1
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
$$256$$
2
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
$$\left( {\matrix{ {2n} \cr n \cr } } \right)$$
3
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
$$\left( {\matrix{ {m - kn + n + k - 2} \cr {n - k} \cr } } \right)$$
4
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
$$n - 2\left[ {n/2} \right] + 2$$
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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