1
GATE CSE 2007
+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
$$\left( {\matrix{ {20} \cr {10} \cr } } \right) - \left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$
2
GATE CSE 2006
+2
-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
A
$$3$$
B
$$4$$
C
$$6$$
D
$$5$$
3
GATE CSE 2006
+2
-0.6
For each elements in a set of size $$2n$$, an unbiased coin in tossed. The $$2n$$ coin tosses are independent. An element is chhoosen if the corresponding coin toss were head.The probability that exactly $$n$$ elements are chosen is
A
$${{\left( {\matrix{ {2n} \cr n \cr } } \right)} \over {{4^n}}}$$
B
$${{\left( {\matrix{ {2n} \cr n \cr } } \right)} \over {{2^n}}}$$
C
$${1 \over {\left( {\matrix{ {2n} \cr n \cr } } \right)}}$$
D
$${1 \over 2}$$
4
GATE CSE 2006
+2
-0.6
What is the cardinality of the set of integers $$X$$ defined below?
$$X =$$ {$$n\left| {1 \le n \le 123,\,\,\,\,\,n} \right.$$ is not divisible by either $$2, 3$$ or $$5$$ }
A
$$28$$
B
$$33$$
C
$$37$$
D
$$44$$
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
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