1
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
$${1 \over 2}$$
2
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
$$44$$
3
GATE CSE 2005
+2
-0.6
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $$(a, b)$$ and $$(c, d)$$ in the chosen set such that $$a \equiv c$$ mod $$3$$ and $$b \equiv d$$ mode $$5$$
A
$$4$$
B
$$6$$
C
$$16$$
D
$$24$$
4
GATE CSE 2005
+2
-0.6
Let $$G\left( x \right) = 1/\left( {1 - x} \right)2 = \sum\limits_{i = 0}^\infty {g\left( i \right)\,{x^1}} \,\,\,,$$
where $$\left| x \right| < 1$$ What is $$g(i)$$?
A
$$1$$
B
$$i + 1$$
C
$$2$$ $$i$$
D
$$2i$$
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