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
$${2^{\log {K \over 3}}}$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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