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- Question
A polygon has 44 diagonals, then the number of its sides are ?
Options- A. 13
- B. 9
- C. 11
- D. 7
- Correct Answer
- 11
ExplanationLet the number of sides be n.
The number of diagonals is given by nC2 - n
Therefore, nC2 - n = 44, n>0
nC2 - n = 44
n2 - 3n - 88 = 0
n2 -11n + 8n - 88 = 0
n(n - 11) + 8(n - 11) = 0
n = -8 or n = 11.As n>0, n will not be -8. Therefore, n=11.
- 1. A decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?
Options- A. 18
- B. 24
- C. 36
- D. 32 Discuss
- 2. In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
Options- A. 4! x 4!
- B. 5! x 5!
- C. 4! x 5!
- D. 3! x 4! Discuss
- 3. There are 5 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next two have 6 choices each?
Options- A. 1112
- B. 2304
- C. 1224
- D. 2426 Discuss
- 4. A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
Options- A. 215
- B. 268
- C. 254
- D. 216 Discuss
- 5. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Options- A. 53400
- B. 17610
- C. 11760
- D. 45000 Discuss
- 6. Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?
Options- A. 120
- B. 256
- C. 192
- D. 244 Discuss
- 7. How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.
Options- A. 64
- B. 63
- C. 62
- D. 60 Discuss
- 8. Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.
Options- A. 28
- B. 14
- C. 21
- D. 7 Discuss
- 9. If nC10=nC12 then,find n.
Options- A. 10
- B. 12
- C. 22
- D. 24 Discuss
- 10. Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle round a table facing each other. Directions: (1) No two ladies or two gentlemen are sitting side by side. (2) C, who is sitting between G and E is facing D. (3) F is between D and A and is facing G. (4) H is to the right of B. Question: 1. Who are immediate neighbours of B? 2. E is facing whom?
Options- A. G & H , H
- B. F & H , B
- C. E & F , F
- D. E & H , G Discuss
Permutation and Combination problems
Search Results
Correct Answer: 36
Explanation:
Required Number of ways = = 36
Correct Answer: 4! x 5!
Explanation:
The word EDUCATION is a 9 letter word, with none of the letters repeating.
The vowels occupy 3rd,5th,7th and 8th position in the word and the remaining 5 positions are occupied by consonants
As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the afore mentioned 4 places and the consonants can occupy1st,2nd,4th,6th and 9th positions.
The 4 vowels can be arranged in the 3rd,5th,7th and 8th position in 4! Ways.
Similarly, the 5 consonants can be arranged in1st,2nd,4th,6th and 9th position in5! Ways.
Hence, the total number of ways = 4! × 5!
Correct Answer: 2304
Explanation:
Number of questions = 5
Possibilities of choices for each question 1 to 5 respectively = 4, 4, 4, 6, 6
Reuired total number of sequences
= 4 x 4 x 4 x 6 x 6
= 2304.
Correct Answer: 215
Explanation:
Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215.
Correct Answer: 11760
Explanation:
Required number of ways = = = 11760
Correct Answer: 192
Explanation:
We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.
The number can be 4 digited but greater than 4000 or 5 digited.
Number of 4 digited numbers greater than 4000 are
4 or 5 or 6 can occupy thousand place => 3 x
= 3 x 24 = 72.
5 digited numbers = = 5! = 120
So the total numbers greater than 4000 = 72 + 120 = 192
Correct Answer: 63
Explanation:
Given digits are 0, 4, 2, 6
Required 4 digit number should be greater than 6000.
So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.
This can be done by
1x4x4x4 = 64
Greater than 6000 means 6000 should not be there.
Hence, 64 - 1 = 63.
Correct Answer: 28
Explanation:
Let x, y, z be the number of balls received by the three persons, then
Let
x + y + z =21
u + 5 + v + 5 + w + 5 = 21
u + v + w = 6
Total number of solutions =
Correct Answer: 22
Explanation:
Using, we get
n ? 10 = 12
or, n = 12 + 10 = 22
Correct Answer: G & H , H
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