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Column – I Column – II
i)
Number of arrangements of the letters of
the word ENGINEER so that all vowels are
together but all E’s are not together
p) 22
ii)
Number of ways of arrangements
of the letters of the word ELEVEN so that no two
vowels are together and no two consonants are
together is K than 10K equals
q) 23
iii)
Number of ways of keeping 5 letters in 5
addressed envelopes such that no letter goes to its
own envelope is P then P is divisible by
r) 5!
iv)
Number of 6 digit numbers greater than 123000
using 1,2,2,3,3,3 is
s) 59
t) 12
The correct option is

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$(I) \to (R), (I I) \to (T), (I I I) \to (P), (I V) \to (S)$

$(I) \to (S), (I I) \to (P), (I I I) \to (Q), (I V) \to (R)$

$(I) \to (P), (I I) \to (S), (I I I) \to (R), (I V) \to (T)$

$(I) \to (T), (I I) \to (R), (I I I) \to (S), (I V) \to (P)$

answer is A.

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Detailed Solution

I) ENGINEER

vowels are E,E,E,I and consonants are N,N,G,R

required number of ways $= (\frac{5!}{2!} \times \frac{4!}{3!}) - (\frac{5!}{2!} \times 2) = 120 = 5!$

II) Required number of ways ELEVEN

$\begin{array}{l} L V N \to c o n s o n a n t s \\ E E E \to v o w e l s \end{array}\} 3! + 3! = 12$

III) number of dearrangements

$= 5! (1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!})$

$= 60 - 20 + 5 - 1 = 44$ is divisible by 22

IV) Number of 6 digit numbers

$= \frac{3!}{2!} + \frac{3!}{2!} + \frac{3!}{2!} + \frac{5!}{2! 2!} + \frac{51}{3!}$

$= 3 + 3 + 3 + 330 + 20 = 59$

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	Column – I		Column – II
i)	Number of arrangements of the letters of the word ENGINEER so that all vowels are together but all E’s are not together	p)	22
ii)	Number of ways of arrangements of the letters of the word ELEVEN so that no two vowels are together and no two consonants are together is K than 10K equals	q)	23
iii)	Number of ways of keeping 5 letters in 5 addressed envelopes such that no letter goes to its own envelope is P then P is divisible by	r)	5!
iv)	Number of 6 digit numbers greater than 123000 using 1,2,2,3,3,3 is	s)	59
		t)	12