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Newton’s First Law – Net Force in Equilibrium
At a manufacturing plant operated by Reliance Industries in Jamnagar, a heavy equipment box rests on the factory floor. Even th...

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Newton’s Second Law – Gravitational Force on a Falling Object
During a relief mission organized by the Indian Air Force, supply packages are dropped from aircraft to remote flood-affected ar...

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Newton’s Second Law – Acceleration of Connected Objects
Engineers at Boston Dynamics are testing two robots connected by a rope on a frictionless surface. Robot A pulls Robot B using ...

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Newton’s Second Law – Force Produced by a Car Engine
Automotive engineers at Tata Motors are testing a new electric car prototype on a straight test track in Pune. The engineers wa...

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Newton’s Third Law – Action and Reaction in Rocket Launch
Scientists at SpaceX are testing a rocket engine before launch from their facility. When the rocket pushes exhaust gases downwa...

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Newton’s Second Law – Normal Force in an Accelerating Elevator
Engineers at Otis Elevator Company are testing a new high-speed elevator installed in the Burj Khalifa. When the elevator accel...

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Newton’s Second Law – Motion on an Inclined Plane
In the mountainous region near Manali, a rescue team is testing a motorized emergency vehicle designed to climb steep slopes. E...

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Newton’s First Law – Force Needed to Start Motion
At Indira Gandhi International Airport, a heavy suitcase is sitting on a stationary conveyor belt. The belt is initially at rest...

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Newton’s Second Law – Acceleration of a Mars Rover
At NASA's robotics laboratory, engineers are preparing a prototype rover for a future mission to Mars. Before sending the rover...

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Newton’s Second Law – Force Required to Accelerate a Rocket Cart
At ISRO's training center, engineering students are testing a small rocket-powered cart on a straight frictionless track. The ca...

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The Dividing River of Balance
After escaping the multiplying vines, Arjun arrives at a wide glowing river. Floating stones appear and disappear mysteriously. ...

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The Multiplying Vines
As Arjun continues deeper into the Lost Forest of Aryavarta, thick magical vines suddenly wrap around the trees and block his pa...

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The Broken Bridge of Difference
fter entering the forest, Arjun walks deeper until he reaches a wide river. The bridge that once crossed it is broken, and only ...

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The Gate of Addition
As Arjun stands at the entrance of the mysterious Lost Forest of Aryavarta, he encounters a massive ancient wooden gate covered ...

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Last non-zero digit
Given a number n, find the last non-zero digit of the factorial of that number. You need to take care of the large values of n....

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Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...

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Spiral Mandala
Generate a clockwise spiral pattern using 1s in an N×N matrix to create an intricate mandala effect. e.g. N = 5; y_correct...

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Starburst Mandala
Create a mandala starburst using diagonal and orthogonal symmetry in a matrix.

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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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Plus Cross Mandala
Create a symmetrical plus (+) shaped pattern centered in an N×N matrix.

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Circular Ring Approximation Mandala
Generate a matrix that approximates a circular ring using distance-based thresholding , a visually rich mandala-inspired challen...

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Diagonal Cross Mandala
Generate an N×N matrix with diagonals highlighted to form an artistic X-shaped mandala pattern. e.g. N = 5; 1 0 0...

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Concentric Squares Mandala
Generate concentric square rings of alternating 1s and 0s to form a layered mandala-style matrix. e.g. N = 5; 1 1 1 1 1;...

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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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Filled Diamond Pattern
Create an N×N binary matrix that forms a filled diamond shape centered in the matrix. The diamond expands symmetrically toward t...

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Simulate full-stop emergency braking scenario.
Emergency braking events demand rapid deceleration to bring the vehicle safely to rest. Given initial vehicle speed and constant...

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Compute optimal regenerative and friction brake torque blending.
Electric and hybrid vehicles combine regenerative braking with traditional friction braking to maximize energy recovery while en...

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Estimate brake disc temperature rise during braking.
During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can ...

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Compute optimal front–rear brake force distribution.
Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping...

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