Discussion
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- Question
- 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
- Correct Answer
- 48
ExplanationTotal number of letters = 5
Number of vowels = 2.
If we consider both vowel as a one letter then,
Required number = 4! 2! = 48. - 1. 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
- 2. 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
- 3. If nP r= 720 nC r than the value r is?
Options- A. 6
- B. 5
- C. 4
- D. 7 Discuss
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. The numbers of straight lines can be formed out of 10 points of which 7 are collinear?
Options- A. 26
- B. 21
- C. 25
- D. None of these Discuss
- 9. The number of different permutations of the word 'BANANA' is?
Options- A. 270
- B. 60
- C. 120
- D. 360 Discuss
- 10. Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is?
Options- A. 11
- B. 12
- C. 13
- D. 14 Discuss
Permutation and Combination problems
Search Results
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: 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: 6
Explanation:
We know that, nPr = nCrr!
? nPr = 720nCr
? nCr.r! = 720nCr
? r! = 720
? r = 6
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: 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.
Correct Answer: 25
Explanation:
If there were no three points collinear. We should have 10C2 lines but since 7 points are collinear we must subtract 7C2 lines and add the one corresponding to the line of collinearity of the seven points.
Thus, the required number of straight lines .
= 10C2 - 7C2 + 1 = 25
Correct Answer: 60
Explanation:
There are 3A's 2N's and one B. We have to find the total number of arrangements of 6 letters out of which 3 are alike of one kind, 2 are alike of second kind, thus the total number of words
= 6! / (3! 2!) = 60
Correct Answer: 12
Explanation:
Let there be n persons in the room. The total number of hand shakes is same as the number of ways of selecting 2 out of n.
nC2 = 66
? n(n - 1) / 2! = 66
? n2 - n - 132 = 0
? (n - 12) (n + 11) = 0
? n = 12
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