1
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :

A
2, 4 or 8
B
3, 6 or 9
C
4 or 8
D
5 or 10
2
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Consider the system of equations $$ax+by=0; cx+dy=0,$$
where $$a,b,c,d$$ $$ \in \left\{ {0,1} \right\}$$

STATEMENT - 1 : The probability that the system of equations has a unique solution is $${3 \over 8}.$$ and

STATEMENT - 2 : The probability that the system of equations has a solution is $$1.$$
A
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False.
D
STATEMENT - 1 is False, STATEMENT - 2 is True.
3
IIT-JEE 2007
MCQ (Single Correct Answer)
+3
-0.75
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is
A
$${1 \over 2}$$
B
$${1 \over 3}$$
C
$${2 \over 5}$$
D
$${1 \over 5}$$
4
IIT-JEE 2007
MCQ (Single Correct Answer)
+3
-0.75
Let $${H_1},{H_2},....,{H_n}$$ be mutually exclusive and exhaustive events with $$P\left( {{H_1}} \right) > 0,i = 1,2,.....,n.$$ Let $$E$$ be any other event with $$0 < P\left( E \right) < 1.$$
STATEMENT-1:
$$P\left( {{H_1}|E} \right) > P\left( {E|{H_1}} \right).P\left( {{H_1}} \right)$$ for $$i=1,2,....,n$$ because

STATEMENT-2: $$\sum\limits_{i = 1}^n {P\left( {{H_i}} \right)} = 1.$$

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True
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