1
GATE CSE 2008
+2
-0.6
Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$.

Which of the following recurrences does $${x_n}$$ satisfy?

A
$${x_n} = 2{x_{n - 1}}$$
B
$${x_n} = {x_{\left[ {n/2} \right]}} + 1$$
C
$${x_n} = {x_{\left[ {n/2} \right]}} + n$$
D
$${x_n} = {x_{n - 1}} + {x_{n - 2}}$$
2
GATE CSE 2008
+2
-0.6
The exponent of $$11$$ in the prime factorization of $$300!$$ is
A
$$27$$
B
$$28$$
C
$$29$$
D
$$30$$
3
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
$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {n!\left( {b + r - 1} \right)!}}$$
4
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
$$n\,\log \sqrt n$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
EXAM MAP
Joint Entrance Examination