Permutations And Combinations
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How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
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8 . 6C4 . 7C4
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6 . 7 . 8C4
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6 . 8 . 7C4
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7 . 6C4 . 8C4
D.
7 . 6C4 . 8C4
Other than S, seven letters M, I, I, I, P, P, I can be arranged in 7!/2! 4!=7 . 5 . 3.
Now four S can be placed in 8 spaces in 8 C4 ways. Desired number of ways = 7 . 5 . 3 . 8C4 = 7 . 6C4 . 8C4.
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How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?
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120
-
480
-
360
-
240
C.
360
A total number of ways in which all letters can be arranged in alphabetical order = 6! There are two vowels in the word GARDEN. A total number of ways in which these two vowels can be arranged = 2!
∴ Total number of required ways
∴ Total number of required ways
If m is the AMN of two distinct real numbers l and n (l,n>1) and G1, G2, and G3 are three geometric means between l and n, then 
equals
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4l2 mn
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4lm2n
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4 lmn2
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4l2m2n2
B.
4lm2n
Given,
m is the AM of l and n
l +n = 2m
and G1, G2, G3, n are in GP
Let r be the common ratio of this GP
G1 = lr
G2 =lr2
G3= lr3
n = lr4
The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is
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216
-
192
-
120
-
72
B.
192
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
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5
- 8C3
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38
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21
D.
21
The required number of ways
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Mock Test Series
Mock Test Series