GATE IT 2005


Question 1
A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is
A
\left(\dfrac{1}{36}\right)
B
\left(\dfrac{1}{6}\right)
C
\left(\dfrac{1}{4}\right)
D
\left(\dfrac{1}{3}\right)
Discrete Mathematics   Probability Theory
Question 2
If the trapezoidal method is used to evaluate the integral obtained \int_{0}^{1} x^2dx, then the value obtained
A
is always > (1/3)
B
is always < (1/3)
C
is always = (1/3)
D
may be greater or lesser than (1/3)
Engineering Mathematics   Numerical Method


Question 3
The determinant of the matrix given below is
\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}
A
-1
B
0
C
1
D
2
Engineering Mathematics   Linear Algebra
Question 4
Let L be a regular language and M be a context-free language, both over the alphabet \Sigma. Let L^c and M^c denote the complements of L and M respectively. Which of the following statements about the language L^c\cup M^c is TRUE?
A
It is necessarily regular but not necessarily context-free.
B
It is necessarily context-free.
C
It is necessarily non-regular.
D
None of the above
Theory of Computation   Context Free Language
Question 5
Which of the following statements is TRUE about the regular expression 01*0?
A
It represents a finite set of finite strings.
B
It represents an infinite set of finite strings.
C
It represents a finite set of infinite strings.
D
It represents an infinite set of infinite strings.
Theory of Computation   Regular Expression




There are 5 questions to complete.

Leave a Comment