1
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
$$\left( {\matrix{ {20} \cr {10} \cr } } \right) - \left( {\matrix{ 8 \cr 4 \cr } } \right) \times \left( {\matrix{ {11} \cr 5 \cr } } \right)$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
$$44$$
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