Where Exploration Leads to Academic Excellence

A Knowledge Hub by Rahul Anand

Mathematical Marvels: Insights from the Field

general aptitude : Loss and Selling Price Problem : Solve cost price and loss-related aptitude questions.

Selling Price Calculation with 20% Loss

Profit and loss questions improve real-world calculation ability.

general aptitude : Probability Aptitude Question : Practice probability questions for aptitude tests.

Probability of Drawing Two Red Balls

Probability is key in logical and math aptitude exams.

general aptitude : Work and Time Aptitude Question : Practice aptitude work problems for exams.

Work Completion Problem with 12 and 20 Men

Men working together to complete tasks faster is a common aptitude question.

general aptitude : Profit and Loss Aptitude Problem : Solve real-life shopkeeper discount and profit questions.

Profit Percentage with Marked Price and Discount

Profit and loss questions test practical business math.

general aptitude : Work Together Aptitude Question : Learn teamwork efficiency in aptitude problems.

Work Completion by A and B Together

Collaboration work problems are frequently tested in exams.

general aptitude : Simple Interest Aptitude Problem : Improve speed with interest-related aptitude questions.

Money Triples in 12 Years Problem on Simple Interest

Interest problems are critical in finance-related aptitude tests.

general aptitude : Average Aptitude Question : Practice averages to strengthen arithmetic aptitude.

Average of Five Numbers Problem with One Removed

Averages are tested often in aptitude exams with practical twists.

general aptitude : Number Series Aptitude Problem : Boost logical thinking with number sequence questions.

Find the Missing Term in the Series 2, 6, 12, 20, 30

Number series problems improve pattern recognition for competitive exams.

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Calculus Castle

Derivative of sinθ using the First Principle

Derivative of \( sinθ \) using the First Principle Let \(y\) = \( sinθ \) ∴ \(y + δy\) = \( sin(θ + δθ) \) ∴ \(δy\) = \( sin(θ + δθ) \) – \( sinθ \)From Trigonometry , we have \( sin(A-B) \) = 2.\( sin \dfrac {(A-B)}{2} \).\( cos \dfrac {(A+B)}{2} \)Using the above…

Derivative of cosθ using the First Principle

Derivative of \( cosθ \) using the First Principle Let \(y\) = \( cosθ \) ∴ \(y + δy\) = \( cos(θ + δθ) \) ∴ \(δy\) = \( cos(θ + δθ) \) – \( cosθ \)From Trigonometry , we have \( cos(A-B) \) = -2.\( sin \dfrac {(A+B)}{2} \).\( sin \dfrac {(A-B)}{2} \)Using the above…

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