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

• 1/36
• 1/6
• 1/4
• 1/3

Question 2

If the trapezoidal method is used to evaluate the integral obtained ₀∫¹x²dx ,then the value obtained

• is always > (1/3)
• is always < (1/3)
• is always = (1/3)
• may be greater or lesser than (1/3)

Question 3

The determinant of the matrix given below is

• -1
• 0
• 1
• 2

Question 4

Let L be a regular language and M be a context-free language, both over the alphabet Σ. Let Lc and Mc denote the complements of L and M respectively. Which of the following statements about the language Lc∪ Mc is TRUE

• It is necessarily regular but not necessarily context-free
• It is necessarily context-free.
• It is necessarily non-regular.
• None of the above

Question 5

Which of the following statements is TRUE about the regular expression 01*0?

• It represents a finite set of finite strings.
• It represents an infinite set of finite strings.
• It represents a finite set of infinite strings.
• It represents an infinite set of infinite strings

Question 6

The language {0ⁿ 1ⁿ 2ⁿ | 1 ≤ n ≤ 10⁶} is  

• regular
• context-free but not regular.
• context-free but its complement is not context-free.
• not context-free

Question 7

Which of the following expressions is equivalent to (A⊕B)⊕C

• (A+B+C)(A¯+B¯+C¯)
• (A+B+C)(A¯+B¯+C)
• ABC+A¯(B⊕C)+B¯(A⊕C)
• None

Question 8

Using Booth\'s Algorithm for multiplication, the multiplier -57 will be recoded as

• 0 -1 0 0 1 0 0 -1
• 1 1 0 0 0 1 1 1
• 0 -1 0 0 1 0 0 0
• 0 1 0 0 -1 0 0 1

Question 9

A dynamic RAM has a memory cycle time of 64 nsec. It has to be refreshed 100 times per msec and each refresh takes 100 nsec. What percentage of the memory cycle time is used for refreshing?

• 10
• 6.4
• 1
• .64

Question 10

A two-way switch has three terminals a, b and c. In ON position (logic value 1), a is connected to b, and in OFF position, a is connected to c. Two of these two-way switches S1 and S2 are connected to a bulb as shown below. Which of the following expressions, if true, will always result in the lighting of the bulb ?

• S1.S2\'
• S1+S2
• (S1⊕S2)\'
• S1⊕S2