**Directions (Q. 1-5): From a class total 360 students appeared in an exam. Three fourth of these are boys. 40 % boys failed in the exam, two third of the girls are failed in the exam and remaining passed.**

**1.What is the ratio of the total number of girls to the number of boys who failed in the exam?**

(a) 4 : 9

(b) 9 : 5

(c) 5 : 6

(d) 6 : 3

(e) None of these

**1. c**

**Ratio: 90/108 = 5/6**

**2.What is the sum of the number of boys who failed and number of girls who passed in the exam?**

(a) 148

(b) 158

(c) 128

(d) 138

(e) None of these

**2. d**

**Sum = 108 + 30 = 138**

**3.What is the difference between the number of boys who are passed and number of girls who are failed?**

(a) 102

(b) 202

(c) 52

(d) 302

(e) None of these

**3. a**

**Diff = 162 - 60 = 102**

**4.What is the ratio of the total number of boys and girls who are passed to the number of boys and girls who are failed?**

(a) 7 : 8

(b) 8 : 7

(c) 9 : 17

(d) 5 : 7

(e) None of these

**4. b**

**Ratio = 192/168 = 8/7**

**5. Total number of boys passed is approximately what percent of total number of girls in the class?**

(a) 60 %

(b) 120 %

(c) 150 %

(d) 180 %

(e) 270 %

**5. d**

**Req% = 162/90 * 100 = 180%**

**Direction (Q. 6 – 10): A bag contains 4 red, 5 brown and 6 white balls. Three balls are drawn randomly:**

**6.What is the probability that balls drawn contains exactly two red balls?**

(a) 54/145

(b) 66/455

(c) 46/105

(d) 31/455

(e) None of these

**6. b**

**n(S) = 15C3 = (15 * 14 * 13)/6 = 455**

**2 red balls can be selected in 4C2 = 6 ways**

**And remaining one ball can be selected in 11C1 = 11 ways**

**P(E) = (6*11)/455 = 66/455**

**7.What is the probability that the balls drawn contains no brown ball?**

(a) 11/65

(b) 31/91

(c) 24/91

(d) 31/455

(e) None of these

**7. c**

**n(S) = 15C3 = 455**

**Three balls have to be selected from 4 red and 6 white balls**

**No. of ways = 10C3 = 120**

**P(E) = 120/455 = 24/91**

**8. What is the probability that the balls drawn are not of the same colour?**

(a) 34/455

(b) 31/105

(c) 74/105

(d) 421/455

(e) None of these

**8. d**

**n(S) = 15C3 =455**

**If all three balls are of same colour, then no. of ways = 4C3 + 5C3 + 6C3 = 4 + 10 + 20 = 34**

**P(E) = 34/455**

**For being different colours P(E) = 1 - 34/455 = 421/455**

**9. If two balls are drawn randomly then what is the probability that both the balls are of same colour?**

(a) 31/105

(b) 74/105

(c) 34/455

(d) 421/455

(e) None of these

**9. a**

**n(S) = 15C2 = 105**

**n(E) = 4C2 + 5C2C + 6C2 = 6 + 10 + 15 = 31**

**P(E) = 31/105**

**10.What is the probability that the three balls drawn are of different colour?**

(a) 21/91

(b) 31/105

(c) 24/105

(d) 24/91

(e) None of these

**10. d**

**n(S) = 15C3 = 455**

**n(E) = 4C1 + 5C1 + 6C1 = 4 * 5 * 6 = 120**

**P(E) = 120/455 = 24/91**