1. A bag contains 6 green, 3 red and 7 yellow balls. 2 balls are drawn at random. What is the probability that all two drawn

are of different colours ?

2. In how many different ways can letters of the word FORMAL be arranged ?

1) 1440 2) 360 3) 720 4) 540 5) 620

3. In how many different ways can the letters of the word INVITATION be arranged in such a way that vowels always come together ?

1) 1800 2) 7200 3) 2400 4) 3600 5) 3800

4. In how many can a group of 6 Man and 3 Women be made out of a total 8 men and 5 women ?

1) 540 2) 720 3) 260 4) 560 5) 280

5. There are 18 students in a class. Find the number of ways in which 6 students can be chosen to form a group ?

1) 18612 2) 18264 3) 18564 4) 18628 5) 18574

Direction (Q. 6 -10) : Study the following information carefully and answer the question given below : There are a certain number of candidate appeared for the state level commission examination conducted by three different states Bihar, Jharkhand and Orissa. All of the candidates have cleared at least one states examination. 32.5 % students cleared Bihar's examination, 42.5 % students cleared Jharkhand examination and 54.5 % students cleared Orissa state examination. 9 % students cleared only Bihar and Jharkhand examination, 6 % students cleared only Jharkhand and Orissa examination and 7.5 % students cleared only Bihar and Orissa examination. If total number of students in the group is 800 then answer the following questions.

6. How many students cleared all three state–level examination ?

1) 28 2) 36 3) 66 4) 56 5) None of these

7. What is the percentage of students who cleared the only examination conducted by state Bihar ?

1) 6 % 2) 9 % 3) 12.5 % 4) 15 % 5) 16 %

8. How many students are there who cleared examinations conducted by at least two states ?

1) 208 2) 224 3) 232 4) 236 5) None of these

9. What is the percentage of students who cleared the exam conducted by Jharkhand but couldn't clear the exam conducted by Orissa state ?

1) 29.5 % 2) 32 % 3) 27.5 % 4) 33 % 5) 35 %

10. How many students are there who have cleared at most one exam conducted by these three states ?

1) 514 2) 508 3) 524 4) 560 5) 592

Answers :-

2.3; FORMAL = 6! = 6 × 5 × 4 × 3× 2 ×1 = 720

(6 to 10)

6.1; Number of students who cleared all the three state – level exams = 25

8.1; Req. number of students = 72 + 48 + 60 + 28 = 208

10.5; Req. number of students = 100+ 192 + 300 = 592

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