GATE CSE 2008 | Combinatorics Question 12 | Discrete Mathematics

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GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

The exponent of $$11$$ in the prime factorization of $$300!$$ is

$$27$$

$$28$$

$$29$$

$$30$$

GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

In how many ways can $$b$$ blue balls and $$r$$ red balls be distributed in $$n$$ distinct boxes?

$${{\left( {n + b - 1} \right)!\left( {n + r - 1} \right)!} \over {\left( {n - 1} \right)!b!\left( {n - 1} \right)!r!}}$$

$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {\left( {n - 1} \right)!\left( {n - 1} \right)!\left( {b + r} \right)!}}$$

$${{n!} \over {b!r!}}$$

$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {n!\left( {b + r - 1} \right)!}}$$

GATE CSE 2008

MCQ (Single Correct Answer)

-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

$$\sqrt n \left( {\log \,n + 1} \right)$$

$$\sqrt n \,\log \,n$$

$$\sqrt n \,\log \,\sqrt n $$

$$n\,\log \sqrt n $$

GATE CSE 2007

MCQ (Single Correct Answer)

-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 $$(0, 0)$$?

$$\left( {\matrix{ {20} \cr {10} \cr } } \right)$$

$${2^{20}}$$

$${2^{10}}$$

None of the above

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