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Compound Interest
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Reading Comprehension
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Professional Knowledge (IT)
Data Structure Compiler

Permutation and Combination

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Q 1. How many total numbers of seven-digit numbers can be formed having sum of whose digits is even is

9000000

4500000

8100000

4400000

None of these

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Q 2. In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?

266

86400

11760

5040

None of these

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Q 3. There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person {tex} 2 ; {/tex} task 2 must be assigned to either person 3 or person 4 . Every person is to be assigned one task. In how many ways can the assignment be done?

144

180

192

360

None of these

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Q 4. 4 boys and 2 girls are to be seated in a row in such a way that the two girls are always together. In how many different ways can they be seated?

120

720

148

240

None of these

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Q 5. Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?

{tex} \frac { 12 } { 13 } {/tex}

{tex} \frac { 11 } { 13 } {/tex}

{tex} \frac { 10 } { 15 } {/tex}

{tex} \frac { 1 } { 15 } {/tex}

None of these

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Q 6. How many three digit numbers can having only two consecutive digits identical is

153

162

168

163

None of these

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Q 7. How many total number of ways in which n distinct objects can be put into two different boxes is

{tex} n ^ { 2 } {/tex}

{tex} 2 ^ { n } {/tex}

{tex} 2 n {/tex}

{tex}3^n{/tex}

None of these

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Q 8. Letters of the word DIRECTOR are arranged in such a way that all the vowels come together. Find out the total number of ways for making such arrangement.

4320

2720

2160

1120

None of these

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Q 9. In how many ways can the letters of the word 'PRAISE' be arranged. So that vowels do not come together?

720

576

440

144

None of these

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Q 10. How many total numbers of not more than 20 digits that can be formed by using the digits {tex} 0,1,2,3 \ \text{and} \ 4{/tex} is

{tex} 5 ^ { 20 } {/tex}

{tex} 5 ^ { 20 } - 1 {/tex}

{tex} 5 ^ { 20 } + 1 {/tex}

{tex} 6 ^ { 20 } {/tex}

None of these

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Q 11. A box contains 5 green, 4 yellow and 3 white marbles, 3 marbles are drawn at random. What is the probability that they are not of the same colour?

{tex} \frac { 13 } { 44 } {/tex}

{tex} \frac { 41 } { 44 } {/tex}

{tex} \frac { 13 } { 55 } {/tex}

{tex} \frac { 52 } { 55 } {/tex}

None of these

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Q 12. The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is

{tex} 3 ^ { 10 } {/tex}

{tex} 2 ^ { 10 } - 1 {/tex}

{tex} 3 ^ { 10 } - 1 {/tex}

{tex} 2 ^ { 10 } {/tex}

None of these

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Q 13. All possible two factors products are formed from the numbers 1, 2, 3, 4, ....., 200. The number of factors out of total obtained which are multiples of 5 is

5040

7180

8150

7280

None of these

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Q 14. In how many different ways can a group of 4 men and 4 women be formed out of 7 men and 8 women?

2450

105

1170

Cannot be determined

None of these

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Q 15. A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of {tex} 5 , {/tex} given that two of the friends will not attend the party together is

56

126

91

94

None of these

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Q 16. In how many different ways can the letters of the word JUDGE be arranged so that the vowels always come together?

48

24

120

60

None of these

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Q 17. The number of six digit numbers that can be formed from the digits {tex} 1,2,3,4,5,6 {/tex} and {tex}7{/tex} so that digits do not repeat and the terminal digits are even is

144

72

288

720

None of these

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Q 18. In a box carrying one dozen of oranges, one-third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one orange out of the three oranges picked up is good?

{tex} \frac { 1 } { 55 } {/tex}

{tex} \frac { 54 } { 55 } {/tex}

{tex} \frac { 45 } { 55 } {/tex}

{tex} \frac { 3 } { 55 } {/tex}

None of these

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Q 19. In how many different ways can be letters of the word SOFTWARE be arranged in such a way that the vowels always come together?

13440

1440

360

120

None of these

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Q 20. The number of ways in which ten candidates {tex} \mathrm { A } _ { 1 } , \mathrm { A } _ { 2 } , \ldots , \mathrm { A } _ { 10 } {/tex} can be ranked so that {tex} \mathrm { A } _ { 1 } {/tex} is always above {tex} \mathrm { A } _ { 2 } {/tex} is

{tex} \frac { 10 ! } { 2 } {/tex}

{tex} 10 ! {/tex}

{tex} 9 ! {/tex}

{tex} \frac { 8 ! } { 2 } {/tex}

None of these

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Q 21. In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?

360

720

480

5040

None of these

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Q 22. If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is

85

100

120

240

None of these

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Q 23. In how many different ways can the letters of the word RUMOUR be arranged?

180

720

30

90

None of these

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Q 24. 765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns. How many chairs will be excluded to make this arrangement possible?

6

36

19

27

None of these

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