The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is
216
192
120
120
If m is the AMN of two distinct real numbers l and n (l,n>1) and G_{1}, G_{2}, and G3 are three geometric means between l and n, then equals
4l^{2} mn
4lm^{2}n
4 lmn^{2}
4 lmn^{2}
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
8 . ^{6}C_{4} . ^{7}C_{4}
6 . 7 . ^{8}C_{4}_{}
6 . 8 . ^{7}C_{4}
6 . 8 . ^{7}C_{4}
The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-
12!/3!(4!)^{3}
12!/3!(3!)^{4}
12!/(4!)^{3}
12!/(4!)^{3}
How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?
120
480
360
360
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
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
5
3^{8}
3^{8}
The number of all numbers having 5 digits, with distinct digits is
99999
$9\times {}^{9}\mathrm{P}_{4}$
${}^{10}\mathrm{P}_{5}$
${}^{9}\mathrm{P}_{4}$
The greatest integer which divides (p + 1) (p + 2) (p + 3) .... (p + q) for all p E N and fixed q $\in $ N is
p!
q!
p
q
The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is
$\frac{7!}{2!2!}$
$\frac{7!}{2!}$
$\frac{6!}{2!}$
$5!\times 2!$