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
EXAM MAP
Medical
NEET