HPCL Electrical Engineer Mock Test - 2 - PSSSB Clerk MCQ

Calculation:

Let's assume a = 1, b = 2, c = 3, then all possible 3-digit numbers formed by a, b, c without repetition are,

123, 132, 213, 231, 312, and 321, so the sum of these numbers = 1332

Here, 1332 is a multiple of 37

∴ The correct answer is 37

Given:

Three successive discounts of 40%, 20% and 10%.

Formula used;

SP = MP × × ×

Calculation:

Let the MP be Rs 100.

SP = MP × × ×

⇒ 100 × × ×

⇒ 100 × × × = Rs. 43.2

So, single equivalent discount

⇒ 100 - 43.2 = 56.8

Discount % = × 100% = 56.8%

Given:

Selling prices = Rs. 13440 and Rs. 10560

Concept:

The cost price is midway between the price sold at a loss and the price sold at a profit.

Solution:

⇒ Cost Price (C.P.) = (13440 + 10560)/2 = Rs. 12000

⇒ Selling Price for 20% profit = 120% of C.P. = 1.2 × 12000 = Rs. 14400

Therefore, the centre table should be sold for Rs. 14400 to make a 20% profit.

Decoding the information,

Given:

(48 × 6)/4

After replacing the signs from left to right and using the BODMAS rule,

= (48 / 6) × 4

= 8 × 4

= 32

Hence, “32” is the correct answer.

To understand the relationship between S and X based on the given information, let's break down the relationships step by step:

R and S are married, making them husband and wife.

A and V are brothers, indicating they share the same parents.

S is the only sister of V, meaning V is S's brother, and S is also A's sister (since A and V are brothers).

V is married to U, making them a married couple.

X is the only son of V, which means X is V's and U's son.

Since S is V's sister and V is X's father, that makes S the Paternal aunt of X.

The correct answer is Option (2) i.e. "wants".

Key Points

• Here "Each one" is the main subject which is singular.
• "Each one of the workers" implies each worker individually which requires a singular verb.
• "Wants" correctly agrees with the singular subject phrase.

Therefore, the correct answer is- "Each one of the workers wants a raise in salary from the coming month."

Additional Information

• Option (1) "are wanting" does not agree with the singular subject phrase.
• Option (3) "have wanted" does not correctly fit the singular subject in present tense.
• Option (4) "want" is plural and does not agree with the singular subject phrase.

Here the correct answer is Imprudence.

Key Points

• The correctly spelt word is "Imprudence".
• Imprudence means the quality of being unwise or indiscreet.
  • Example: His imprudence led to the loss of the entire investment.
• Thus, the correct answer is Option 2.

• The use of "more" before "better" is incorrect as "better" is already a comparative form of the adjective "good".
• The correct comparative form of "good" is "better", and the superlative form is "the best".
• Therefore, the correct sentence should be "The new restaurant is better than the old one."

Hence, option 2 is the correct answer.

Important Points

• The comparative and superlative forms of adjectives are used to compare and describe different degrees of a particular quality.

• Comparative Form:

  • Usage: The comparative form is used when you are comparing two things or two groups.

  • Formation: Most adjectives form the comparative by adding "-er" (e.g., faster, taller) or by using "more" before the adjective (e.g., more beautiful, more interesting).

  • Example: The cat is faster than the dog.

• Superlative Form:

  • Usage: The superlative form is used when you are comparing more than two things or groups, indicating the highest degree of quality.

  • Formation: Most adjectives form the superlative by adding "-est" (e.g., fastest, tallest) or by using "most" before the adjective (e.g., most beautiful, most interesting).

  • Example: The cheetah is the fastest land animal.

The correct answer is: had done

Key Points

• The third conditional is used when the condition is impossible.
• The condition is "if she had done her homework".
• The result is "she would have gotten a better grade".
• The verb in the if-clause is in the past perfect tense.
• The verb in the main clause is in the conditional perfect tense. Therefore, the correct answer is- had done

Additional Information

• Did is incorrect because it is in the past tense, not the past perfect tense.
• Would do is incorrect because it is in the conditional tense, but the condition is not possible.
• Does is incorrect because it is in the present tense, not the past perfect tense.

According to the given information,

‘That’ is written as either ‘sa or pa’.

Hence. “sa or pa” is the correct answer.

Given:

200 mm lengths can be cut from 10 m of ribbon

Concept:

1m = 1000 mm

10 m = 10000 mm

Calculation;

We have,

Number of 200 mm lengths that can be cut from 10 m of ribbon

⇒

⇒ 50

∴ 50 lengths can be cut from 10 m of ribbons.

% of income in year 2 = 26

% of income in year 3 = 30

So, 56% in these two years

7500000 × 56/100

⇒ 4200000

∴ The total income from year 2 to year 3 is Rs. 4200000

Given:

Five digit number is given = 9x34y, which is divisible by 24.

Concept used:

Divisibility rule of 8 and 3 which is factor of 24.

Divisibility rule of 8 is last three digit of number is divisible by 8.

Divisibility rule of 3 is sum of all digits of given number is divisible by 3.

Calculation:

The number is = 9x34y

First we check divisibility rule of 8,

According to this rule, last three digits is divisible by 8,

⇒ 34y is divisible by 8,

⇒ 34y / 8

When we divide 34y by 8 ,for complete divisibisible by 8 y should be 4 ⇒344 / 8 (Let y = 4)

Check the divisibility rule of 3,

According to this rule, sum of all digits is divisible by 3.

⇒ 9 + x + 3 + 4 + y = 16 + x + y is divisible by 3.

Put y = 4,

⇒16 + x + 4 = 20 + x

Which is completely divisible by 3 when x = 1 and 7

We take maximum value because question ask maximum value, x = 7

⇒ 20 + 7 = 27 is divisible by 3.

X = 7 and y = 4

x + y = 7 + 4 = 11

∴Option 1 is correct.

Statements:

All cricketers are wealthy.

Some wealthy are Indians.

All Indians are honest.

The Venn diagram as per the given statements:

Conclusions:

I. All Indians are cricketers. → Does not follow (Because there is no definite relation given between Indians and cricketers, so it can be possible only but not definitely true)

II. Some cricketers are honest. → Does not follow (Because there is no definite relation given between cricketers and honest, so it can be possible only but not definitely true)

Hence, the correct answer is "Neither conclusions I nor II follow".

Given:

Five People A, B, C, D and E are sitting in a row facing south.

1) A and B are sitting together. C is sitting immediate left of A.

2) C sits in the extreme left end of the row.

3) D sits second to the right of A.

4) Remaining Person will be placed in left space

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Hence, "Option 3" is the correct answer.

Given:

Statements: “It is difficult to form true selfless friendship with women after their marriage because they always give priority to their family over their friends.” – A woman complains to her husband.

Conclusion:

I. Families should be given priority by the elders to maintain good relations within the family → False (Because it is given in the statement that women always give priority after their marriage to their family over their friends and there is no such information mentioned regarding elders.)

II. Friendship with a married person is not possible → False (Because no such information is given regarding married person.)

Hence, the correct answer is "Option 4".

Concept:

• The electronic power supply integrated with the switching regulator for converting the electrical power efficiently from one form to another form with desired characteristics is called a Switch-mode power supply.
• It is used to obtain a regulated DC output voltage from unregulated AC or DC input voltage.
• Ideally, the output voltage is expected to be pure DC, but practically some ripples of the alternating input are always present at the output.

Two common coupling modes of an oscilloscope are:

DC Coupling: DC Coupling shows the whole input signal (DC + AC).

AC Coupling: AC Coupling blocks the DC component of a signal.

Application:

Given input to the oscilloscope is 12 V SMPS supply.

Since the oscilloscope is AC coupled, it will block the DC part and will show ripples alone since some ripples of the alternating input are always present at the output of SMPS.

Note: If the oscilloscope was DC coupled, the output would be 12 V DC along with ripple.

Concept:

Zero sequence networks for different 3-phase loads are shown below.

The zero sequence equivalent circuits of 3-phase transformers can be drawn by using the following general circuit.

Z is the zero sequence impedance of the windings of the transformer. These are two series and two shunt switches. One series and one shunt switches are for both sides separately.

The series switch of a particular side is closed if it is star grounded and the shunt switch is closed if that side is delta connected, otherwise they are left open.

Application:

In the given circuit diagram, both the shunt switches are closed. Therefore, both the primary and secondary are delta-connected.

Energy meter:

An energy meter or watt-hour meter is used to measure the energy consumed in kWh.

It is an integrating type instrument.

Recording mechanism:

It is required for the energy meter to record the no. of revolutions made by the aluminum disc which is proportional to the energy consumed in kWh.

The meter constant can be calculated as

k = (No. of revolutions / Energy consumption in kWh)

Units of meter constant are revolutions per kWh

1 unit means 1 kWh.

Calculation:

Given:

Voltage V= 200 V

Current I = 10 A

Time = 2 hour

cosϕ = 0.8

Energy consumed = V × I × cosϕ × time = 200 × 10 × 0.8 × 2 = 3.2 kWh

Meter constant = No. of revolution by meter/Energy consumed = 1800/3.2 = 562.5 rev/kWh.

Points to remember:

Braking torque obtained by a permanent magnet inside the meter used to control the speed of the disc.

• A TRIAC is defined as a three terminal, four layer, bi-directional semiconductor device that controls AC power, which is different from the other silicon controlled rectifiers in the sense that TRIAC can conduct in both the directions that is whether the applied gate signal is positive or negative, it will conduct. Thus, this device can be used for AC systems as a switch.
• TRIAC gives a two-quadrant operation, but Triacs can be triggered in any of the four quadrants, and two of the four possible quadrants are needed to trigger conduction during the two (positive and negative) half cycles of the AC wave.
• Quadrants I, and III or quadrants II, and III are the favored methods of triggering, as quadrant IV is much less sensitive to triggering because of the way the DIAC is constructed.
• So if quadrant IV is used with any of the other three quadrants, the positive and negative half cycles would need different values of trigger current, creating an unnecessary complication.

Characteristics of a TRIAC: The Triac characteristics is similar to SCR but it is applicable to both positive and negative Triac voltages. The operation can be summarized as follows:

​​​​​​​

• First Quadrant Operation of Triac: The voltage at terminal MT₂ is positive with respect to terminal MT₁ and the gate voltage is also positive with respect to the first terminal.
• Second Quadrant Operation of Triac
• The voltage at terminal 2 is positive with respect to terminal 1 and the gate voltage is negative with respect to terminal 1.
• Third Quadrant Operation of Triac: The voltage of terminal 1 is positive with respect to terminal 2 and the gate voltage is negative.
• Fourth Quadrant Operation of Triac: The voltage of terminal 2 is negative with respect to terminal 1 and the gate voltage is positive.

Concept:

where, SDR = Scale division reading

FSR = Full scale reading

D = No. of divisions on scale

Resolution =

Calculation:

Given, FSR = 10 A

D = 50 divisions

Resolution =

Resolution = 0.1 A

Single-phase controlled rectifier with SCR:

• The bridge rectifier circuit is made of four SCRs T1, T2, T3, T4, and a load.
• The input signed is applied across terminals A and B and the output DC signal is obtained across the load.
• The four SCRs are arranged in such a way that only two SCRs conduct electricity during each half cycle.
• SCRs T1 and T2 are pairs that conduct electric current during the positive half-cycle.
• Similarly, SCRs T3 and T4 conduct electric current during a negative half-cycle only if T3 would be normal, but to some issue, it damaged and gets open-circuited.
• Now due to the open-circuit, there will be no conduction in the negative half.
• Due to the inductive nature of the load, a negative voltage spike will come.
• As the free-wheeling diode is connected, no negative voltage spike will appear in the final waveform.
• Finally, this circuit will only conduct in the positive half cycle.
• The formula of average output voltage (Vavg or e0avg) for half-wave rectifier is

Where Vm = Maximum Voltage

α = Firing angle of the thyristor / SCR

Concept:

Drawing the balanced 3-phase star connected circuit

Where, V_an = phase voltage and V_ab = line voltage.

Now drawing the Phasor Diagram to find the line voltage:

From the above phasor diagram,

Line voltage V_ab leads the phase voltage by 30 degrees.

So, we can establish the relation between line and phase voltage of a star-connected balanced system.

Calculation:

In ABC sequence:

Phase B lags Phase A by 120^o and phase C leads phase A by ,120^o.

, ,

The equivalent inductance of series opposing inductors:

In the RLC network given in the question, we can observe that inductors are connected in series opposing connection,

If two inductors are connected in series opposing connection with self inductances L1 and L2 and mutual inductance between them is M.

Then the equivalent inductance of such connection is given by

Leq = L1 + L2 - 2M

Resonance in series RLC circuit:

Seris resonance is the state of the network at which the impedance value of the network reaches a minimum and hence accepts the maximum current.

The frequency at which this state happens is called the resonance frequency.

The resonance frequency of the series RLC circuit is given by

rad/sec.

Where

L is the inductance of the coil, C is the capacitance of the capacitor

Calculation:

Given that,

C = 4 F

L1 = L2 = 4 H

M = 2 H

⇒ L_eq = 4 + 4 - 2 × 2 = 4 H

And resonance frequency

= 1 / √(4×4) = 1/4 = 0.25 rad/sec

Concept:

• The electronic power supply integrated with the switching regulator for converting the electrical power efficiently from one form to another form with desired characteristics is called a Switch-mode power supply.
• It is used to obtain a regulated DC output voltage from unregulated AC or DC input voltage.
• Ideally, the output voltage is expected to be pure DC, but practically some ripples of the alternating input are always present at the output.

Two common coupling modes of an oscilloscope are:

DC Coupling: DC Coupling shows the whole input signal (DC + AC).

AC Coupling: AC Coupling blocks the DC component of a signal.

Application:

Given input to the oscilloscope is 12 V SMPS supply.

Since the oscilloscope is AC coupled, it will block the DC part and will show ripples alone since some ripples of the alternating input are always present at the output of SMPS.

Note: If the oscilloscope was DC coupled, the output would be 12 V DC along with ripple.

Concept:

In moving iron instruments, the deflecting torque is unidirectional (acts in the same direction) whatever may be the polarity of the current.

The deflecting torque is given by

Where,

I is operating current

L is self-inductance

θ is deflection

So that the deflection torque of the moving iron instrument is proportional to the square of the RMS value of the operating current and change in self-inductance.

Calculation:

When the current through a moving iron instrument is increased by 20%, then deflection torque is

∴ T'_d = 1.44 T_d

Hence deflection torque is increased by 44%

Total harmonic distortion or THD is a common measurement of the level of harmonic distortion present in power systems.

THD can be related to either current harmonics or voltage harmonics.

It is defined as the ratio of rms value of all the harmonic components to the rms value of the fundamental component.

Mathematically, it can be represented as

Given that,

Rate of radius (dr/dt) = 1 m/s

Magnetic field (B) = 0.8 wb/m²

Radius of the loop (r) = 2 m

Emf induced

= 2π × 2 × 0.8 × 1 = 3.2π V

Concept:

Voltage regulation:

Voltage regulation is the change in secondary terminal voltage from no load to full load at a specific power factor of load and the change is expressed in percentage.

E2 = no-load secondary voltage

V2 = full load secondary voltage

Voltage regulation for the transformer is given by the ratio of change in secondary terminal voltage from no load to full load to no load secondary voltage.

Voltage regulation

It can also be expressed as,

Regulation

+ sign is used for lagging loads and

- sign is used for leading loads

Explanation:

% voltage regulation

Given that, no load voltage = 100 V

full load voltage = 95 V

In the given circuit, the switch is on position 1 till the steady-state is reached, in the steady-state the inductor acts like a short circuit,

The circuit at t = 0^-

I(0^-) = I_L(0^-) = 50 / 10 = 5 A

As inductor does not allow a sudden change in the current so I_L (0⁺) = 5 A

Circuit at t = 0⁺

Now the circuit is a simple RL source free circuit, Inductor will start discharging and when it reaches the steady stage it will completely discharge i.e the energy stored by the inductor is zero.

So at the steady-state, the current passing through the inductor is in source free RL circuit is zero

IL (0+) = 5 A = initial current.

I_L (∞) = 0 A = final value

The expression for I_L(t) for t ≥ 0 of source free RL circuit is given by

I_L(t) = I_L(∞) + [I_L(0⁺) - IL(∞)] e^-t/τ

Where

τ = time constant = L / R

τ = 0.2 / 10 = 0.02

I(t) = I_L(t) = 0 + ( 5 - 0) e^{-t / 0.02}

= 5 e^-50t for t ≥ 0