1
GATE CSE 2007
MCQ (Single Correct Answer)
+1
-0.3
The maximum number of binary trees that can be formed with three unlabeled nodes is:
A
1
B
5
C
4
D
3
2
GATE CSE 2007
MCQ (Single Correct Answer)
+1
-0.3
Consider the following two statements about the function $$$f\left( x \right) = \left| x \right|:$$$

$$P.\,\,f\left( x \right)$$ is continuous for all real values of $$x$$
$$Q.\,\,f\left( x \right)$$ is differentiable for all real values of $$x$$

Which of the following is True?

A
$$P$$ is true and $$Q$$ is false.
B
$$P$$ is false and $$Q$$ is true.
C
Both $$P$$ and $$Q$$ are true.
D
Both $$P$$ and $$Q$$ are false.
3
GATE CSE 2007
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
$$\left( {\matrix{ {20} \cr {10} \cr } } \right) - \left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$
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