A particle covers the first half of a track at 30 m/s and the second half of the track at 60 m/s. What is its average speed?
PhysicsFormula Selection
Variable vs. Constant Acceleration Formula Guard
Rule: Never use v = u + at or s = ut + ½at² if acceleration varies with time a(t) or position a(x). Use calculus: a = dv/dt or a = v(dv/dx).
The position of a particle along the x-axis is given by x(t) = 6t² - t³ (in metres, t in seconds). Which approach correctly finds its velocity when acceleration becomes zero?
PhysicsConceptual Gaps
Zero Velocity vs. Non-Zero Acceleration at the Apex
Rule: Acceleration is the rate of change of velocity (dv/dt), not velocity itself. A body can have v = 0 at an instant while a ≠ 0.
A ball is projected vertically upward under gravity (neglecting air resistance). At the highest point of its trajectory, which statement is true?
Rule: Leading zeros are NEVER significant (0.0025 has 2 sig figs). In multiplication/division, round the result to the FEWEST significant figures among the inputs.
How many significant figures are present in 0.005080 g, and how many significant figures should be reported for the product (0.024 × 1.325)?
ChemistryFormula Selection
Molarity (M) vs. Molality (m) & Temperature Independence
Rule: Molarity M = moles of solute / L of SOLUTION (depends on T). Molality m = moles of solute / kg of SOLVENT (independent of T).
18 g of glucose (M = 180 g/mol) is dissolved in 250 g of water. Which formula and value correctly give the molality (m) of the solution?
ChemistryFormula Selection
Limiting Reagent Identification Formula (n_given / stoichiometric coeff)
Rule: Always divide initial moles by the balanced stoichiometric coefficient (n_i / ν_i). The reactant with the SMALLEST ratio is the limiting reagent.
In the Haber process N₂ + 3H₂ → 2NH₃, 2.0 mol of N₂ is mixed with 4.5 mol of H₂. Which reactant is limiting and how many moles of NH₃ form?
ChemistryConceptual Gaps
Avogadro's Law: Molecules vs. Total Atoms in Polyatomic Gases
Rule: Equal moles have equal MOLECULES (n × N_A), but total ATOMS = (moles × N_A × atomicity).
Which of the following samples contains the MAXIMUM number of atoms?
BiologyCalculation & Units
DNA Double-Helix Pitch & Base-Pair Length Unit Conversion (nm ↔ m)
Rule: Distance between adjacent base pairs = 0.34 nm = 0.34 × 10⁻⁹ m. Keep track of whether the question gives total nucleotides (2 × bp) or base pairs (bp).
A double-stranded B-DNA fragment contains 4,000 nucleotides in total. What is the length of this DNA helix in nanometres (nm)?
BiologyFormula Selection
Chargaff's Base-Ratio Rule & Semiconservative Hybrid Density Selector
Rule: In dsDNA: %A = %T, %G = %C, and %A + %G = 50%. In Meselson-Stahl replication after n generations in ¹⁴N: Hybrid molecules = 2 (always), Total molecules = 2ⁿ.
If Adenine makes up 20% of a double-stranded DNA molecule, what is the percentage of Cytosine? Also, if this E. coli DNA (initially ¹⁵N/¹⁵N) replicates for 3 generations in ¹⁴N medium, what fraction of DNA molecules are hybrid (¹⁵N/¹⁴N)?
Rule: Moving from Species → Kingdom DECREASES shared common characteristics. In transcription, the coding strand is 5'→3' (same as mRNA with T→U), while RNA polymerase reads the 3'→5' template strand.
Which of the following statements is conceptually CORRECT according to NCERT?
Physics examples only. Other subjects keep their usual explanations.