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Every AI-generated question goes through two verification authorities: SymPy computation + NCERT source grounding. Teachers review the flagged ones below.
A manufacturing company produces two types of furniture: chairs and tables. Each chair requires 4 hours of carpentry and 2 hours of finishing. Each table requires 3 hours of carpentry and 5 hours of f…
- Sympy recompute MISMATCH: intersection of 4x+3y=120 and 2x+5y=100 is (21.4, 11.4), not (15,14)
- Claimed Z=3180 at (15,14) fails constraint check: 4(15)+3(14)=102 ≠ 120
- Aligned with NCERT Chapter 12 scope
- Blocked from auto-publish — sent to teacher review
Define the feasible region of a linear programming problem and explain why the optimal value of the objective function always occurs at a corner point.
- Source grounding verified — traces to §12.2 definition
- Conceptual question — no numeric computation possible
- Routed to teacher review (proof_like — engine cannot verify)
A diet must contain at least 80 units of vitamin A and 100 units of minerals. Two foods cost ₹4 and ₹3 per unit. Minimise cost. (Trust score flagged for unbounded region.)
- Feasible region appears unbounded for the given constraints
- Cost coefficients differ from NCERT example
Graph the constraints x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0 and identify the corner points of the feasible region.
- Corner points verified
- Aligned with NCERT Chapter 12
Find the angle between the lines whose direction ratios are (2, 2, 1) and (4, 1, 8).
- Formula application verified
- Rounding of final angle should be specified to 2 d.p.
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