**GATE Instrumentation questions with answeers**

**GATE Engg questions with answers**

1 In an 8085 microprocessor, which one of the following is the correct sequence of the machine cycles for the execution of the DCR M instruction?

Options

A) op-code fetch

B) op-code fetch, memory read, memory write

C) op-code fetch memory read

D) op-code fetch memory write, memory write

Correct Answer B

2 lim x ® p /4 sin 2 [ x - p 4 ] x - p 4 equals

Options

A) 0

B) 1 2

C) 1

D) 2

Correct Answer D

3 Three DC currents I 1 , I 2 and I 3 meet at a node with I 1 entering and I 2 and I 3 leaving the node. I 1 and I 2 are measured as 100mA and 99 mA with a ± 1% accuracy. Then the value of I 3 and the accuracy of I 3 are Options

A) 1 mA ± 2%

B) 199 mA ± 2%

C) 1 mA ± 2%

D) 1 mA ± 199%

Correct Answer C

4 The input-output characteristic of a Schmidt trigger has a hysteresis band of ± 0.1 V. If the input voltage is 5 sin (1000 p t),the delay between the corresponding zero cross-over points of the output and input signals is Options

A) 6.37 m s

B) 0.02 m s

C) 63.7 m s

D) 2.0 m s

Correct Answer A

5 In a spirit level, 2.5mm of movement of the bubble corresponds to a tilt angle of 25 seconds. The radius of curvature of the tube of the spirit level is

Options

A) 52.1 m

B) 34.4 m

C) 26.3 m

D) 15.6 m

Correct Answer B

6 The loop transfer function of a system is given by G(S)h(s) = 10 e -Ls s . The phase cross-over frequency is 5 rad/s. The value of the dead time L is

Options

A) p /20

B) p /10

C) - p /20

D) zero

Correct Answer B

7 An 8-bit microcontroller has an external RAM is the memory map from 8000H to 9FFFH. The number of bytes this RAM can store is

Options

A) 8193

B) 8191

C) 8192

D) 8000

Correct Answer C

8 Two copper-constantan thermocouples are connected such that the two constantan wires are joined together. The two copper wires are connected to the input of a low noise chopper stabilized differential amplifier having a gain of 1000. One of the thermocouple junctions is immersed in a flask containing ice and water in equal proportion. The other thermocouple is at a temperature T. If the output of the amplifier is 2.050V, the temperature T is Options

A) 205°C

B) 102.5°C

C) 51.25°C

D) 50°C

Correct Answer D

9 The vectored address corresponding to the software interrupt command RST7 in 8085 microprocessor is

Options

A) 0017H

B) 0027H

C) 0038H

D) 0700H

Correct Answer C

10 For a first order instrument a 5% settling time is equal to

Options

A) three times the time constant

B) two times the time constant

C) the time constant

D) time required for the output signal to reaches 5% of the final value

Correct Answer A

11 The measurements of a source voltage are 5.9V, 5.7V and 6.1V. The sample standard deviation of the readings is

Options

A) 0.013

B) 0.04

C) 0.115

D) 0.2

Correct Answer D

12 In an INTEL 8085 microprocessor the ADDRESS-DATA bus and the DATA bus are

Options

A) Non multiplexed

B) Multiplexed

C) Duplicated

D) Same as CONTROL bus

Correct Answer B

13 The number of comparators required in an 8-bit flash-type AID converter is

Options

A) 256

B) 255

C) (8 + 2)

D) 8

Correct Answer B

14 An ultrasonic beam of frequency 1 MHz and intensity 0.5 W/cm 2 passes through a layer of soft tissue of thickness t with an attenuation coefficient of 1.18cm -1 . The ratio of output to input power is 1/e 2 . The thickness of the tissue is

Options

A) 1 cm

B) 1.695 cm

C) 2.408 cm

D) 3.712 cm

Correct Answer B

15 A twisted pair of wires is used for connecting the signal source with the instrumentation amplifier, as it helps reducing

Options

A) the effect of external interference

B) the error due to bias currents in the amplifier

C) the loading of the source by the amplifier

D) the common mode voltage

Correct Answer C

16 The output from a 633 nm He-Ne laser comes out from the mirror with a beam diameter of lmm and diverges to the far field. It is brought to a focus by a convex lens of focal length of 17 mm. The spot size diameter of the beam at the focal point is

Options

A) 20 m m

B) 26 m m

C) 52 m m

D) 13 m m

Correct Answer C

17 International temperature scale in the range 0-630oC is defined by means of a

Options

A) mercury pressure spring thermometer

B) platinum-platinum. 10% rhodium thermocouple

C) platinum resistance thermometer

D) total radiation pyrometer.

Correct Answer D

18 A microprocessor has an instruction XOR (r 1 , r 2 ) which performs an Exclusive OR operation of registers r 1 ,r 2 and stores the result in r 1 . After the following instructions are executed XOR (r 2 , r 1 ) XOR (r 1 ,r 2 ) XOR (r 2 ,r 1 ) Which one of the following is true?

Options

A) Content of register r 1 is half sum of r 1 and r 2

B) Content of register r 2 is half sum of r 1 and r 2

C) Contents of registers r 1 and r 2 remain unaltered

D) Contents of registers r 1 and r 2 are swapped Correct Answer D

19 A second order feedback system is found to be oscillating with a high frequency. The oscillations

Options

A) can be reduced by increasing the proportional action

B) can be reduced by increasing the integral action

C) can be reduced by increasing the derivative action

D) cannot be reduced

Correct Answer B

20 For a suppressed carrier amplitude modulator (AM-SC) system, the carrier and the modulating inputs are x c (t) = cos w c t and x m (t) = 0.5 sin w m t, respectively. The output of the system is proportional to

Options

A) sin ( w c + w m ) t – sin ( w c - w m ) t

B) sin ( w c + w m ) t + cos ( w c - w m ) t

C) (1 + 0.5 sin w m t) cos w c t

D) (1- 0.5 sin w m t) cos w c t

Correct Answer B

Sample papers Engg Mathematics

Que. 1 A relation R is defined on the set of integers as x Ry if f(x + y) iseven. Which of the following state?ments is true?

A R is not an equivalence relation

B R is an equivalence relation having 1 equivalence class

C R is an equivalence relation having 2 equivalence classes

D R is an equivalence relation having 3 equivalence classes

Que. 2 Let a, b, c, d be propositions. Assume that the equivalences a<-> (b V-b) and b<->c hold. Then the truth value of the formula (a ? b) -J. (a? c) ? d) is always

A True

B False

C Same as the truth value of b

D Same as the truth value of d

Que. 3 Consider the following relations:

R1 (a, b) if f(a + b) is even over the set of integers

R2 (a, b) if f(a + b) is odd over the set of integers

R3 (a, b) if f a.b > 0 over the set of non-zero rational numbers

R4 (a, b) iff |a - b | Which of the following statements is correct?

A R1 and R2 are equivalence relations, R3 and R4 are not

B R1 and R3 are equivalence relations, R2 and R4 are not

C R1 and R4 are equivalence relations, R2 and R3 are not

D R1, R2, R3 and R4 are all equivalence relations

Que. 4 Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?

A (1/7)^7

B (1/7)^6

C (1/2)^7

D (7/2)^7

Que. 5 In the interval {0, (pi)}the equation x=cosx has

A no solution

B exactly one solution

C exactly two solution

D an infinite number of solution

Que. 6 In a room containing 28 people,there are 18 peoples who speaks english,15 people who speak hindi and 22 people who speak kannada.9 persons speak both english and hindi,11 persons speak both hindi and kannada.Where as 13 persons speak both english and kannada.how many people speak all the three languages?

A 9

B 8

C 7

D 6

Que. 7 Given the following relation instance X Y Z 1 4 2

1 5 3 1 6 3 3 2 2 Which of the following functional dependencies are satisfied by the instance?

A XY->Z and Z ->Y

B YZ->X and Y->Z

C YZ->X and X->Z

D XZ->Y and Y->X

Que. 8 Let f(n) = (n^2)1 g n and g(n) = n (1 g n)^10 be two positive functions of n. Which of the following statements is correct ?

A f(n) = O(g(n) and g(n)!= O(f(n))

B g(n) = O(f(n) and f(n) != O(g(n))

C f(n) != O(g(n)) and g(n) != O(f(n))

D f(n) = O(g(n)) and g(n) = O(f(n))

Que. 9 The proposition P^(~pvq) is

A A tautology

B logically equivalent to p^q

C logically equivalent to pvq

D A contradiction

Que. 10 Let A and B be real symmetric matrices of size n*n.Then which one of thefollowing is true?

A A(A^t)=1

B A=(A^-1)

C AB=BA

D (AB)^t=BA

Que. 11 The number of distinct simple graph with upto three nodes is

A 15

B 10

C 7

D 9

Que. 12 The Newton-Raphson method is used to find the root of the equation x^2-2=0. if the iteration are started from -1,the iteration will

A converage to -1

B converage to [(sqrt)2]

C converage to -[(sqrt)2]

D not converage

Que. 13 What is the converse ofthe following assertion? I stay onlyif you go

A I stay if you go

B if I stay then you go

C if you do not go then i donot stay

D if i do not stay then you go

Que. 14 In a room containing 28 people,there are 18 peoples who speak english,15people who speak hindiand 22 people who speak kannada.9 persons speak both english and hindi 11 persons speak both hindi and kannads whereas

13 persons speak both kannada and english.how many people speak all therr languages?

A 9

B 8

C 7

D 6

Que. 15 Let L be the set of all binary strings whoes last two symbols are same.the number of states in the minimum state determinimstc finite 0 state automaton accepting L is

A 2

B 5

C 8

D 3

Que. 16 Which oneof the following operations is commutative but not associative?

A AND

B OR

C NAND

D EXOR

Que. 17 What is the maximum value of the function f(x)=2(x^2) -2x +6 in the interval [0,2]?

A 6

B 10

C 12

D 5.5

Que. 18 The function f(x,y)=(x^2)y-3xy+2y+x has

A no local extremun

B one local minimum but no local maximum

C one local maximum but no local minimum

D one local minimum and one local maximum

Que. 19 Let L be a set with a relation R which istransitive,anti symmetric and reflexive and for any two elements a, b ? L let the least upper bound lub (a, b) and the greatest lower bound glb (a, b) exist. Which of the following is/are true?

A L is a poset

B L is a boolean algebra

C L is a lattice

D None of the above

Que. 20 The number of binary strings of n zeros and k ones that no two ones are adjacent is

A n-1 C k

B n C k

C n C k+l

D None of the above

Que. 21 A polynomial p(x) satisfies the following: p (1) = p(3) = p(5) = 1 p(2) = p(4) = -1 The minimum degree of such a polynomial is

A 1

B 2

C 3

D 4

Que. 22 Suppose the adjacency relation of vertices in a graph is represented in a table Adj(X, Y). Which of the following queries cannot be expressed by a relational algebra expression of constant length?

A List all vertices adjacent to a given vertex

B List all vertices which have self loops

C List all vertices which belong to cycles of less than three vertices

D List all vertices reachable from a given vertex

Que. 23 Let r and s be two relations over the relation schemes R and S respectively, and let A be an attribute in R. Then the relational algebra expression s A=a (r |X| s) is always equal to

A s A=a (r)

B r

C s A=a (r) |X| s

D none of the above

Que. 24 Let f : A->B be a function, and let E and F be subsets of A. Consider the following statements about images. S1 :f (E(union)F)=f (E)(union) f (F) S2 :f (E (intersection) F)=f(E)(intersection)f (F) Which of the

following is true about S1 and S2 ?

A Only S1 is correct

B Only S2 is correct

C Both S1 and S2 are correct

D None of S1 and S2 is correct

Que. 25 The proposition p <-> q means

A p if and only if q

B which is true if both p and q are true

C it is false when p is true and q is false

D all of the above

Que. 26 If A={a,b}then A+ is

A {a,b}(union) {{a,b}}

B {{a,b}(union) {a,b}}

C {a,b}(union) {a,b}}

D none of these

Que. 27 What is the number of ways to point 12 offices so that 3 of them will be green,2 of them pink,2 of them yellow and the remaining onces white

A 166324

B 166328

C 166320

D 166322

Que. 28 The number of binary relations on a set with n elements is

A n^2

B 2^n

C 2^(n^2)

D none of these

Que. 29 Let A,B,C,D be n*n matrices,each with non-zero determinant.If ABCD=1 then B^(-1) is

A D(-1)C(-1)A(-1)

B CDA

C ADC

D Does not necessarily exist

Que. 30 Given the following input (4322,1334,1471,1989,6171,6173,4199) ans the following hash function x mod 10,which of the following statments are

true? (i) 9679,1989,4199 hash to the same value

(ii) 1471,6171 hash to the same value (iii)all elements

hash to the same value (iv)Each element hashes to a different

value

A (i) only

B (ii) only

C (i) and (ii) only

D (iii) or (iv)

Que. 31 In a group of 30 persons,a total of 16 take tea while 9 take tea but not

coffee. how many persons in this group take coffee but not tea?

A 27

B 20

C 25

D 11

Que. 32 The less than relation,<,on reals is

A A partical ordering since it is asymmetric and reflexive

B A partical ordering since it is antiymmetric and reflexive

C not a partical ordering it is not asymmetric and not reflexive

D not a partical ordering it is not asymmetric and reflexive

(E)none of these

Que. 33 The number of element in the power set P(S) of the set S={(fi),1,(2,3)}is

A 2

B 4

C 8