1
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
$$2i$$
2
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
$$p\left( {p - 1} \right)\left( {q - 1} \right)$$
3
GATE CSE 2004
+2
-0.6
Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of $$k$$ colours, such that the colour-pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $$k$$ that satisfies this requirement?
A
9
B
8
C
7
D
6
4
GATE CSE 2004
+2
-0.6
In how many ways can we distribute 5 distinct balls, $${B_1},{B_2},......,{B_5}$$ in 5 distinct cells, $${C_1},{C_2},.....,{C_5}$$ such that Ball $${B_i}$$ is not in cell $${C_i}$$, $$\forall i = 1,2,....,5$$ and each cell contains exactly one ball?
A
$$44$$
B
$$96$$
C
$$120$$
D
$$3125$$
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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