GATE CSE 2008 | Combinatorics Question 14 | Discrete Mathematics

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

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

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 $$(0,0)$$?

$${2^{9}}$$

$${2^{19}}$$

$$\left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$

$$\left( {\matrix{ {20} \cr {10} \cr } } \right) - \left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$

GATE CSE 2006

MCQ (Single Correct Answer)

-0.6

Consider the polynomial $$P\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3},$$ where $${a_i} \ne 0,\forall i$$. The minimum number of multiplications needed to evaluate $$p$$ on an input $$x$$ is

$$3$$

$$4$$

$$6$$

$$5$$

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