1
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
$$44$$
2
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
$$24$$
3
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
$$2i$$
4
GATE CSE 2005
+2
-0.6
Let $$n = {p^2}q,$$ where $$p$$ and $$q$$ are distinct prime numbers. How many numbers $$m$$ satisfy $$1 \le m \le n$$ and $$gcd\left( {m.n} \right) = 1?$$ Note that $$gcd(m,n)$$ is the greatest common divisor of $$m$$ and $$n$$.
A
$$p(q-1)$$
B
$$pq$$
C
$$\left( {{p^2} - 1} \right)\left( {q - 1} \right)$$
D
$$p\left( {p - 1} \right)\left( {q - 1} \right)$$
GATE CSE Subjects
EXAM MAP
Medical
NEET