ISRO technical questions for practice s
ISRO electronics and electrical model questions
1. A is m x n full rank matrix with m>n and I is an identity matrix. Let matrix A' = (AT A)-1AT. Then, which one of the following statements is false ?
a) AA' A = A
b) (AA' )2 (Ans)
c) A' A = I
d) AA' A = A
Expl : Given AT = (ATA)-1AT
= A-1 (AT)-1 AT [:. AA-1 = 1]
= A-1 (AT) (AT)-1
= A-1 / = A-1 ------(1)
(a) LHS = AAT A
= A[(AT A)-1 AT ].A = (A.A-1)A
= I.A = A (True)
(b) (AA1)2 = [AA-1]2 [From Eqn. (i)]
=[l]2 = l (False)
=> it is not an orthogonal matrix
(c) LHS ATA = A-1A [From Eq.(i)]
= l (True)
= orthogonal matrix
2. A differential equation dx/dt = e-2t u(t) has to be solved using trapezoidal rule of integration with a step size h = 0.01 s. Function u(t) indicates a unit step function. If x(0-) =0, then value of X at t = 0.01 s will be given by
a) 0.00099
b) 0.00495
c) 0.0099 (Ans)
d) 0.0198
3. The surface S (x, y) = 2x + 5y-3 is integrated once over a path consisting of the points that satisfy (x+1)2 + (y-1)2 = √2. The integral evaluates to
a) 17√2
b) 17/√2
c) √2/17
d) 0 (Ans)
4. A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is
a) 1/8
b) 1/2 (Ans)
c) 3/8
d) 3/4
Expl : Total samples = (H,T), (H,T),(H,T)
Given, first toss produces a head,
Then, total chance becomes = H, (H,T), (H,T)
For exactly two heads in three tosses = H,H,H
So, probability = Total favourable events = 6 = 1
Total sample 3 2
5. For the function f(x) = x2e-x, the maximum occurs when x is equal to
a) 2 (Ans)
b) 1
c) 0
d) -1
Expl : Given, f(x) = x2e-x
f'(x) = x2(e-x) + 2xe-x
= e-x (2x - x2)
For max and min values of f-1(x),
f '(x) = 0
e-x (2x - x2) = 0
=> x(2-x) = 0 => x=0, 2
f"(x) = e-x(2-2x)- e-x (2x-x2)
At x = 0
f"(0) = e0(2-0) - e0(0-0) => 2>0 (Minima)
At (x=2),
f"(2) = e-2 (2-4) - e-2 (4-4)
-2/e2 - 0 = <o (Maxima)
So, the f (x) is maximum at x=2
6. For the scalar field u = x2 + y3, magnitude of the gradient at the point (1,3) is
a) √13/9
b) √ 9/2
c) √ 5 (Ans)
d) √9/2
7. For the equation x"(t) + 3x'(t)+2x(t) = 5, the solution x(t) approaches which of the following values as t —> ∞ ?
a) 0
b) 5/2 (Ans)
c) 5
d) 10
8. Which of the following statements holds for the divergence of electric and magnetic flux densities ?
a) Both are zero
b) These are zero for static densities but no-zero for time varying densities
c) It is zero for the electric flux density
d) It is zero for the magnetic flux density (Ans)
9. The inductance of a long solenoid of length 1000 mm wound uniformly with 3000 turns on a cylindrical paper tube of 60 mm diameter is
a) 3.2 μH
b) 3.2mH
c) 32.0 mH (Ans)
d) 3.2 H
Expl : Inductance of solenoids is given by
L = μ0N2Ax
Where, N = number of turns
A = cross -sectional area = πd2 (d is diameter)
X = length
L = 4 x 10-7 x (3000)2 x π x 602 x10-6
4
= 31.97 mH = 32mH
10. Two incandescent light bulbs of 40W and 60W ratings are connected in series across the mains. Then
a) the bulbs together consume 100 W
b) the bulbs together consume 50 W
c) the 60 W bulb glows brighter (Ans)
d) the 40 W bulb glows brighter
11. A unit step voltage is applied at t=0 to a series R-L circuit with zero initial conditions
Which of the following statements is correct ?
a) The possible for the current to the oscillatory
b) The voltage across the resistor at t=0+ is zero (Ans)
c) The energy stored in the inductor in the steady state is zero
d) The resistor current eventually falls to zero
Expl : The inductor does not allow change in current instantaneously. The voltage across inductor
VL = L dl
dt
VL (t =0+) = L dl ( 0+)
dt
dl ( 0+) = 0
dt
VL (t =0+) = 0
12. A passive 2-port network is in a steady state. Compared to its input, the steady state output can never offer
a) highest voltage
b) lower impedance
c) greater power (Ans)
d) better regulation
13. An electron with velocity u is placed in an electric field E and magnetic field B. The force experienced by the electron is given by
a) -eE
b) -eu x B
c) -e (u x E + B)
d) -e(E + u x B) (Ans)
14. A voltage waveform V(t) = 12t2 is applied across a 1H inductor for t>0, with initial current through it being zero. The current through the inductor for t>0 is given by
a) 12 t
b) 24 t
c) 12 t3
d) 4 t 3 (Ans)
15. A capacitor made with a polymeric dielectric having an ε, of 2.26 and a dielectric breakdown strength of 50 kV/cm. The permittivity of free space is 8.85 pF/m. If the rectangular plates of the capacitor have a width of 20 cm and a length of 40 cm then the maximum electric charge in the capacitor is
a) 2μC
b) 4μC
c) 8μC (Ans)
d) 10μ C
16. A zero mean random square value is uniformly distributed between limits - a and +a and its mean square value is equal to its variance. Then the rms value of the signal is
a) a (Ans)
√3
b) a
√2
c) a√2
d) a√3
Expl : Mean square value = variance = [a- (-a)]
12
= 4a2 = a
12 3
= /a2 = a
:. rms value √ 3 √3
17. A lossy capacitor Cx, rated for operation at 5 kV, 50 Hz is represented by an equivalent circuit with an ideal capacitor Cp in parallel with a resistor Rp. The value of Cp is found to be 0.102 μF and the value of Rp = 1.25 MΩ. Then the power loss and tan δ of the lossy capacitor operating at the rated voltage, respectively, are
a) 10 W and 0.0002
b) 10 W and 0.0025
c) 20 W and 0.025 (Ans)
d) 20 W and 0.04
18. A parallel plate capacitor has an electrode area of 100 mm2, with a spacing of 0.1 mm between the electrodes. The dielectric between the plates is air with a permittivity of 8.85 x 10-12 F/m. The charge on the capacitor is 100 V. The stored energy in the capacitor is
a) 8.85 pJ
b) 440 pJ
c) 22.1 nJ
d) 44.3 nJ (Ans)
19. In an AC voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of
a) Only the peak values
b) Only the rms values
c) Only the average values
d) all the three measures (peak, rms and average values) (Ans)
20. In a transformer, zero voltage regulation at full load is
a) not possible
b) possible at unity power factor load
c) possible at leading power factor load (Ans)
d) possible at lagging power factor load
21. The DC motor, which can provide zero speed regulation at full load without any controller , is
a) series
b) shunt (Ans)
c) cumulative compound
d) differential compound
22. In transformers, which of the following statements is valid ?
a) In an open circuit test, copper losses are obtained while in short circuit test, core losses are obtained
b) In an open circuit test, current is drawn at high power factor
c) In a short circuit test, current is drawn at zero power factor
d) In an open circuit test, current is drawn at low power factor (Ans)
23. For a single -phase capacitor start induction motor, which, of the following statements is valid ?
a) The capacitor is used for power factor improvement
b) The direction of rotation can be changed by reversing the main winding terminals (Ans)
c) The direction of rotation cannot be changed
d) The direction of rotation can be changed by interchanging the supply terminals
24. In a DC machine, which of the following statements is true ?
a) Compensating winding is used for neutralizing armature reaction while interpole winding is used for producing residual flux.
b) Compensating winding is used for neutralizing armature reaction while interpole winding is used for improving commutation (Ans)
c) Compensating winding is used for improving commutation while interpole winding is used for neutralizing armature reaction
d) Compensating winding is used for improving commutation while interpole winding is used for producing residual flux.
25. The equivalent circuit of a transformer has leakage reactances X1, X'2 and magnetizing reactance XM. Their magnitudes satisfy
a) X1>>X'2>>XM
b) X1<<X'2<<XM
c) X1≈ X'2>>XM
d) X1≈X'2<<XM (Ans)
Expl : The magnetizing reactance XM has very high value to reduce magnetizing current.
:. X'2 = a2X2
But in approximate equivalent circuit,
X1 ≈ a2X2 ≈ a2. X'2
—
a2
:. X1 ≈ X'2
=> X1 ≈ X'2 <<XM
26. Which three -phase connection can be used in a transformer to introduce a phase difference of 30oC between its output and corresponding input time voltages ?
a) Star-Star
b) Star-Delta (Ans)
c) Delta-Delta
d) Delta -Zigzag
Expl : The phase difference of can be introduced only in Δ -Y and Y- Δ connections of transformer windings
27. On the torque/speed curve of induction motor shown in the figure four points of operation are marked as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1 ?
a) W (Ans)
b) X
c) Y
d) Z
28. The output of a logic gate is 1 when all its inputs are at logic 0. The gate is either
a) a NAND or an Ex-OR gage
b) a NOR or an Ex-OR gate
c) an AND or an Ex-NOR gate
d) a NOR or an Ex-NOR gate (Ans)
Expl : The output of NOR or an Ex-NOR gate is 1 when all its inputs are at logic 0.
29. A 500 MW, 3-phase Y-connected synchronous generator has a rated voltage of 21.5 kV at 0.85 PF. The line current when operating at full load rated conditions will be
a) 13.43kA
b) 15.79 kA (Ans)
c) 23.25 kA
d) 27.36 kA
Expl : Power = 500 MW
or 3 VLIL cos Φ = 500
IL = 500
3 * 21.5*103 * 0.85 = 15.79 kA
30. A rotating electrical machine having its self -inductances of both the stator and the rotor windings, independent of the rotor position will be definitely not developed.
a) starting torque
b) synchronizing torque
c) hysteresis torque
d) reluctance torque
31. Modern warfare has changed from larger scale clashes of armies to suppresion, of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishment who think that chemical agents are useful tools for their cause.
Which of the following best sums up the meaning of the above passage ?
a) Modern warfare has resulted in civil strife
b) Chemical agents are useful in modern strife
c) Use of chemical agents in warfare would be undesirable
d) People in military establishments like to use chemical agents in war (Ans)
32. If 137 + 276 = 435, how much is 731 + 672 ?
a) 534 (Ans)
b) 1403
c) 1623
d) 1513
Expl : If 137 and 276 are written in reverse order, then 731 and 672 are obtained
So, 731 + 672 = reverse order of 435 =534
33. 5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall ?
a) 20 days
b) 18 days
c) 16 days
d) 15 days (Ans)
Expl : 5 skilled workers can build a wall in 20 days
:. 2 skilled workers can build the wall in 20 x 5 days = 50 days
2
8 semi-skilled workers can build the wall in 25 x 8 days = 100 days
6 3
10 unskilled workers can build a wall in 30 days
:. 5 unskilled workers can build the wall in 60 days.
One day work of a team of 2 skilled, 6 semi-skilled and 5 unskilled worker
=1/50 + 3/100 + 1/60
= 6+9+5 = 20 = 1
300 300 15
So, this team can complete the work in 15 days.
34. Given digits 2,2,3,3,3,4,4,4,4, how many distinct 4 digit numbers greater than 3000 can be formed ?
a) 50
b) 51 (Ans)
c) 52
d) 54
35. Hari (H), Gita(G), Irfan(I) ans Sara (S) are siblings (i.e., brothers and sisters). All were born on 1st January. The age difference between any two successive sibling (that is born one after another) is less than 3 year. Given the following facts :
I. Hari's age + Gita's age > Irfan's age + Saira's age
II. The age difference between Gita and Saira is 1 yr. However, Gita is not the oldest and Saira is not the youngest
III. There are not twins
In what order were they born (oldest first)?
a) HSIG
b) SGHI (Ans)
c) IGSH
d) IHSG
36. Instead of walking along the adjacent sides of a rectangular field, a boy takes a short cut along the diagonal of the field and saves a distance equal to half the longer side. The ratio of the shorter side to that of the longer side is
a) 1:2
b) 2:3
c) 1:4
d) 3:4 (Ans)
37. The proportion of milk and water in two samples is 5:2 and 7:5. If a mixture comprising of equal quantities of two samples is made, the proportion of milk and water in the mixture is
a) 12:7
b) 7:12
c) 109:59 (Ans)
d) 59:109
38. An express train moving at a speed of 80 km/h, overtakes a goods train twice as long as the express train and moving in the same direction at a speed of 40 km/h, in 54s. The time taken by express train to go through a station 400 m long is
a) 27 s (Ans)
b) 54 s
c) 18 s
d) None of these
39. A child was asked to add first few natural numbers (that is 1+2+3+.....) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong the child discovered he had missed one number in the sequence during addition. The number he missed was
a) less than 10
b) 10
c) 15
d) more than 15 (Ans)
40. A colony of bacteria in a container grows by each bacterium splitting into eight next generation bacteria. However, because of environmental conditions only 50% of the bacteria in a generation can split as above. A colony of first generation was put in container and it was found that the number of seventh generation bacteria was 4096 million. What was the size of the first generation population initially put in the container ?
a) 2 million
b) 8 million
c) 1 million (Ans)
d) 4 million
41. Out of the following plant categories
(i) Nuclear
(ii) Run-of-river
(iii) Pump storage
(iv) Diesel
The base load power plants are
a) (i) and (ii)
b) (ii) and (iii)
c) (i), (ii) and (iv) (Ans)
d) (i), (iii) and (iv)
42. For a fixed value of complex power flow in a transmission line having a sending end voltage V, the real power loss will be proportional to
a) V
b) V2
c) 1/V2 (Ans)
d) 1/V
43. A 50 Hz, 4-pole, 500 MVA, 22kV turbo-generator is delivering rated MVA at 0.8 power factor. Suddenly a fault occurs reducing is electric power output by 40%. Neglect losses and assume constant power input to the shaft. The accelerating torque in the generator in MNm at the time of the fault will be
a) 1.528 (Ans)
b) 1.018
c) 0.848
d) 0.509
Expl : P = 500 * 0.8 = 400 MW
After fault, P = 0.6 x 400 = 240 MW
Torque = 240 = 1.528 MW
2π * 1500/60
44. A hydraulic turbine having rated speed of 250 rpm is connected to a synchronous generator. In order to produce power at 50 Hz, the number of poles required in the generator are
a) 6
b) 12
c) 16
d) 24 (Ans)
Expl : No. of poles = 120 f = 120 * 50 = 24
n 250
45. For a linear electromagnetic circuit, which of the following statements is true ?
a) Field energy is equal to the co-energy (Ans)
b) Field energy is greater than the co-energy
c) Field energy is lesser than the co-energy
d) Co-energy is zero
46. High Voltage DC (HVDC) transmission is mainly used for
a) bulk power transmission over very long distances (Ans)
b) interconnecting two systems with the same nominal frequency
c) eliminating reactive power requirement in the operation
d) minimizing harmonics at the converter stations
47. The insulation strength of an EHV transmission line is mainly governed by
a) load power factor
b) switching over voltages (Ans)
c) harmonics
d) corona
48. A cascade of 3 linear time-invariant systems is causal and unstable. From this, we conclude that
a) each system in the cascade is individually causal and unstable (Ans)
b) at least one system is unstable and at least one system is causal
c) at least one system is causal and all systems are unstable
d) the majorities are unstable and the minorities are causal
Expl : A cascade of 3 linear systems is causal and unstable. If each system in the cascade is individually causal and unstable
49. For economic operation, the generator with highest prohibitive incremental transmission loss will operate at
(a) the highest positive incremental cost of production
(b) the highest negative incremental cost of production
(c) the lowest positive incremental cost of production (Ans)
(d) the lowest negative incremental cost of production
50. During no load test an induction motor draws power
(a) for core, windage and friction loss (Ans)
(b) for core, loss and copper loss
(c) for copper, windage and friction loss
(d) only for the very small copper loss