel contains a mixture of milk and water in the ratio 5:3. If 8 liters of the mixture are removed and replaced with pure milk, the ratio becomes 3:1. What was the initial quantity of the mixture?
43. In what ratio should tea at Rs. 60 per kg be mixed with tea at Rs. 80 per kg so that by selling the mixture at Rs. 84 per kg, there is a profit of 20%?
44. 10 liters of a mixture contains milk and water in the ratio 3:2. How much pure milk should be added to the mixture so that the ratio of milk to water becomes 2:1?
45. A shopkeeper mixes two types of rice, one costing Rs. 40 per kg and another costing Rs. 55 per kg. In what ratio should he mix them to get a mixture costing Rs. 48 per kg?
46. In what ratio should 25% alcohol solution be mixed with 50% alcohol solution so that the resulting mixture has 40% alcohol?
47. A and B invest in a business. A invests Rs. 30,000 for 10 months and B invests Rs. 40,000 for 8 months. If C joins them with Rs. 50,000 for 6 months, and the total profit is Rs. 86,000, what is A's share?
48. P, Q, and R enter into a partnership. P invests Rs. 40,000 and Q invests Rs. 50,000. After 6 months, R joins with Rs. 60,000. If the profit at the end of the year is Rs. 72,000, and P and Q invested for the entire year, what is R's share?
49. A and B start a business with initial investments of Rs. 75,000 and Rs. 90,000 respectively. After 8 months, A withdraws half of his investment. If the total profit at the end of the year is Rs. 52,000, what is B's share?
50. Three friends, Ram, Shyam, and Mohan, start a business. Ram invests Rs. 20,000 for 12 months, Shyam invests Rs. 30,000 for 8 months, and Mohan invests Rs. 40,000 for 6 months. If the total profit is Rs. 63,000, what is Shyam's share?