Given, f(x) = x³ – 12x² + 45x + 8. At which point does f(x) has its minimum?
Applying the basic concept, after simplifying, 5 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI and XII
General Mathematics 3
The General Mathematics 3 category gathers a range of problems covering core topics in mathematics. It includes practice questions, step‑by‑step solutions, and explanations to help learners deepen their understanding and prepare for assessments.
Filter questions
Given, f(x) = x³ – 12x² + 45x + 8. At which point does f(x) has its maximum?
In easy words, using formula we get 3. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 3.
Ref: NCERT Mathematics Class XI and XII
What will be the nature of the equation sin(x + α)/sin(x + β)?
The trick is after simplifying, Does not possess a maximum or minimum value is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI and XII
If y = enx, then nth derivative of y is:
Look at it this way: complete solution: write formula, plug data, do arithmetic. Final value matches nny. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
The values of x which statisfied |3x| ≥ |6 − 3x| A. (0, 1] B. [1, 4] C. (4, ∞) D. (−1, 0) E. (−∞, 0) Choose the correct
The logic is straightforward: complete solution: write formula, plug data, do arithmetic. Final value matches C and E only. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
The system of linear inequalities 2x − 1 ≥ 3 and x − 3 > 5 has solution:
Recall the rule solving fully: apply relevant formula, put numbers, compute. Result comes as (8, ∞). Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI and XII
A pipe can empty (5/6)th part of a cistern in 20 minutes. The part of cistern which will be empty in 9 minutes is:
From the definition, complete solution: write formula, plug data, do arithmetic. Final value matches 3/8. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
Which of the following is the reversal law of transposes?
We can see that complete solution: write formula, plug data, do arithmetic. Final value matches (AB)’ = B’A’. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
Which of the following is not a type of binary operation?
Understanding this is easy: complete solution: write formula, plug data, do arithmetic. Final value matches Transitive. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
Let ‘*’ be a binary operation defined by a * b = 3ab + 5. Find 8 * 3.
Notice that complete solution: write formula, plug data, do arithmetic. Final value matches 1541. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
Let ‘*’ be a binary operation defined by a * b = 4ab. Find (a * b) * a.
We know that we verify 16a² b by full calculation: use standard identity, substitute, simplify step by step to reach 16a² b.
Ref: NCERT Mathematics Class XI and XII
If f: N→N, g: N→N and h: N→R is defined f(x) = 3x - 5, g(y) = 6y2 and h(z) = tanz, find ho(gof).
Understanding this is easy: using formula we get tan(6(3x - 5)²). Calculation gives this directly, check steps: apply rule, substitute values, simplify to get tan(6(3x - 5)²).
Ref: NCERT Mathematics Class XI and XII
