## 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
Engineering-Mathematics       Probability
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
Engineering-Mathematics       Linear-Algebra
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
Engineering-Mathematics       Bisection-Method
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
Engineering-Mathematics       Calculus
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
Engineering-Mathematics       Propositional-Logic
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
Engineering-Mathematics       Sets-And-Relation
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
Engineering-Mathematics       Sets-And-Relation
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
Engineering-Mathematics       Sets and Functions
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
Theory-of-Computation       Regular-Expressions
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, ………..}
Theory-of-Computation       Finite-Automata
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
Theory-of-Computation       NFA
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
Theory-of-Computation       Regular-Expressions
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
Digital-Logic-Design       EX-OR
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
Digital-Logic-Design       Multiplexer
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
Digital-Logic-Design       Threshold-Voltage
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
Computer-Organization       Serial-Communication
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
Digital-Logic-Design       Number-Systems
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
Computer-Organization       Interrupt
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?

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.
Computer-Organization       Interrupt
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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