Question
How many 8 digit numbers can be formed using the digits
1, 2, 0, 2, 4, 1, 2, 4 ?Solution
There are 8 digits 1, 2, 0, 2, 4, 1, 2, 4 in which 1 occurs 2 times, 2 occurs 3 times and 4 occurs 2 times ∴ Number of 8 digit numbers = 8!/(2! ×3! ×2!) = 1680 But out of these 1680 numbers there are some numbers which begin with ‘0’ and they are not 8 digit numbers The numbers of such numbers beginning with ‘0’ = 7!/(2! ×3! ×2!) = 210 Hence the required number of 8 digit numbers = 1680 – 210 = 1470
Statements: I > J = K ≥ M; D ≥ F ≤ E = I
Conclusions:
I. M < E
II. D ≥ MStatements: C ≤ A ≥ B > D; F > E ≥ G ≥ A
Conclusions:
I. E ≥ B
II. F > DWhat should come in the place of question mark, in the given expressions to make ‘N ≤ T’ always true?
L > M = N ≤ O ≤ P _?_ Q = R ≤ S...
Statements:
P > Q ≥ M ≤ N; Y ≥ Z ≥ A = P
Conclusion:
I. Y > N
II. N ≥ Y
Statements: H > S ≥ V ≥ I; T ≤ G = I; U < J ≤ T
Conclusions:
I. S > J
II. U < I
III. H ≥ G
Statements: P < Q ≤ R ≤ S; P > T = V ≥ X; S ≤ W = Y < U
Conclusions:
I. U > R
II. W > X
III. Q < Y
Statements:Â Â Â Â Â Â A @ D % M % N; M $ P $ Q
Conclusions :     I. D % Q                              I...
Statements:         N # L,     L @A,    A % I,    I & E
Conclusions :Â Â Â Â Â Â Â Â Â
I.E $ LÂ Â Â Â Â
...Statements:Â
A $ B * X © Y @ ZÂ
Conclusions:Â
I. X @ ZÂ
 II. Z * AÂ
III. Z % X
Statement: M>T≤Z; T>Q ; X ≥R>Q
I. X ≥ M
II. Q < M