GATE 1998
Question 1 
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is
1/6  
3/8  
1/8  
1/2 
Total no. of possibilities are 8.
Probability of getting exactly one odd = 3/8
Question 2 
Consider the following set of equations
x + 2y = 5 4x + 8y = 12 3x + 6y + 3z = 15
This set
has unique solution  
has no solutions  
has finite number of solutions  
has infinite number of solutions 
Question 3 
Which of the following statements applies to the bisection method used for finding roots of functions:
converges within a few iterations  
guaranteed to work for all continuous functions  
is faster than the NewtonRaphson method  
requires that there be no error in determining the sign of the function

Question 4 
Consider the function y = x in the interval [1,1]. In this interval, the function is
continuous and differentiable  
continuous but not differentiable  
differentiable but not continuous  
neither continuous nor differentiable 
→ The left side values of x=0 be negative and right side values are positive.
→ If the function is said to be differentiable then left side and right side values are to be same.
Question 5 
What is the converse of the following assertion?
I stay only if you go.
I stay if you go  
If I stay then you go  
If you do not go then I do not stay  
If I do not stay then you go 
⇒ i.e., A→B
Where A = If I stay; B = you go
Converse for (A→B) is (B→A)
⇒ If you go then I stay.
Question 6 
Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A is
n  
n^{2}  
1  
n+1 
⇒ n×n
⇒ n^{2}
Question 7 
Let R_{1} and R_{2} be two equivalence relations on a set. Consider the following assertions:
 (i) R_{1} ∪ R_{2} is an equivalence relation
(ii) R_{1} ∩ R_{2} is an equivalence relation
Which of the following is correct?
Both assertions are true  
Assertion (i) is true but assertion (ii) is not true  
Assertion (ii) is true but assertion (i) is not true  
Neither (i) nor (ii) is true 
(i) R_{1} ∩ R_{2} is also transitive.
(ii) R_{1} ∪ R_{2} is need not to be transitive.
Question 8 
The number of functions from an m element set to an n element set is
m + n  
m^{n}  
n^{m}  
m*n 
n×n×n×n×...×n (m times)
= n^{m}
Question 9 
If the regular set A is represented by A = (01 + 1)* and the regular set ‘B’ is represented by B = ((01)*1*)*, which of the following is true?
A ⊂ B  
B ⊂ A  
A and B are incomparable  
A = B 
Question 10 
Both A and B are equal, which generates strings over {0,1}, while 0 is followed by 1.
The numbers 1, 2, 4, 8, ……………., 2^{n}, ………… written in binary  
The numbers 1, 2, 4, ………………., 2^{n}, …………..written in unary  
The set of binary string in which the number of zeros is the same as the number of ones  
The set {1, 101, 11011, 1110111, ………..} 
10, 100, 1000, 10000 .... = 10*
which is regular and recognized by deterministic finite automata.
Question 11 
Regarding the power of recognition of languages, which of the following statements is false?
The nondeterministic finitestate automata are equivalent to deterministic finitestate automata.  
Nondeterministic Pushdown automata are equivalent to deterministic Push down automata.  
Nondeterministic Turing machines are equivalent to deterministic Pushdown automata.  
Both B and C 
C: Power (TM) > NPDA > DPDA.
Question 12 
The string 1101 does not belong to the set represented by
110*(0 + 1)  
1 ( 0 + 1)* 101  
(10)* (01)* (00 + 11)*  
Both C and D 
C & D are not generate string 1101.
Question 13 
What happens when a bitstring is XORed with itself ntimes as shown:
[B⊕(B⊕(B⊕(B........ n times)]
complements when n is even  
complements when n is odd  
divides by 2^{n} always  
remains unchanged when n is even 
Consider:
B⊕(B⊕B)
= B⊕0
= 0 (if consider n times it remains unchanged)
Question 14 
A multiplexor with a 4 bit data select input is a
4:1 multiplexor  
2:1 multiplexor  
16:1 multiplexor  
8:1 multiplexor 
For 4 bit data it selects 2^{4} : 1 = 16: 1 input
Question 15 
The threshold level for logic 1 in the TTL family is
any voltage above 2.5 V  
any voltage between 0.8 V and 5.0 V  
any voltage below 5.0 V  
any voltage below V_{cc} but above 2.8 V 
Question 16 
In serial communication employing 8 data bits, a parity bit and 2 stop bits, the minimum band rate required to sustain a transfer rate of 300 characters per second is
2400 band  
19200 band  
4800 band  
1200 band 
(8+2+1+1) * 300
= 3600
Minimum band rate required is 4800 band.
Question 17 
The octal representation of an integer is (342)_{8}. If this were to be treated as an eightbit integer is an 8085 based computer, its decimal equivalent is
226  
98  
76  
30 
If this can be treated as 8 bit integer, then the first becomes sign bit i.e., '1' then the number is negative.
8085 uses 2's complement then
⇒ 30
Question 18 
Which of the following devices should get higher priority in assigning interrupts?
Hard disk  
Printer  
Keyboard  
Floppy disk 
Question 19 
Which of the following addressing modes permits relocation without any change whatsoever in the code?
Indirect addressing  
Indexed addressing  
Base register addressing  
PC relative addressing 
Question 20 
Which of the following is true?
Unless enabled, a CPU will not be able to process interrupts.  
Loop instructions cannot be interrupted till they complete.  
A processor checks for interrupts before executing a new instruction.  
Only level triggered interrupts are possible on microprocessors. 
Option 'C' also false. A processor checks for the interrupt before fetching an instruction.