GATE 1998

Question 1

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is

A
1/6
B
3/8
C
1/8
D
1/2
Question 1 Explanation: 
The possibilities of getting exactly one odd number is {OEE, EOE, EEO}.
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

A
has unique solution
B
has no solutions
C
has finite number of solutions
D
has infinite number of solutions
Question 2 Explanation: 
Question 3

Which of the following statements applies to the bisection method used for finding roots of functions:

A
converges within a few iterations
B
guaranteed to work for all continuous functions
C
is faster than the Newton-Raphson method
D
requires that there be no error in determining the sign of the function
Question 3 Explanation: 
The Bisection method guaranteed to converge to a root of f if f is a continuous function on the interval [a,b] and f[a] and f[b] can have opposite signs.
Question 4

Consider the function y = |x| in the interval [-1,1]. In this interval, the function is

A
continuous and differentiable
B
continuous but not differentiable
C
differentiable but not continuous
D
neither continuous nor differentiable
Question 4 Explanation: 
The given function y = |x| be continuous but not differential at x= 0.
→ 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. 
A
I stay if you go
B
If I stay then you go
C
If you do not go then I do not stay
D
If I do not stay then you go
Question 5 Explanation: 
"I stay only you go" = "If I 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

A
n
B
n2
C
1
D
n+1
Question 6 Explanation: 
In a largest equivalence relation the every element is related to other element
⇒ n×n
⇒ n2
Question 7

Let R1 and R2 be two equivalence relations on a set. Consider the following assertions:

    (i) R1 ∪ R2 is an equivalence relation
    (ii) R1 ∩ R2 is an equivalence relation

Which of the following is correct?

A
Both assertions are true
B
Assertion (i) is true but assertion (ii) is not true
C
Assertion (ii) is true but assertion (i) is not true
D
Neither (i) nor (ii) is true
Question 7 Explanation: 
If R1 and R2 be two equivalence relations on a set 'S' then the transitive property tells
(i) R1 ∩ R2 is also transitive.
(ii) R1 ∪ R2 is need not to be transitive.
Question 8

The number of functions from an m element set to an n element set is

A
m + n
B
mn
C
nm
D
m*n
Question 8 Explanation: 
Here each m element we have n choices i.e.,
n×n×n×n×...×n (m times)
= nm
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
A ⊂ B
B
B ⊂ A
C
A and B are incomparable
D
A = B
Question 9 Explanation: 
Both A and B are equal, which generates strings over {0,1}, while 0 is followed by 1.
Question 10

Both A and B are equal, which generates strings over {0,1}, while 0 is followed by 1.

A
The numbers 1, 2, 4, 8, ……………., 2n, ………… written in binary
B
The numbers 1, 2, 4, ………………., 2n, …………..written in unary
C
The set of binary string in which the number of zeros is the same as the number of ones
D
The set {1, 101, 11011, 1110111, ………..}
Question 10 Explanation: 
The numbers are to be like
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?

A
The non-deterministic finite-state automata are equivalent to deterministic finite-state automata.
B
Non-deterministic Push-down automata are equivalent to deterministic Push- down automata.
C
Non-deterministic Turing machines are equivalent to deterministic Push-down automata.
D
Both B and C
Question 11 Explanation: 
B: No conversion possible from NPDA to DPDA.
C: Power (TM) > NPDA > DPDA.
Question 12

The string 1101 does not belong to the set represented by

A
110*(0 + 1)
B
1 ( 0 + 1)* 101
C
(10)* (01)* (00 + 11)*
D
Both C and D
Question 12 Explanation: 
Options A & B are generates string 1101.
C & D are not generate string 1101.
Question 13

What happens when a bit-string is XORed with itself n-times as shown:

  [B⊕(B⊕(B⊕(B........ n times)]  
A
complements when n is even
B
complements when n is odd
C
divides by 2n always
D
remains unchanged when n is even
Question 13 Explanation: 
B⊕(B⊕(B⊕...) n times
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

A
4:1 multiplexor
B
2:1 multiplexor
C
16:1 multiplexor
D
8:1 multiplexor
Question 14 Explanation: 
For 'n' bit data it selects 2n : 1 input
For 4 bit data it selects 24 : 1 = 16: 1 input
Question 15

The threshold level for logic 1 in the TTL family is

A
any voltage above 2.5 V
B
any voltage between 0.8 V and 5.0 V
C
any voltage below 5.0 V
D
any voltage below Vcc but above 2.8 V
Question 15 Explanation: 
Voltage is to be below Vcc = 5V but above 2.8V
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

A
2400 band
B
19200 band
C
4800 band
D
1200 band
Question 16 Explanation: 
Stop bit is given, it is asynchronous communication and 1 start bit also implied then
(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 eight-bit integer is an 8085 based computer, its decimal equivalent is

A
226
B
-98
C
76
D
-30
Question 17 Explanation: 
(342)8 = (011 100 010)2 = (1110 0010)2
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?

A
Hard disk
B
Printer
C
Keyboard
D
Floppy disk
Question 18 Explanation: 
Hard disk has the higher priority in assigning interrupts.
Question 19

Which of the following addressing modes permits relocation without any change whatsoever in the code?

A
Indirect addressing
B
Indexed addressing
C
Base register addressing
D
PC relative addressing
Question 19 Explanation: 
In PC relative addressing there is no change in the code.
Question 20

Which of the following is true?

A
Unless enabled, a CPU will not be able to process interrupts.
B
Loop instructions cannot be interrupted till they complete.
C
A processor checks for interrupts before executing a new instruction.
D
Only level triggered interrupts are possible on microprocessors.
Question 20 Explanation: 
Option B & D are false.
Option 'C' also false. A processor checks for the interrupt before fetching an instruction.
There are 20 questions to complete.

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