IIT-JEE 2012 Paper 2 Offline | Permutations and Combinations Question 21 | Mathematics

1

IIT-JEE 2012 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-1

Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let $${{b_n}}$$ = the number of such n-digit integers ending with digit 1 and $${{c_n}}$$ =the number of such n-digit integers ending with digit 0.

Which of the following is correct?

A

$${a_{17}} = {a_{16}} + {a_{15}}$$

B

$${c_{17}} \ne {c_{16}} + {c_{15}}$$

C

$${b_{17}} \ne {b_{16}} + {c_{16}}$$

D

$${a_{17}} = {c_{17}} + {b_{16}}$$

2

IIT-JEE 2012 Paper 1 Offline

MCQ (Single Correct Answer)

+4

-1

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

A

75

B

150

C

210

D

243

3

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

A

55

B

66

C

77

D

88

4

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-1

Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

	Column I		Column II
(A)	The number of permutations containing the word ENDEA is	(P)	5!
(B)	The number of permutations in which the letter E occurs in the first and the last position is	(Q)	2 $$\times$$ 5!
(C)	The number of permutations in which none of the letters D, L, N occurs in the last five positions is	(R)	7 $$\times$$ 5!
(D)	The number of permutations in which the letters A, E, O occur only in odd positions is	(S)	21 $$\times$$ 5!

A

(A) - p ; (B) - s; (C) - q ; (D) - q

B

(A) - q ; (B) - q ; (C) - s ; (D) - p

C

(A) - p ; (B) - s; (C) - p ; (D) - r

D

(A) - p ; (B) - r ; (C) - q ; (D) - p