1
GATE CSE 2003
+1
-0.3
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$, the values of $$P\,(A\,\left| {B) \,} \right.$$ and $$P\,(B\,\left| {A) \,} \right.$$ respectively are
A
$${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}},\,{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
B
$${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}},\,{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}$$
C
$${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}},\,1$$
D
$$1,\,\,{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
2
GATE CSE 2003
+1
-0.3
Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. How many distinct pairs of sequence, $$B$$ and $$C$$ are there such that
i) Each is sorted in ascending order.
ii) $$B$$ has $$5$$ and $$C$$ has $$3$$ elements, and
iii) The result of merging $$B$$ $$C$$ gives $$A$$?
A
$$2$$
B
$$30$$
C
$$56$$
D
$$256$$
3
GATE CSE 2003
+1
-0.3
$$n$$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is
A
$$\left( {\matrix{ {2n} \cr n \cr } } \right) * {2^n}$$
B
$${3^n}$$
C
$${{\left( {2n} \right)!} \over {{2^n}}}$$
D
$$\left( {\matrix{ {2n} \cr n \cr } } \right)$$
4
GATE CSE 2003
+1
-0.3
$$m$$ identical balls are to be placed in $$n$$ distinct bags. You are given that $$m \ge kn$$, where $$k$$ is a natural number $$\ge 1$$. In how many ways can the balls be placed in the bags if each bag must contain at least $$k$$ balls?
A
$$\left( {\matrix{ {m - k} \cr {n - 1} \cr } } \right)$$
B
$$\left( {\matrix{ {m - kn + n - 1} \cr {n - 1} \cr } } \right)$$
C
$$\left( {\matrix{ {m - 1} \cr {n - k} \cr } } \right)$$
D
$$\left( {\matrix{ {m - kn + n + k - 2} \cr {n - k} \cr } } \right)$$
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