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Translating even-degree polynomial by its vertex to the origin
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting ...

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Translating parabola by its vertex to the origin
Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the ...

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Shifting vertically a function's graph
Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k. For a ...

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Is it Possible? ( Easy )
In the first part of series, we simplify the problem. Given two jugs with capacities A and B, and a target amount T, determine i...

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Power of Moving Vehicle
Engineers at Tesla calculate how much power is required to maintain vehicle motion.

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Spring Energy Storage
Engineers at Bosch design suspension systems using springs. They calculate the energy stored when the spring compresses.

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Machine Efficiency Test
Engineers at Siemens test how efficiently a motor converts electrical energy into mechanical work.

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Falling Object Velocity
Scientists at ISRO drop test equipment from a height to study motion under gravity. They must calculate the velocity just befor...

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Pushing a Heavy Machine
At a factory operated by Bharat Heavy Electricals Limited in Haridwar, engineers must move a heavy generator across the floor. ...

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Power of Elevator Motor
P=W/t

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Total Energy of Moving Object
E=KE+PE

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Roller Coaster Height Energy
At Imagicaa Theme Park, engineers calculate potential energy at the top of a roller coaster.

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Kinetic Energy of a Moving Car
Engineers at Mahindra & Mahindra test how much kinetic energy a car gains when accelerating.

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Work Done in Lifting an Object
Engineers at Larsen & Toubro are testing a crane used to lift heavy construction materials at a building site in Mumbai. They n...

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Maximum Power Transfer
Engineers at Texas Instruments design circuits for maximum efficiency. Internal resistance = 4 Ω Find load resistance for maxi...

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Kirchhoff’s Loop Law
Engineers at ISRO design spacecraft circuits. Battery = 10 V Total resistance = 2 Ω Find current in loop.

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Drift Velocity in Conductor

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Power Loss in Transmission Lines
Electricity transmitted by Power Grid Corporation of India experiences power loss due to resistance. Current = 10 A Resistance...

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Car Battery Internal Resistance
Engineers at Tata Motors test a car battery with: EMF = 12 V Internal resistance = 1 Ω External resistance = 5 Ω Find curren...

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Parallel Circuit in Home Wiring
Home appliances connected in parallel in a house in Gurgaon have resistances of 6 Ω and 3 Ω. Find equivalent resistance.

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Series Circuit in Street Lights
Street lights installed by the Delhi Electricity Distribution Company use three resistors of 2 Ω, 3 Ω, and 5 Ω in series. Find ...

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Mobile Charging Cable Resistance

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Electric Heater Safety Test
Engineers at Havells test a heater connected to 220 V supply. The heater resistance is 44 Ω. They need to calculate power consu...

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Emergency Torch in a Power Cut
During a power outage in Lucknow, Riya uses an emergency torch powered by a battery of 6 V connected to a bulb with resistance 3...

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[Master Regular Expression] Reformat Phone Number
You are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'. You would like to re...

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[Master Regular Expression] Unique Email Addresses
Every valid email consists of a local name and a domain name, separated by the '@' sign. Besides lowercase letters, the email ma...

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[Master Regular Expression] Keyboard Row
Given an array of strings words, return the words that can be typed using letters of the alphabet on only one row of American ke...

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Hollow Diamond Pattern
Create an N×N matrix that forms a hollow diamond shape using 1s, leaving the interior empty. This challenge emphasizes boundary ...

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Hourglass Mandala
Generate an hourglass shape using matrix geometry and symmetry. e.g. N = 5; 1 1 1 1 1; 0 1 1 1 0; ...

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Vertical Mirror Mandala
Create a symmetric left-right mirrored pattern in an N×N matrix to emulate mandala reflection symmetry. e.g. N = 5; ...

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