Practice technical discipline questions for Electrical Machines, Power Systems, Power Electronics & Drives, Control Systems, Network Theory, and Switchgear with worked solutions.
Marking scheme: +1.00 positive, 0.00 negative (CIL CBT Pattern).
A student has an average score of $75$ in $4$ subjects. After the score of a $5\text{th}$ subject is included, the student's average score becomes $78$. What score did the student obtain in the $5\text{th}$ subject?
A chef prepares a premium hemispherical chocolate dessert that is packed with exactly two-thirds of liquid caramel sauce. If the diameter of each dessert is $42\text{ mm}$ and the price of one cubic mm of caramel sauce is $50\text{ paisa}$, then the total cost of the caramel sauce used to make $50$ of these desserts is:
An apparel manufacturing unit operates identical eco-friendly looms to fulfill global export orders. If $12$ looms running simultaneously can weave a total of $360\text{ metres}$ of fabric in $6\text{ days}$, how many metres of fabric can $15$ looms weave in $8\text{ days}$?
The difference between the present ages of Lata and Smita is $29\text{ years}$. Five years ago, the sum of their ages was $39\text{ years}$. If Lata is older than Smita, what is Smita's present age (in years)?
Let $x$ be a positive integer. If the Highest Common Factor of the fractions $\frac{6}{x}$ and $\frac{x}{2}$ is exactly equal to their Least Common Multiple, then the value of $x$ is:
In a custom board game, two players, Kevin and Maya, roll their respective biased dice simultaneously in sequential rounds until a winner is decided. Kevin rolls a "Star" with a probability of $1/3$, while Maya rolls a "Star" with a probability of $2/7$, independent of each other. A player wins the game immediately in any given round if their die lands on a "Star" while the opponent's die does not. Conversely, if both players roll a "Star" or if both fail to do so, the round is declared a draw and they proceed to an identical next round. The probability that Maya ultimately wins the game is:
If $X \div 9 = \frac{1}{1.5} \times \left\{ \frac{5}{6} \div 1\frac{1}{4} \text{ of } \frac{2}{3} \right\} \div 3$, then the value of $X$ is:
A plant produces Smartphones and Tablets in the initial ratio of $3 : 2$. To meet holiday demand, the plant increases the production of Smartphones by $40\%$. By what percentage must the production of Tablets be increased so that the new production ratio of Smartphones to Tablets becomes exactly $7 : 4$?
A solid toy is shaped as a right circular cylinder with a hemisphere on one base and a cone on the other. The cylindrical part has a diameter of $12\text{ cm}$ and its height is $1.5$ times of radius of base. The hemispherical and conical parts share the same radius as the cylinder. If the height of the conical part is $K\text{ cm}$ and the total cost of making this toy at the rate of ₹$21$ per cubic cm is ₹$37,224$, then the value of $K$ is: $\left(\text{Use } \pi = \frac{22}{7}\right)$
A person travelled $10\text{ km}$, $15\text{ km}$ and $x\text{ km}$, in $15$, $12$ and $13\text{ minutes}$, respectively. If their average speed is $67.5\text{ kmph}$, then find the value of $x$.
The cost of a washing machine is $25\%$ less than the cost of a television. If the cost of the washing machine increases by $80\%$ and that of the TV decreases by $16\%$, then what is the percentage change in the total cost of $6$ washing machines and $9$ televisions?
A sum, when invested at $20\%$ simple interest per annum, amounts to ₹$8,160$ after $4\text{ years}$. What is the simple interest (in ₹, rounded off to two decimal places) on the same sum at the same rate in $2\text{ years}$?
In a division sum, the divisor is $17$ times the quotient and $8$ times the remainder. If the remainder is $51$, what is the dividend?
A wholesale trader purchases a certain number of identical gadgets. He sells $40\%$ of the gadgets at a profit of $25\%$, and $50\%$ of the remaining gadgets at a loss of $10\%$. If he sells the final left-over gadgets at his exact cost price, then the overall net profit percentage on the entire transaction is:
The total time ($T$, in hours) required to transport a heavy cargo shipment across a fixed shipping lane varies inversely as the square root of the engine horsepower $H$ of the cargo ship. When a ship with an engine capacity of $100\text{ horsepower}$ is used, the transit takes exactly $24\text{ hours}$. If the logistics company switches to a more powerful freight ship equipped with a $400\text{ horsepower}$ engine, how many hours will the same transit take?
A solid metallic sphere of diameter $32\text{ cm}$ is melted and drawn into a wire of uniform cross-section. If the radius of the wire is $8\text{ cm}$, then find the length (in $\text{cm}$) of the wire.
A logistics company analyzes delivery times (in hours) for five remote locations: $12.4$, $14.1$, $13.7$, $19.2$, and $16.6$. A manager mistakenly computes the mean deviation from the highest value rather than from the mean. Which of the following best describes the impact of this error on the interpretation of variability in delivery times?
As part of a final selection trial, three candidates—A, B, and C—are assigned a technical task. Working independently, Candidate A can complete the task in $24\text{ days}$, Candidate B in $32\text{ days}$, and Candidate C in $60\text{ days}$. They begin working on the task simultaneously. However, Candidate A leaves the trial after $6\text{ days}$, and Candidate B leaves after working for a total of $8\text{ days}$. Candidate C continues alone to finish the assignment. How many additional days are required by Candidate C to complete the remaining work?
Four venture capitalists evaluate their quarterly portfolio performance based on the ratio of returns received to their initial capital investments. The recorded performance ratios are as follows:
Which investor received the lowest return percentage on their investment?
If the compound interest earned on a sum in $2\text{ years}$ at a rate of $10\text{ percent}$ per annum is ₹$210$, then the principal amount (in ₹) is:
A wholesaler purchases $500\text{ kg}$ of flour but actually receives $10\%$ more quantity because of a faulty weighing machine used by the supplier. He then sells the flour at $5\%$ above cost price. During the sale, his weighing machine delivers $8\%$ less quantity than the indicated weight. What is his overall profit percentage (rounded off to one decimal place)?
A cyclist starts from point P and rides towards point Q, which is $120\text{ km}$ away. For the first $40\text{ km}$, the cyclist travels at $12\text{ km/h}$. For the next $50\text{ km}$, the cyclist travels at $10\text{ km/h}$. For the remaining distance, the cyclist increases speed by $20\%$ over the previous speed. What is the average speed (in $\text{km/h}$) of the cyclist for the entire journey? (Rounded off to two decimal places)
Simplify: $\sqrt[3]{99^3 - 88^3 - 11^3}$
An academic admissions panel calculates a candidate's final selection score as the weighted average of four components: Mathematics, Physics, Chemistry, and a Personal Interview. Chemistry carries a weight of $40\%$ of the total score. The remaining $60\%$ is distributed among the other three components such that the weight assigned to Physics is twice the weight assigned to the Personal Interview, and the weight assigned to Mathematics is equal to the combined weights of Physics and the Personal Interview. If a candidate scores $80$ in Mathematics, $70$ in Physics, $85$ in Chemistry, and $90$ in the Personal Interview, what is the candidate's final weighted average score?
A concrete flood barrier is in the shape of a right prism. Its cross-section is an isosceles trapezoid with parallel sides of lengths $10\text{ m}$ and $22\text{ m}$, and the two equal non-parallel sides each measure $10\text{ m}$. The prism is $50\text{ m}$ long. Find the volume (in $\text{m}^3$) of the prism.