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QUESTION: 1

Statement: All bags are cakes. All lamps are cakes.

Conclusions:

I. Some lamps are bags.

II. No lamp is bag.

Deduce which of the above conclusion logically follows statements:

Solution:

Since the middle term 'cakes' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.

QUESTION: 2

Man does not live by __________ alone.

Solution:

Man does not live by bread alone.

QUESTION: 3

Extreme focus on syllabus and studying for tests has become such a dominant concern of Indian students that they close their minds to anything ___________ to the requirements of the exam.

Solution:

Extraneous – irrelevant or unrelated to the subject being dealt with

QUESTION: 4

Select the pair that best expresses a relationship similar to that expressed in the pair:

LIGHT : BLIND

Solution:

QUESTION: 5

If = log(a + b), then:

Solution:

a+b = 1

QUESTION: 6

In an exam, the average was found to be 50 marks. After deducting computational errors the marks of the 100 candidates had to be changed from 90 to 60 each and average came down to 45 marks. Total number of candidates who took the exam was:

Solution:

Let number of candidates be n

50 × n – 100 × 30 = 45 × n

n = 600

QUESTION: 7

A solid 4cm cube of wood is coated with red paint on all the six sides. Then the cube is cut into smaller 1cm cubes. How many of these 1cm cubes have no colour on any side?

Solution:

Number of cubes with 3 faces red = 8

Number of cubes with 2 faces red = 24

Number of cubes with 1 face red = 24

Number of cubes with no face red = 64-(24+24+8) = 8

QUESTION: 8

One of the warmest winters on record has put consumers in the mood to spend money.Spending is to be the strongest in thirteen years. During the month of February, sales of existing single family homes hit an annual record rate of 4.75 million. This paragraph best supports the statement that:

Solution:

QUESTION: 9

The age of father is 4 times more than the age of his son Amit. After 8 years, he would be 3 times older than Amit. After further 8 years, how many times will he be older than Amit?

Solution:

Let Amit’s age be n years

Age of his father = (4n + n) = 5n years

After 8 years:

Amit’s age = n + 8

Father’s age =

3(n + 8) = 5n + 8

3n + 24 = 5n + 8

16 = 2n

n = 8 years

After further 8 years:

Amit’s age = 24 years

Father’s age = 5n +16 = 56 years

So father is 2.33 times older than Amit.

QUESTION: 10

Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?

Solution:

A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.

A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.

A and B together can fill 1t of the tank in a minute. A alone can fill 13t of the tank in a minute. So, in a minute, B can fill 1t−13t=23t. Or, B takes 3t2 minutes to fill an entire tank.

To fill one-third the tank, B will take t2 minutes. B is kept open for t - 10 minutes.

t2 = t - 10, t = 20 minutes.

A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.

C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes. Choice (D)

QUESTION: 11

The Theven's equivalent resistance to the left of AB in figure given below is given by

Solution:

For finding the Thevenin’s equivalent resistance, 8 A current source will be open circuited while V volt voltage source will be short circuited.

Hence

QUESTION: 12

What is the time period of the sinusoidal signal

x(n) = 10 cos(0.4n)

Solution:

Period N= K

=5K

= 5 {K = 1}

QUESTION: 13

In a radar system, the range of R_{1} is achieved at a frequency *f _{1}*. Then the range R

Solution:

QUESTION: 14

Gate function is defined as ______________

Solution:

A gate function is a rectangular function defined as

Where τ is pulse width.

QUESTION: 15

A signal m(t) = 5 cos(2100t) is frequency modulated a carrier. The resulting FM signal is

The approximate bandwidth of the FM signal would be

The approximate bandwidth of the FM signal would be:

Solution:

=

= 3.2 KHz

QUESTION: 16

A system has a receiver noise resistance of It connected to an antenna with an input resistance of The noise figure of the system is:

Solution:

Noise figure = 1 +

Where, is the equivalent receiver noise resistance & is the resistance of antenna So, F = 1+ =2

QUESTION: 17

A phase lead compensating network has its transfer function The maximum phase lead occurs at a frequency of:

Solution:

Comparing with the standard phase lead compensating network

= 50 rad /sec

QUESTION: 18

The time taken for the output to settle within 2% of step input for the control system represented by is given by:

Solution:

Comparing the above transfer function with the standard second order transfer function

QUESTION: 19

If diameter of a circular cross-sectional antenna is 2m, and it is transmitted a signal at frequency 100MHz, determine the minimum distance for far field approximation.

Solution:

For far field approximation,

QUESTION: 20

A load impedance is to be matched to a lossless transmission line by using a quarter wave line transformer. The characteristics impedance of the quarter wave transformer.

Solution:

QUESTION: 21

What is the velocity of a plane wave in a lossless medium having a relative permittivity of 5 and relative permeability of unity?

Solution:

Velocity of propagation is given by

QUESTION: 22

A dipole antenna of/2 length has an equivalent total loss resistance is 0.5. The efficiency of antenna is:

Solution:

Radiation resistance of antenna,

QUESTION: 23

If an electrical system is compared to a fluid system, the electrical current corresponds to the:

Solution:

QUESTION: 24

For the circuit shown below, the collector to emitter voltage is

Solution:

Let the transistor be operating under active region.

QUESTION: 25

A power supply has a full load voltage of 24V. What is its no-load voltage for 5% regulation.

Solution:

Voltage - Regulation,

QUESTION: 26

Two 100 W, 220 V bulbs are required to be connected across a 400 volts supply. The value of resistance to be inserted in the line so that the voltage across the bulbs does not exceed 220 V is

Solution:

Total power drawn from the circuit = 2 x 100 = 200 W

Hence, supply current is

Let R be the series resistance to be inserted in the circuit such that the voltage across the bulbs is 220 V.

Applying KVL, we get

QUESTION: 27

For a given op-amp, CMMR = 10^{5} and differential gain A_{d} = 10^{5}. The common-mode gain of the op-amp is

Solution:

QUESTION: 28

The system of linear equations:

3x + 4y = 6

2x + 3y = 5

has:

Solution:

Auguemented matrix,

Since rank of matrix A as well as auguemented matrix is 2, therefore it has unique solution.

QUESTION: 29

Which of the following is a solution to the differential equation

Solution:

QUESTION: 30

The value of the integral dz where C is the circle z = 1

Solution:

Since both the poles lie outside the unit circle therefore according to Cauchey – Integral,

the integration is zero.

QUESTION: 31

A fair dice is tossed two times. The probability that the second results in a value that is higher than the first toss is:

Solution:

In the first toss, results can be 1, 2, 3, 4, 5

For 1, the second toss results can be 2, 3, 4, 5, 6

For 2, the second toss results can be 3, 4, 5, 6

For 3, the second toss results can be 4, 5, 6

For 4, the second toss results can be 5, 6

For 5, the second toss results can be 6

So the required probability

QUESTION: 32

where P is a vector is equal to:

Solution:

QUESTION: 33

A certain multiplexer can switch one of 32 data inputs to its output. The number of control inputs in this multiplexer

Solution:

No. of input lines = 2^{m} (where, m = No. of select/ control inputs)

or, 32 = 2^{m} or m=5.

QUESTION: 34

The initial of MOD-16 down counter is 0110. After 37 clock pulses, the state of the counter will be:

Solution:

After 37 clock pulses, the state of MOD-16 DOWN counter will be five states below the present state.

QUESTION: 35

12 MHz clock frequency is applied to a cascaded counter of modulus-3 counter, modulus-4 counter, and modulus-5 counter. Determine the output frequency.

Solution:

Modulus of cascaded counter

=60

So, frequency of the output signal,

= 200 KHz

QUESTION: 36

The value of Z_{22} (Ω) for the circuit shown below is

Solution:

Applying KVL, we get

Putting the value of V_{1} from equation (ii) into equation (i), we get

QUESTION: 37

An ac voltage of 220 V is applied to a pure inductance of 50 H. If the current is 5 A, the instantaneous value of voltage and current will be respectively given by

Solution:

Max. value of current,

Assuming voltage as the reference phasor,

QUESTION: 38

For the circuit shown below, a resistance R is to be connected across an active network, it is given that when

(i) R = infinity, V = 5 volts

(ii) R = 0, current output of the active source is 2.5 A.

What would be the current when the value of R is 5 Ω?

Solution:

When R = ∞, V_{oc}= V = 5 volts

When R = 0 , I_{SC} = 2 .5 A

Hence, the Thevenin's equivalent circuit will be drawn as shown below.

QUESTION: 39

The output y(t) of a continuous – time system S for the input x(t) is given by

Which one of the following is correct?

Solution:

Therefore s(t) = u(t)

Which is linear and time-invariant

QUESTION: 40

What is the output of the system with in response to the input

Solution:

QUESTION: 41

The 3-dB bandwidth of the low-pass filter having impulse response is is:

Solution:

QUESTION: 42

What is the inverse fourier transform of u(w)?

Solution:

By duality property

QUESTION: 43

The signal flow graph shown below has M number of forward path and N number of individual loops.

Q. What are the values of M and N ?

Solution:

QUESTION: 44

The transfer functions of the sytem is given by The impulse response of the system is

Solution:

QUESTION: 45

Determine the value of K for a unity feedback system with to have a peak overshoot of 50%

Solution:

QUESTION: 46

Assuming an operating temperature T = 300K and =26 mV. What is the change in semi-conductor silicon diode forward voltage to produce a 10:1 change in dioide current while operating in the forward bias region (<25mA)?

Solution:

For silicon diode

QUESTION: 47

An n-type semiconductor is illuminated by a steady flux of photons with energy greater than band gap energy. The change in conductivity obey which relation?

Solution:

When the semiconductor is illuminated by a steady flux of photons, the number of new hole-election pairs is proportional to the number of incident photons and also they are equal

i.e.

Therefore, change in conductivity

QUESTION: 48

A single-phase full-bridge diode rectifier delivers a load current of 10 A, which is ripple free. The rms and average values of diode currents are respectively

Solution:

Given, I_{0} = 10A

The rms value of diode current,

The average value of diode current,

QUESTION: 49

What is the value of inductance to be used in the inductor filter connected to a full-wave rectifier operation at 60 Hz to provide a DC output with 4% ripple for a 100 Ω load?

Solution:

The ripple factor for an inductor filter is

∴

or

QUESTION: 50

For the circuit shown below, the output voltage is given by

Solution:

Using superposition theorem, the output voltage is given by

QUESTION: 51

An amplifier using BJT has two identical stages each having a lower cut-off (3dB) frequency of 64Hz due to coupling capacitor. The emitter bypass capacitor also provides a lower cut-off (3dB) frequency due to emitter degeneration alone of 64Hz. The lower 3dB frequency of the overall amplifier is nearly.

Solution:

So overall lower cut-off frequency

= 100 Hz

QUESTION: 52

What is the value of where

Here, s is the surface bounded by x = 0, x = 1, y = 0, y = 1, z = 0, z =1 and are unit vectors along x, yand z axes respectively.

Solution:

By divergence theorem,

Since, the surface s is bounded by x = 0, 1; y = 0, 1 and z = 0, 1 so, putting the limits, we have

QUESTION: 53

For sea water with = 5 mho/m and = 80, what is the distance for which radio signal can be transmitted with 90% attenuation at 25 KHz?

Solution:

= 44938.6

Since

hence sea water is a acting as a good conductor Since attenuation is 90%, so transmission is 10%

So,

x = 3.27 m

QUESTION: 54

A lossless transmission line with = 50 and = 1.5m connects a voltage source to a load If = 60V and = 50 then determine the current I supplied by the source at a frequency 100 MHz.

Solution:

Here,

So current supplied by the generator

= (0.48 – j 0.24) A

QUESTION: 55

A pulse train with a frequency of 1MHz is counted using a mod-1024 ripple counter built with J–K flip-flops. For proper operation of the counter the maximum permissible propagation delay per flip-flop stage is:

Solution:

Here mod – 1024

So to count 1024 number of flip-flops requires

n = 10

of counter

So propagation delay per flip flop

QUESTION: 56

In a binary adder with two inputs X and Y, the correct set of logical expression for the output S (sum) and C (carry) are respectively

Solution:

The truth table for half adder is shown below

Here, sum output and carry output is C= XY

QUESTION: 57

Consider the following statements:

1. When a MUX is used to implement a logic function, the logic variables are applied to the MUX’s data inputs.

2. The circuit for a DEMUX is basically the same as that for a decoder.

Of these:

Solution:

When a MUX is used to implement a logic function, the logic variables are applied to the MUX's select or control input.

For example, if we want to implement a NOT gate using a 2 x 1 MUX, then the circuit will be represented as shown below:

Hence, statement-1 is not correct.

Statement-2 is correct because the internal circuit for a DEMUX (data distributor) and a decoder are basically same.

QUESTION: 58

A liner system has the transfer function When it is subjected to an input white noise process with a constant spectral density A, the spectral density of the output will be:

Solution:

PSD of output =

QUESTION: 59

A 3 x 8 decoder with two enable inputs is to be used to address 8 blocks of memory. What will be the size of each memory block when addressed from a sixteen bit bus with two MSBs used to enable the decoder?

Solution:

QUESTION: 60

Four signals are to be multiplexed and transmitted. and have a bandwidth of 4 KHz, and remaining two signals have bandwidth of 8KHz. Each sample requires 8 bits for encoding. What is the minimum transmission bit rate of the system?

Solution:

=48 K samples / sec

= 384 Kbps

QUESTION: 61

A telephone channel has bandwidth B of 3KHz and SNR of 30dB. It is connected to a telephone machine having 32 different symbols. The symbol rate required for errorless transmission is nearly:

Solution:

The symbol rate required for error tree transmission, i.e. nyquist sampling rate is

= 6000 symbols/sec

QUESTION: 62

A modem is classified as low speed if data rate handled is:

Solution:

QUESTION: 63

The divergence of the vector field

Solution:

at point (1, 2, 1)

= 8

QUESTION: 64

A solution for the differential equation with initial condition =0 is:

Solution:

Taking Laplace transform both sides we get,

QUESTION: 65

For the transistor circuit shown below, the Q-point values are given as I_{CQ }= 1 mA and V_{CEQ }= 6V

If V_{BE} (on) = 0.7 V, the values of the R_{B} and R_{c} will be respectively

Solution:

The collector resistance is:

Base current is,

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