Discussion
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- Question
- If nP r= 720 nC r than the value r is?
Options- A. 6
- B. 5
- C. 4
- D. 7
- Correct Answer
- 6
ExplanationWe know that, nPr = nCrr!
? nPr = 720nCr
? nCr.r! = 720nCr
? r! = 720
? r = 6 - 1. If 2n + 1P n - 1 : 2n - 1P n = 3 : 5, then n is equal to?
Options- A. 4
- B. 6
- C. 3
- D. 8 Discuss
- 2. If 35C n + 7 = 35C 4n - 2, then all the values of n are given by?
Options- A. 28
- B. 3, 6
- C. 3
- D. 6 Discuss
- 3. If nC r - 1 = 36, nC r = 84 and nC r + 1 = 126 then?
Options- A. n = 8, r = 4
- B. n = 9, r = 3
- C. n = 7, r = 5
- D. None of these Discuss
- 4. The total number of arrangements of the letters in the expression a 3b 2c 4 when written at full length is?
Options- A. 1260
- B. 2520
- C. 610
- D. None of these Discuss
- 5. The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges is?
Options- A. 39
- B. 315
- C. 512
- D. None of these Discuss
- 6. If S= {2, 3, 4, 5, 7, 9} , then the number of different three-digit number (with all distinct digits) less than 400 that can be formed from S is?
Options- A. 20
- B. 40
- C. 80
- D. 120 Discuss
- 7. If 7 points out of 12 are in the same straight line, then the number of triangles formed is?
Options- A. 19
- B. 158
- C. 185
- D. 201 Discuss
- 8. In how many different ways can the letters of word JUDGE be arranged so that the vowels always come together?
Options- A. 48
- B. 24
- C. 120
- D. 60 Discuss
- 9. From 4 officers and 8 Jawans in how many ways can 6 be chosen to include at least one officer?
Options- A. 896
- B. 986
- C. 886
- D. 996 Discuss
- 10. From a group of 6 men and 4 women a committee of 4 persons is to be formed?
Options- A. 210
- B. 225
- C. 195
- D. 185 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 4
Explanation:
We have If 2n + 1Pn - 1 / 2n - 1Pn = 3/5
? 5 x 2n + 1Pn - 1 = 3 x 2n - 1Pn
? {5 x (2n + 1)!} / {(n + 2 )!} = 3 x {(2n - 1)!} / {(n - 1)!}
? 10(2n + 1) = 3(n + 2) (n + 1)
? 3n2 - 11n - 4 = 0
?(3n + 1 ) (n - 4) = 0
? n = 4
Correct Answer: 3, 6
Explanation:
35Cn + 7 = 35C4n - 2
We know that if nCx = nCy then, Either x = y or x + y = n
Case 1: x + y = n
? n + 7 + 4n - 2 = 35
? 5n + 5 = 35
? 5n = 30
? n = 6
Case 2: x = y
? n + 7 = 4n - 2
? 4n - n = 2 + 7
? 3n = 9
? n = 3
Correct Answer: n = 9, r = 3
Explanation:
nCr - 1 = 36, nCr = 84 and nCr + 1 = 126
? nCr / nCr - 1 = 84/36
? 3n - 10r + 3 = 0 ....(i)
nCr + 1 / nCr = 126/84
? 2n - 5r - 3 = 0 .............(ii)
From (i) and (ii) r = 3, n = 9
Correct Answer: 1260
Explanation:
We have 9 letters 3 a's, 2 b's and 4 c's. These 9 letters can be arranged in 9! / (3! 2! 4!) = 1260 ways.
Correct Answer: None of these
Explanation:
Required number of ways = (2 + 1) (3 + 1) (4 + 1) - 1 = 59
Correct Answer: 20
Explanation:
The hundred place will be reserved for 3 or 2
5 digits are free to fill rest two places i,e., of tens and unit.
Number of required 3 digit number = 2 x 5C2 = 20
Correct Answer: 185
Explanation:
The number of ways of selecting 3 points out of 12 points is 12C3. The number of ways of selecting 3 points out of 7 points, on the same straight line is 7C3, Hence, the number of triangle formed will be 12C3 - 7C3 = 210 - 35 = 185.
Correct Answer: 48
Explanation:
Total number of letters = 5
Number of vowels = 2.
If we consider both vowel as a one letter then,
Required number = 4! 2! = 48.
Correct Answer: 896
Explanation:
We may choose 1 officer and 5 jawans or 2 officers and 4 jawans ......... or 4 officers and 2 jawans.
So Required answer = [4C1 x 8C5] + [4C2 x 8C4] + [4C3 x 8C3] + [4C4 x 8C2]
= 224 + 420 + 224 + 28 = 896.
Correct Answer: 195
Explanation:
Required no. of ways = [4C1 x 6C3] + [4C2 x 6C2] + [4C3 x 6C1] + [4C4]
= 80 + 90 + 24 + 1 = 195.
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