1
GATE CSE 2008
+2
-0.6
In how many ways can $$b$$ blue balls and $$r$$ red balls be distributed in $$n$$ distinct boxes?
A
$${{\left( {n + b - 1} \right)!\left( {n + r - 1} \right)!} \over {\left( {n - 1} \right)!b!\left( {n - 1} \right)!r!}}$$
B
$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {\left( {n - 1} \right)!\left( {n - 1} \right)!\left( {b + r} \right)!}}$$
C
$${{n!} \over {b!r!}}$$
D
$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {n!\left( {b + r - 1} \right)!}}$$
2
GATE CSE 2008
+2
-0.6
When $$n = {2^{2k}}$$ for some $$k \ge 0$$, the recurrence relation $$T\left( n \right) = \sqrt 2 T\left( {n/2} \right) + \sqrt n ,\,\,T\left( 1 \right) = 1$$\$
evaluates to
A
$$\sqrt n \left( {\log \,n + 1} \right)$$
B
$$\sqrt n \,\log \,n$$
C
$$\sqrt n \,\log \,\sqrt n$$
D
$$n\,\log \sqrt n$$
3
GATE CSE 2007
+2
-0.6
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $$(i, j)$$ then it can move to either $$(i+1, j)$$ or $$(i, j+1)$$

How many distinct path are there for the robot to reach the point $$(10, 10)$$ starting from the initial position $$(0, 0)$$?

A
$$\left( {\matrix{ {20} \cr {10} \cr } } \right)$$
B
$${2^{20}}$$
C
$${2^{10}}$$
D
None of the above
4
GATE CSE 2007
+2
-0.6
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $$(i, j)$$ then it can move to either $$(i+1, j)$$ or $$(i, j+1)$$

Suppose that the robot is not allowed to traverse the line segment from $$(4, 4)$$ to $$(5,4)$$. With this constraint, how many distinct path are there for the robot to reach $$(10, 10)$$ starting from $$(0,0)$$?

A
$${2^{9}}$$
B
$${2^{19}}$$
C
$$\left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$
D
$$\left( {\matrix{ {20} \cr {10} \cr } } \right) - \left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$
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
EXAM MAP
Joint Entrance Examination