The Mathematics category gathers practice questions covering core topics such as algebra, geometry, calculus, and more. It helps learners reinforce concepts and build confidence for upcoming exams. Resources are organized for easy navigation and focused study.
Simply put, complete solution: write formula, plug data, do arithmetic. Final value matches d²y/dx² + (dy/dx)³ d²x/dy² = 0. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
We can see that using formula we get dy/dx = [(xy – 2) ± √(1 – xy)]/ x². Calculation gives this directly, check steps: apply rule, substitute values, simplify to get dy/dx = [(xy – 2) ± √(1 – xy)]/
Ref: NCERT Mathematics Class XII — Differential Equations
Notice that we verify 32 by full calculation: use standard identity, substitute, simplify step by step to reach 32.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
We know that using formula we get (log y)² - (9/5)(log x)² = 0. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get (log y)² - (9/5)(log x)² = 0.
Ref: NCERT Mathematics Class XII — Differential Equations
The trick is solving fully: apply relevant formula, put numbers, compute. Result comes as satisfies constraints and non-negativity restrictions. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Linear Programming
Applying the basic concept, solving fully: apply relevant formula, put numbers, compute. Result comes as only the corner points of the feasible region. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Linear Programming
We can see that complete solution: write formula, plug data, do arithmetic. Final value matches Var (X) = E[(X - μ)]². Simple and accurate.
Ref: NCERT Mathematics Class XII — Probability
Understanding this is easy: using formula we get point of inflexion at = 0. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get point of inflexion at = 0.
Ref: NCERT Mathematics Class XI and XII
Recall the rule solving fully: apply relevant formula, put numbers, compute. Result comes as f is increasing in [1,∞). Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI and XII
From the definition, solving fully: apply relevant formula, put numbers, compute. Result comes as m = n. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
The logic is straightforward: we verify all x ∈ (R−I) by full calculation: use standard identity, substitute, simplify step by step to reach all x ∈ (R−I).
Ref: NCERT Mathematics Class XI and XII
The logic is straightforward: after simplifying, 2 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Differential Equations
