1
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
$$\left( {\matrix{ {m - kn + n + k - 2} \cr {n - k} \cr } } \right)$$
2
GATE CSE 2002
+1
-0.3
The minimum number of colors required to color the vertices of a cycle with $$n$$ nodes in such a way that no two adjacent nodes have the same colour is:
A
$$2$$
B
$$3$$
C
$$4$$
D
$$n - 2\left[ {n/2} \right] + 2$$
3
GATE CSE 2000
+1
-0.3
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is
A
3
B
8
C
9
D
12
4
GATE CSE 2000
+1
-0.3
The solution to the recurrence equation
$$T\left( {{2^k}} \right)$$ $$= 3T\left( {{2^{k - 1}}} \right) + 1$$,
$$T\left( 1 \right) = 1$$ is:
A
$${{2^k}}$$
B
$$\left( {{3^{k + 1}} - 1} \right)/2$$
C
$${3^{\log {K \over 2}}}$$
D
$${2^{\log {K \over 3}}}$$
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