# IBPS PO Quantitative Aptitude Permutation and Combination For Prelims: 16th February

Numerical Ability or Quantitative Aptitude Section has given heebie-jeebies to the aspirants when they appear for a banking examination. As the level of every other section is only getting complex and convoluted, there is no doubt that this section, too, makes your blood run cold. The questions asked in this section are calculative and very time-consuming. But once dealt with proper strategy, speed, and accuracy, this section can get you the maximum marks in the examination. Following is the Quantitative Aptitude quiz to help you practice with the best of latest pattern questions.

**Q1. In how many different ways can the letters of the word ‘DRASTIC’ be arranged in such a way that the vowels always come together ?**

720

360

1440

540

None of these

Solution:

Total letters = D, R, A, S, T, I, C (7)

Total vowels = A, I (2)

∴ Required no. of ways = 6! × 2!

= 1440

Total vowels = A, I (2)

∴ Required no. of ways = 6! × 2!

= 1440

**Q2. In how many ways can Prabhat arrange the letters of the word ALLAHABAD ?**

7650

7560

6750

5760

7660

**Q3. How many numbers between 2000 and 3000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 (repetition of digits not allowed) ?**

42

210

336

440

120

Solution:

Total required numbers between 2000 and 3000

= 1 × 7 × 6 × 5 (For eg. 2035, 2345)

= 210

= 1 × 7 × 6 × 5 (For eg. 2035, 2345)

= 210

**Q4. In how many ways can a person sent invitation cards to 6 of his friends if he has four servants to distribute the cards ?**

6⁴

4⁶

24

120

36

**Q5. A captain and a vice captain are to be chosen out of a team having eleven players. How many ways are there to achieve this ?**

10.9

¹¹C₂

110

10.9!

11.10!

Solution:

Total ways = 11 × 10

= 110

= 110

**Q6. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?**

159

194

205

209

224

**Q7. 3 men and 3 women are to sit at a round table. In how many different ways can they sit so that no 2 women sit together?**

16

12

18

21

10

Solution:

**Q8. If (n + 2)! = 2550 (n)!, find n.**

49

-47

54

53

63

**Q9. How many four digits number can be formed by using the digits 0, 2, 4, 6, 7 if repetition of digits is allowed.**

625

96

500

36

72

Solution:

Total digits = 5

First place can be filled up by using only one of 4 digits (except 0, since 0 at the first place is meaning less).

Second place can be filled up by using all the five digits (as repetition is allowed).

Similarly, third and fourth place can be filled up by using all the five digits.

Thus,

Places: 0 0 0 0

Digit: 4 5 5 5

Total numbers = 4 × 5 × 5 × 5 = 500

First place can be filled up by using only one of 4 digits (except 0, since 0 at the first place is meaning less).

Second place can be filled up by using all the five digits (as repetition is allowed).

Similarly, third and fourth place can be filled up by using all the five digits.

Thus,

Places: 0 0 0 0

Digit: 4 5 5 5

Total numbers = 4 × 5 × 5 × 5 = 500

**Q10. Find the numbers between 100 and 1000 in which all digits are distinct.**

548

648

748

448

684

Solution:

There are three digits numbers between 100 and 1000.

Total digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 which are 10.

First place can be filled up by using any one of 9 digits (except 0, since 0 at the first place is meaningless).

Second place can be filled up by using any one of 9 digits (as one digit has been used at first place)

Third place can be filled up by using only one of 8 digits.

Thus,

Places : 0 0 0

Digits : 9 9 8

Total number = 9 × 9 × 8 = 648

Total digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 which are 10.

First place can be filled up by using any one of 9 digits (except 0, since 0 at the first place is meaningless).

Second place can be filled up by using any one of 9 digits (as one digit has been used at first place)

Third place can be filled up by using only one of 8 digits.

Thus,

Places : 0 0 0

Digits : 9 9 8

Total number = 9 × 9 × 8 = 648

**Q11. The letters of the word ‘PARADISE’ are to be arranged so that all vowels should not come together. Find the number of arrangements.**

20160

18720

38880

16720

37440

**Q12. If P(5, 2) = P(n, 2), find n.**

5

2

1

3

4

**Q13. Group of 6 students sitting around a circular table, find probability of 2 specified students sits together.**

6!/2!

3

2!/5!

2/5

none of these.

**Q14. In how many ways the word ‘SCOOTER’ can be arranged such that ‘S’ and ‘R’ are always at two ends?**

720

120

2520

5040

None of these

**Q15. Find total number of the 3 digits odd numbers by using the digits 2, 3, 4, 5 when repetitions of digits are not allowed.**

12

22

15

18

24

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