1

As you grow older, an injury to your ______ may take longer to ______.

2

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m. What is the distance between P and Q (in m) when P wins the race?

3

Three bells P, Q and R are rung periodically in a school. P is rung every 20 minutes, Q is rung every 30 minutes and R is rung every 50 minutes. If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?

4

Given below are two statements and four conclusions drawn based on the statements.

Statement 1 : Some bottles are cups.

Statement 2 : All cups are knives.

Conclusion I : Some bottles are knives.

Conclusion II : Some knives are cups.

Conclusion III : All cups are bottles.

Conclusion IV : All knives are cups.

Which one of the following options can be logically inferred?

5

The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random. What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

6

Altruism is the human concern for the wellbeing of others. Altruism has been shown to be motivated more by social bonding, familiarity and identification of belongingness to a group. The notion that altruism may be attributed to empathy or guilt has now been rejected.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

7

There are two identical dice with a single letter on each of the faces. The following six letters : Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes : Q, U and V?

8

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges ₹150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved ₹100.

What is the price of the item at the online store S (in ₹ ) if there are no other charges than what is described above?

9

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements :

• The line segment joining R and S is longer than the line segment joining P and Q.
• The line segment joining R and S is perpendicular to the line segment joining P and Q.
• The line segment joining R and U is parallel to the line segment joining T and Q.

Based on the above statements, which one of the following options is CORRECT?

10

An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.

Which one of the following is a part of a possible trajectory of the ant during the movement?

11

The transfer function of a real system, H(s) , is given as :

H(s)=$\frac{\mathrm{As+B}}{{\mathrm{s}}^2+Cs+D}$

where A, B, C and D are positive constants. This system cannot operate as

12

For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is

13

The most commonly used relay, for the protection of an alternator against loss of excitation, is

11

The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘r’, as shown in the figure below, is

15

The valid positive, negative and zero sequence impedance (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are

16

The steady state output (V_out) , of the circuit shown below, will

17

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is -180⁰ . This system has

18

A balanced Wheatstone bridge ABCD has the following arm resistances :R_AB=1 kΩ±2.1%;R_BC=100 kΩ±0.5%; R_CDis an unknown resistance;R_DA=300 kΩ±0.4%.The value of R_CD and its accuracy is

19

The open loop transfer function of a unity gain negative feedback system is given by,

G(s)=$\frac{\mathrm{K}}{{\mathrm{s}}^2+4s-5}$

The range of K for which the system is stable, is

20

Consider a 3X3 matrix A whose ( i,j)-th element,a_i,j=(i-j)³.Then the matrix A will be

21

In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced threephase supply of 100 √3V with phase sequence ABC. The star connected load has Z_A=10Ω and Z_B=20∠60⁰Ω The value of Z_C in Ω , for which the voltage difference across the nodes n and n' is zero, is

22

A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?

23

A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is J=j_ar³z for the region r < b where r is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for r < b) is

24

The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is

25

For the circuit shown below with ideal diodes, the output will be

26

A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD _____ counter. (in integer)

27

An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ______. (rounded off to nearest integer)

28

The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The Q-factor of the network is ______. (round off to nearest integer)

29

The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of 20 ns, is _______. (round off to one decimal place).

30

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is _______. (round off to nearest integer)

31

In the circuit shown below, the switch S is closed at t = 0. The magnitude of the steady state voltage, in volts, across the 6Ω resistor is ______. (round off to two decimal places).

32

A single-phase full-bridge diode rectifier feeds a resistive load of 50Ω from a 200 V, 50 Hz single phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is ______. (round off to nearest integer)

33

The voltage at the input of an AC-DC rectifier is given by v(t)=230√2 sinωt where ω=2πx50 rad/sec.The input current drawn by the rectifier is given by

i(t)=10sin(ωt-$\frac{\mathrm{\pi }}{3}$)+4 sin (3ωt-$\frac{\mathrm{\pi }}{6}$)+3 sin(5ωt-$\frac{\mathrm{\pi }}{3}$)

The input power factor, (rounded off to two decimal places), is, ________ lag.

34

Two balanced three-phase loads, as shown in the figure, are connected to a 100√3V , three phase, 50 Hz main supply. Given : Z₁=(18+j24)Ω and Z₂=(6+j8)Ω. The ammeter reading, in amperes, is ______. (round off to nearest integer)

35

The frequencies of the stator and rotor currents flowing in a three-phase, 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is ______. (round off to nearest integer)

36

The output impedance of a non-ideal operational amplifier is denoted by Z_out. The variation in the magnitude of Z_out with frequency, f , in the circuit shown below, is best represented by

37

An LTI system is shown in the figure where G(s)=$\frac{100}{{\mathrm{s}}^2+{\mathrm{0.1s}}_{}100}$.The steady state output of the system, to the input r(t), is given as y(t)=a+bsin(10t+θ).The values of ‘ a ’ and ‘b ’ will be

38

The open loop transfer function of a unity gain negative feedback system is given as G(s)=$\frac{1}{\mathrm{s(s+1)}}$The Nyquist contour in the s-plane encloses the entire right half plane and a small neighborhood around the origin in the left half plane, as shown in figure below. The number of encirclements of the point (-1+j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

39

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted a ζ and ω_n, respectively. The values of ζ and ω_n

40

e^Adenotes the exponential of a square matrix A. Suppose λ is an eigenvalue and v is the corresponding eigen-vector of matrix A

Consider the following two statements :

Statement 1 : e^λ is an eigenvalue of e^A .

Statement 2 : v is an eigen-vector of e^A.

Which one of the following options is correct?

41

Let f(x)=∫^x₀e^t(t-1)(t-2)dt.Then f(x) decreases in the interval

42

Consider a matrix A= $\left[\begin{array}{ccc}\frac{1}{}& \frac{0}{}& \frac{0}{}\\ \frac{0}{}& \frac{4}{}& \frac{-2}{}\\ \frac{0}{}& \frac{1}{}& \frac{1}{}\end{array}\right]$

The matrix A satisfies the equation 6A^-1=A²+cA+dl,where c and d are scalars and I is the identity matrix. Then (c+d) is equal to

43

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by

Plant 1 :C₁=350+6P₁+0.004P₁²

Plant 1 :C₂=450+aP₂+0.003P₂²

where P₁ and P₂ are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power (λ) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are

44

The current gain (I_out /I_in ) out in in the circuit with an ideal current amplifier given below is

45

If the magnetic field intensity (H) in a conducting region is given by the expression,H=x,²i+x²y²j+x² y²z²k A/m.The magnitude of the current density, in 2 A/m , at x = 1 m, y = 2 m and z = 1 m, is

46

Let a causal LTI system be governed by the following differential equation y(t)+$\frac{1}{4}$$\frac{\mathrm{dy}}{\mathrm{dt}}$=2x(t), where x(t) and y(t) are the input and output respectively. Its impulse response is

47

Let an input x(t)=2 sin(10πt)+5cos(15πt)+7sin(42πt)+4cos(45πt) is passed through an LTI system having an impulse response,

h(t)=2$\left(\frac{\mathrm{sin(10\pi t)}}{\mathrm{\pi t}}\right)$cos(40πt)

The output of the system is

48

Consider the system as shown below

where y(t)=x(e^t) . The system is

49

The discrete time Fourier series representation of a signal x[n] with period N is written as x[n]=Σ^N-1_k=0a_ke^j(2knπ/N) A discrete time periodic signal with period N =3, has the non-zero Fourier series coefficients : a_-3=2 and a₄=1 . The signal is

50

Let, f(x, y, z)=4x²+7xy+3xz²The direction in which the function f(x,y,z) increases most rapidly at point P=(1, 0, 2) is

51

Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counterclockwise direction. Which of the following expressions does not represent the area of the region R?

25

For the circuit shown below with ideal diodes, the output will be

25

For the circuit shown below with ideal diodes, the output will be