GATE CSE 2008 | Combinatorics Question 15 | Discrete Mathematics

PREVIOUS NEXT

GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$.

The value of $${x_5}$$ is

$$5$$

$$7$$

$$8$$

$$13$$

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

$$3$$

$$4$$

$$6$$

$$5$$

PREVIOUS NEXT