1 P a g e.

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1 1. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are important in their own ways. each B. both C. all either. Which of the options given below best completes the following sentence? She will feel much better if she. will get some rest B. gets some rest C. will be getting some rest is getting some rest 3. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not the thought of the election to her bitter rival. bear, loosing B. bare, loosing C. bear, losing bare, losing 4. A regular die has si sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1.167;.167; 3.1; 4.166;.168; We call this die irregular B. biased C. Gaussian insufficient. Fill in the missing number in the series B.4 C. 6. Find the odd one in the following group Q, W, Z, B B, H, K, M W, C, G, J M, S, V, X Q, W, Z, B B. B, H, K, M C. W, C, G, J M, S, V, X 7. Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct? The number of red lights is equal to the number of blue lights B. The number of green lights is equal to the number of yellow lights C. The sum of the red and green lights is equal to the sum of the yellow and blue lights The sum of the red and blue lights is equal to the sum of the green and yellow lights 8. The sum of eight consecutive odd numbers is 66. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? 1 B.144 C The total eports and revenues from the eports of a country are given in the two charts shown below. The pie chart for eports shows the quantity of each item eported as a percentage of the total quantity of eports. The pie chart for the revenues shows the percentage of the total revenue generated through eport of each item. The total quantity of eports of all the items is thousand tonnes and the total revenues are crore rupees. Which item among the following has generated the maimum revenue per kg? Item B. Item 3 C. Item 6 Item 1. It takes 3 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 1 minutes? 4 times the draining rate B. 3 times the draining rate C.. times the draining rate times the draining rate 11. The determinant of matri A is and the determinant of matri B is 4. The determinant of matri AB is. 1 B. 8 C Let X be a random variable which is uniformly chosen from the set of positive odd numbers less than 1. The epectation E[X]is. 4 B. C P a g e

2 13. For t, the maimum value of the function t f t e e occurs at 1 t log e 4 B. t log e C. t t log e The value of ln B. 1. C. e 1 lim1 X is 1. If the characteristic equation of the differential equation d y dy y d d has two equal roots, then the values of a are ± 1 B., C. ± j ±1/ 16. Norton s theorem states that a comple network connected to a load can be replaced with an equivalent impedance in series with a current source B. in parallel with a voltage source C. in series with a voltage source in parallel with a current source 17. In the figure shown, the ideal switch has been open for a long time. If it is closed at t=, then the magnitude of the current (in ma) through the 4k resistor at t = + is. 19. An increase in the base recombination of a BJT will increase the common emitter dc current gain B. the breakdown voltage BV CEO C. the unity-gain cut-off frequency f T the trans conductance g m. In CMOS technology, shallow P-well or N-well regions can be formed using low pressure chemical vapour deposition B. low energy sputtering C. low temperature dry oidation low energy ion-implantation 1. The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is Voltage shunt feedback B. Current series feedback C. Current shunt feedback Voltage series feedback. In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are A cm and A d, respectively. If the resistance RE is increased, then 1 Amp B. 1. Amp C.1. Amp Amp 18. A silicon bar is doped with donor impurities ND =. 1 1 atoms / cm 3. Given the intrinsic carrier concentration of silicon at T = 3 K is n i = cm -3. Assuming complete impurity ionization, the equilibrium electron and hole concentrations are B. C. n 1.1 cm, p 1. 1 cm , , , 1 1 n cm p cm n cm p cm n cm p cm A cm increases B. common-mode rejection ratio increases C. A d increases common-mode rejection ratio decreases 3. A cascade connection of two voltage amplifiers A1 and A is shown in the figure. The open-loop gain A v, input resistance R in, and output resistance R O for A1 and A are as follows: P a g e

3 A1: A 1, R 1 k, R 1k v in A: A, R k, R v in The approimate overall voltage gain V out /V in is. 8. B. 3. C For an n-variable Boolean function, the maimum number of prime implicants is n 1 B. n / C. n n1. The number of bytes required to represent the decimal number in packed BCD(Binary Coded Decimal) form is. 1 B. C In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by M X, Y, N XY B. M XY, N X Y C. M XY, N X Y M XY N X Y 7. An FIR system is described by the system function H z 1 z z The system is maimum phase B. minimum phase C. mied phase zero phase 8. Let n n. Let X z be the z-transform of n.. j. is a zero o X(z), which one of the following must also be a zero of X(z).. j. B. 1/ (. j.) C. 1/ (. j.) j4 9. Consider the periodic square wave in the figure shown. If The ratio of the power in the 7 th harmonic to the power in the th harmonic for this waveform is closest in value to.. B. 1. C. 1. D. 3. The natural frequency of an undamped second-order system is 4 rad/s. If the system is damped with a damping ratio.3, the damped natural frequency in rad/s is. rad/sec B. 3 rad/sec C. 3. rad/sec 38.1 rad/sec 31. For the following system, When C. X1 s, the transfer function s 1 s s s s1 B. 1 s 1 s 1 s s s y s is 3. The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by P C Wlog 1 w bits per second (bps), where W is the channel bandwidth, P is the average power received and is the one-sided power spectral density of the AWGN. For a fied P 1,, W is kbps) with infinite bandwidth approimately 1.44 B. 1.8 C the channel capacity (in 33. Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation inde (μ) when the maimum and minimum values of the envelope, respectively, are 3 V and 1 V, is. 1. B.. C P a g e

4 34. To maimize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a /4transformer as shown. 41. In the h-parameter model of the -port network given in the figure shown, the value of h (in S) is. The characteristic impedance (in ) of the /4 transformer is. 6.8 B.67. C.7.7 D Which one of the following field patterns represents a TEM wave travelling in the positive direction? E 8 yˆ, H 4zˆ B. E yˆ, H 3zˆ C. ˆ ˆ E z, H y E 3 yˆ, H 4zˆ 36. The system of linear equations 1 3 a 3 1 b 4 has 1 c 14 a unique solution B. infinitely many solutions C. no solution eactly two solutions 37. The real part of an analytic function f(z) where z. jy is given by e -y cos(). The imaginary part of f(z) is y e cos( ) y B. e sin( ) y C. e sin( ) y e sin( ) 1.4 B. 1.8 C In the figure shown, the capacitor is initially uncharged. Which one of the following epressions describes the current I(t) (in ma) for t >? 1 e, msec 3 3 t/ 1 e, msec 3 1 t/ e, 3 m sec 1 t/ e, 3 m sec t/ B. C. 43. In the magnetically coupled circuit shown in the figure, 6 % of the total flu emanating from one coil links the other coil. The value of the mutual inductance (in H) is. 38. The maimum value of the determinant among all real symmetric matrices with trace 14 is. 4 B. 4 C If r aˆ yaˆ zaˆ and r y z r thendiv r, ln r. 1 B. C A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1, respectively, the operating angular frequency (in rad/s) is.. rad/sec B..3 rad/sec C..4 rad/sec.4 rad/sec. H B..4 H C..46H.49 H 44. Assume electronic charge 19 q 1.6 C, kt / q mv and electron mobility 1 /. If the concentration gradient of n cm V s electrons injected into a P-type silicon sample is cm, the magnitude of electron diffusion current density (in A/cm) is. / 8 A / cm A cm B. 4 / A cm C. 6 / A cm D 4 P a g e

5 4. Consider an abrupt PN junction (at T = 3 K) shown in the figure. The depletion region width X n on the N-side of the junction is. μm and the permittivity of silicon 1 si is F / cm. At the junction, the approimate value of the peak electric field (in kv/cm) is..6 B..7 C B. 8.3 C For the MOSFETs shown in the figure, the threshold voltage 1 W Vt V and K C ma V L.1 /. value of ID (in ma) is. The 46. When a silicon diode having a doping concentration of N A 91 cm 16 3 on p-side and N 16 3 D 11 cm on n- side is reverse biased, the total depletion width is found to be 3μm. Given that the permittivity of silicon is F / cm, the depletion width on the p-side and the maimum electric field in the depletion region, respectively, are B. C / / / / 47. The diode in the circuit shown has V on =.7 Volts but is ideal otherwise. If V i = sin t Volts, the minimum and maimum values of V O (in Volts) are, respectively,.6 ma B..7 ma C..8 ma.9 ma. In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W1, W, W3 and W4 and.7 B..7 and C. and and 48. For the n-channel MOS transistor shown in the figure, the threshold voltage V Th is.8 V. Neglect channel length modulation effects. When the drain voltage V D = 1.6 V, the drain current I D was found to be. m If V D is adjusted to be V by changing the values of R and V DD, the new value of I D (in ma) is P a g e

4. The input-output relationship of a causal stable LTI y n y n 1 n. system is given as If the impulse response h[n] of this system satisfies the condition n hn, the relationship between and is 1 / B.

6 4. The input-output relationship of a causal stable LTI y n y n 1 n. system is given as If the impulse response h[n] of this system satisfies the condition n hn, the relationship between and is 1 / B. 1 / C.. The value of the integral c. B..4 C.. D.8 sin t dt is. W1 B. W C. W3 W4 1. The outputs of the two flip-flops Q1, Q in the figure shown are initialized to,. The sequence generated at Q upon application of clock signal is 111 B. 11 C An unforced liner time invariant (LTI) system is represented by If the initial conditions are 1() = 1 and () = -1, the solution of the state equation is t 1, t 1 B. t t e, t e 1 t e, t e C. t 1 t t e, t e t 1 t t 7. The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.. For the 88 microprocessors, the interfacing circuit to input 8-bit digital data (DI DI 7) from an eternal device is shown in the figure. The instruction for correct data transfer is If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is.. B.. C Consider the state space system epressed by the signal flow diagram shown in the figure. MVI A, F8H B. IN F8H C. OUT F8H LDA F8F8H 3. Consider a discrete-time signal n for n 1 n otherwise If y[n] is the convolution of [n] with itself, the value of y[4] is. 1 B. 1 C. 3 6 P a g e The corresponding system is always controllable B. always observable

C. always stable always unstable 9. The input to a 1-bit quantizer is a random variable X with pdf f e for and, f for for For outputs to be of equal probability, the quantizer threshold should be.. B.

7 C. always stable always unstable 9. The input to a 1-bit quantizer is a random variable X with pdf f e for and, f for for For outputs to be of equal probability, the quantizer threshold should be.. B..3 C Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s t cos f t and s t cos f t, where 4 mv. 1 1 Assume an AWGN channel with two-sided noise power spectral density N receiver and the relation 1. 1 W / Hz. Using an optimal Q v 1 u / e du the bit v error probability for a data rate of kbps is Q B. Q Q Q 4 C The power spectral density of a real stationary random process.x(t) is given by c w t cos f A t, where f A The cutoff frequencies of both the filters are f c The bandwidth of the signal at the output of the modulator (in Hz) is. 4 B. 6 C If the electric field of a plane wave is, ˆ3cos 3 yˆ4sin t kz 4 mv / m E Z t t kz the polarization state of the plane wave is left elliptical B. left circular C. right elliptical right circular 64. In the transmission line shown, the impedance Z in (in ohms) between node A and the ground is. c The value of the epectation 1 E X tt is. 4w B. 4 C In the figure, M(f) is the Fourier transform of the message signal.m(t) where A = 1 Hz and B = 4 Hz. v t cos f t and Given c. B C For a rectangular waveguide of internal dimensions a b(a > b), the cut-off frequency for the TE11 mode is the arithmetic mean of the cut-off frequencies for TE1 TE mode. If a cm, mode and is. 1 cm B. cm C. 4 cm 8 cm the value of b (in cm) *** 7 P a g e

Exercise The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is.

Exercise The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is. Exercise 1. The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is.. Let X be a random variable which is uniformly chosen from the set of positive odd numbers