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Solution :-
1.(4) The word LEASE consists of 5 letters in which E
comes twice.
∴ Number of arrangements = 5| /2|
= (5 × 4 × 3 × 2 × 1)/(2 × 1) = 60
2.(5) The word CYCLE has 5 letters in which letters
comes twice.
∴ Number of arrangements = 5| / 2|
= (5 × 4 × 3 × 2 × 1)/(2 × 1) = 60
3.(2) Required number of committees
= (4c
× 5c2
×
3c2 )
= (4 × 3)/(1× 2) × (5 × 4)/(1 × 2) × (3 × 2 )/(1 × 2)
= 6 × 10 × 3 = 180
4.(4) Required number of committees
= Selection of 6 teachers from science and arts teachers
=9c6
= 9c3
[∴ nCr = nCn-r ]
= (9 × 8 × 7)/ (1 × 2 × 3) = 84
5.(3) Required number of committees = Selection out
of all the teachers
= 12C6
= (12 × 11 × 10 × 9 × 8 × 7)/(1 × 2 × 3× 4 × 5× 6) = 924
6.(1) The word PRAISE consists of 6 distinct letters.
∴ Number of arrangements = 6|
= 6 × 5 × 4 × 3× 2× 1 = 720
7.(4) The word THERAPY consists of 7 distinct letters
in which E,A are two vowels.
We get THRPY (EA) keeping EA together as single entity.
Number of permutations when vowels are together
= 6| × 2|
∴ Required number of arrangements = 7| – 1440
= 5040 – 1440 = 3600
8.(1) The word VISITING has 8 letters in which I comes
thrice.
∴ Number of arrangements = 8| / 3|
= 8 × 7 × 6 × 5 × 4 = 6720
9.(5) The word REPLACE consists of 7 letters in which
‘E’ comes twice.
∴ Number of arrangements = 7| /2|
= 7 × 6 × 5 × 4 × 3 = 2520
10.The Word SACRED consists of 4 consonants (SCRD)
and two vowels (AE). On keeping vowels together we
get SCRD (AE).
∴ Number of arrangements
= 5| × 2|
= 5 × 4 × 3 × 2 × 1 × 1 × 2
= 240
