IIT-JEE 2008 Paper 1 Offline | Probability Question 57 | Mathematics

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-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 $$1.$$

STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT - 1

STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1

STATEMENT - 1 is True, STATEMENT - 2 is False.

STATEMENT - 1 is False, STATEMENT - 2 is True.

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let $${E^c}$$ denote the complement of an event $$E.$$ Let $$E, F, G$$ be pairwise independent events with $$P\left( G \right) > 0$$ and $$P\left( {E \cap F \cap G} \right) = 0.$$ Then $$P\left( {{E^c} \cap {F^c}|G} \right)$$ equals

$$P\left( {{E^c}} \right) + P\left( {{F^c}} \right)$$

$$P\left( {{E^c}} \right) - P\left( {{F^c}} \right)$$

$$P\left( {{E^c}} \right) - P\left( F \right)$$

$$P\left( E \right) - P\left( {{F^c}} \right)$$

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

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

$$\frac{1}{2}$$

$$\frac{1}{3}$$

$$\frac{2}{5}$$

$$\frac{1}{5}$$

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let H$$_1$$, H$$_2$$, ..., H$$_n$$ be mutually exclusive and exhaustive events with P(H$$_i$$) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1.

Statement 1 : P(H$$_i$$ | E) > P(E | H$$_i$$). P(H$$_i$$) for $$i=1,2,...,n$$.

Statement 2 : $$\sum\limits_{i = 1}^n {P({H_i}) = 1} $$.

Statement 1 is True, Statement 2 is True, Statement 2 is a CORRECT explanation for Statement 1

Statement 1 is True, Statement 2 is True, Statement 2 is NOT a CORRECT explanation for Statement 1

Statement 1 is True, Statement 2 is False

Statement 1 is False, Statement 2 is True

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