EDUCRUCIAL

  Question : A generator is connected through a 20 MVA, 13.8/138 kV step down transformer, to transmission line. At the receiving end of the line a load is supplied through a step-down transformer of 10 MVA, 138/69 kV rating. A 0.72 pu load, evaluated on load side transformer ratings as base values, is supplied from the above system. For system base values of 10 MVA and 69 kV in load circuit, the value of the load (in per unit) in generator circuit will be  (a) 36 (b) 1.44 (c) 0.72 (d) 0.18  [GATE E.E. 2006] Answer : Load = 0.72 pu at load side base of 10 MVA and 69 kv. We have to find load in generating circuit. So it is required to convert 0.72 pu to new generating side base of 20 MVA, 13.8 kV. Z(new) = Z(old) * (KVA(new)/KVA(old)) * (kV(old)/kV(new))² Z(new) = 0.72 * (20/10) * (69/13.8)² Z(new) = 36 pu For any further queries, please comment below. 

  Question : A 220 Ω resistor is connected in series with the gate of an SCR as shown in fig. The gate current required to fire the SCR is 7 mA. What is the input voltage (Vin) required to fire the SCR? Answer : Vin will not be equal to only IG * R but we have to add junction voltage 0.7 volt also.  So correct Vin = 0.7 + IG*R = 0.7 + (7mA)(220 ohm) Vin = 2.24 V

  Question: A 25 MVA, 4-pole, 50 Hz turbo-alternator has an inertia constant H = 5 kW sec/kVA. The stored kinetic energy in the rotor at synchronous speed is Explanation: Machine rating G = 25 MVA Inertia constant H = 5 kW sec/kVA Now kinetic energy stored (K. E.) = Machine rating * inertia constant K. E. = G*H K. E. = (25 MVA) * (5 kWsec/kVA) K. E. = 125 MJ

  Question : A college biology class consists of 8% freshmen, 27% sophomores, 45 % juniors and 20% seniors. During an exam, 22% of the freshmen, 17% of the sophomores, 12 % of the juniors, and 5% of the seniors wrote their answers in pen. If you would select an exam at random and find that the answers were written in pen, what is the probability that the exam was written by a freshmen? Explanation : Let us consider following events.  E1 = A college biology class consists of freshmen E2 = A college biology class consists of sophomores E3 = A college biology class consists of juniors E4 = A college biology class consists of seniors And P = student wrote their answers in pen  If answers were written in pen, probability that the exam was written by a freshmen P(E1 | P) = 0.1380

 QUESTION :- Find the LCM and HCF Of the following integers by applying the prime factorisation method.  1) 12,15 and 21  2) 17,23 and 29  3) 8,9 and 25 ANSWER :- 1) 12,15 and 21 Product of prime factor 12=2×2×3 = 2² × 3 15=3×5 21=3×7 Here, 3 is common among 12,15 and 21 SO, HCF(12,15,21) = 3 In LCM we have to multiply all number with highest power but number should not be repeated.  LCM(12,15,21)= 2² × 3¹ × 5¹ × 7¹ = 420 2) 17,23 and 29 17=1×17 23=1×23 29=1×29 Here, 1 is common among 17,23 and 29. So, HCF (17,23,29)=1 In LCM we have to multiply all number with highest power but number should not be repeated. LCM(17,23,29)=17×23×29=11,339 3) 8,9 and 25 8= 2×2×2×1 9=3×3×1 25=5×5×1 Here, 1 is common among 8,9 and 25. So,  HCF (8,9,25)=1 In LCM we have to multiply all number with highest power but number should not be repeated.  LCM(8,9,25)=2×2×2×3×3×5×5=1100

 Question : An Excel printout of some descriptive statistics for a set of data is shown below. What is the IQR?  Options:- A) 15.5 B) 38 C) 5.5 D) 15 Explanation :- IQR (Interquartile range) : IQR is a measure of where the middle fifty percent data is in a data set.  IQR is defined as first quartile(Q1) subtracted from third quartile(Q3).  IQR = Q3 - Q1 Here five number summary of data is given in question. We can calculate IQR from it.  From five number summary,  First quartile (Q1) = 5 Third quartile (Q3) = 20.5 IQR = Q3 - Q1 IQR = 20.5 - 5 IQR = 15.5  Comment below if you still have any queries. 

  Question: What is the equivalent resistance of the following arrangement between M and N?   Answer: For simplification, circuit is redrawn as shown below.  After redrawing circuit, we can see that all three resistances are in parallel. Each resistance has value R. Equivalent resistance of three parallel resistances of value R is R/3. So answer is R/3. Note: If n number of resistances having value R are connected in parallel then equivalent resistance is R/n.  For any query regarding above solution, please comment below. 

Question:-   Assume that post MBA salaries are normally distributed with mean $77,500 and standard deviation $13,750 What is the probability that that a randomly selected MBA graduate (6 Marks)  a) Earns more than $100,000?  b) Earns less than $60,000?  c) Earns between $75,000 and $95,000  d) Earns less than $55,000 or more than $80,000 Answer :- Detailed explanation is provided below: Part A:- Probability that earning is more than $100,000  P(x>100000)= 1-p(x<100000) When Earning capacity is more than $100000 p(x>100000)=0.0509 Part B:- Probability that earning less than $60,000  P(x<60000) When earning capacity is less than $60,000 p(x<60000)=0.1015  Part C:- Probability that earning between $75,000 and $92000 P(75000<X<95000) When earning capacity is between $75,000 and $95,000 p(75000<x<95000)=0.4747 Part D:- Probability that earning less than $55000 or more than $80000 P(x<55000) or P(x>80000) P(x<550...

Question:   A step down DC chopper has a resistive load of R = 15 ohm and input Vdc = 200 V. When the chopper remain ON, it's voltage drop is 2.5V. The chopper frequency is 1 kHz. If the duty cycle is 50%, determine:  a) Average output voltage  b) RMS output voltage  c) Chopper efficiency  d) The effective input resistance of the chopper Answer: We can get answers directly by applying relevant formulas as shown below.  (a) Average output voltage = 98.75 V (b) RMS output voltage = 139.6536 V (c) Chopper efficiency = 98.75% (d) The effective input resistance = 30.3799 ohm Additional information : Waveforms for step down chopper are shown below : For any queries regarding above solution please comment below. Thank you! 

  Question: Use a sum identity and the fact that 105° = 60° + 45° to find the exact value of cos(105°). Answer: If you have any query regarding above explanation then please comment below.  Thank you!  

Question: In New South Wales, each adult on the electoral roll has a 10% of being called up for jury duty in any year. A company has 25 employees on the electoral roll. What is the probability that more than two employees are called up for jury duty in any year? Answer: This question can be solved by using binomial distribution formula.  So probability that more than two employees are called up for jury duty in any year is 0.4629 . For any further queries regarding above explanation please comment below. Thank you! 

Question: Three loads are connected in parallel with a terminal voltage of 250 V(rms). Load 1 absorbs 16kW and 18 KVAR. Load 2 absorbs 10KVA with a 0.8 leading power factor. Load 3 absorbs 8kVA at a unity power factor.  (a) Find the combined load impedance of the three loads.  (b) Draw the power triangle of the combined load. Answer: Z = 1.7 + j0.64

  Question : If LCM of two number is 24255 then their HCF can be ........( select one option ).   Options:   A) 297   B) 315   C) 462   D) 275  Solution : As we all know, HCF is a factor of LCM . therefore , 315 is a factor of 24255. so that HCF can be a 315 . all other options are not a factor of 24255. 24255=315 x 77 . correction option : B 

  Question: If 3x−y=12, what is the value of 8^x/2^y? A) 2^12 B) 4^4 C) 8^2 D) The value cannot be determined from the information given. Explanation: 8^x can be written as 2^3x because 8 = 2^3 So we need to find value of 2^3x/2^y It is given that 3x-y=12 So 3x = 12+y Substituting value of 3x in 2^3x/2^y (2^3x) /(2^y) = (2^(12+y))/(2^y) = 2^((12+y)-y) = 2^12 Handwritten solution is provided below: So answer is option (A) : 2^12

  Question: In the circuit of Figure, determine: a) Thevenin's equivalent circuit between A and B; b) power dissipated in a 4.5 ohm resistor placed between A and B. Explanation: Thevenin's theorem statement: "Any linear circuit containing several voltages and resistances can be replaced by just one single voltage in series with a single resistance connected across the load"  Steps to solve questions: Step 1 : Remove load resistor or component concerned.  Step 2 : Find thevenin's equivalent voltage Vth by using any suitable method.  Step 3 : Find equivalent resistance Rth.  Case 1 - if independent voltage source is present in a circuit then replace it by short circuit.  Case 2 - if independent current source is present in a circuit then replace it by open circuit.  Case 3 - if dependent source is present in a circuit then Rth can be obtained by taking ratio of open circuit voltage to short circuit current.  Step 4 : Draw thevenin's equivalent circu...

Superposition Theorem Requirement: Power System is a complex network having number of voltage and current sources and number of loads. Now to analyze the network we need to find voltage/current at particular branch or load.  In such cases calculations for thevenin's and norton's theorem becomes difficult. We can use superposition theorem to find voltage/current at any branch or load in complex network. In this theorem only one source considered at a time and total voltage/current is sum of voltage/current obtained by considering individual source.   Statement of Superposition Theorem:

 Question: To achieve an output of 10 V with an input of 300 mV, what voltage gain is required? Explanation: Gain: Ratio of output quantity to input quantity is called gain.

Question: What is the probability of randomly arranging the word CHALLENGING so that the first two letters are GG ? Please explain.  Answer: Explanation of above question is provided below:

Question : Find the number of ways of arranging the letters in the word BEACHFRONT if the second and third letters must be vowels and the last letter must be a consonant. Please explain Answer :  Explanation of above question is provided below: Last letter must be consonant and there are 7 consonants. So number of ways to fill last letter = 7 P 1 .  Second and third letter must be vowels and there are 3 vowels. So number of ways to fill second and third letters = 3 P 2 . Now 7 positions are remaining and there are 7 letters remaining. So number of ways for remaining 7 letters = 7 P 7 Total number of ways is multiplication of above 3 cases. Calculation is shown below. 

Question: Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 4 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If 6 jurors are selected at random from this group of 20, find the probability that the number of potentially prejudiced jurors among the 6 selected jurors is a. exactly 1  b. none  c. at most 2 Explanation: Detailed explanation is provided in below: Part (a) explanation: