# 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 1 Explanation:
 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 2 Explanation:

 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 3 Explanation:
 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 4 Explanation:
 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
Question 5 Explanation:

There are 5 questions to complete.