AdvanceReview
Path to 300

Multi-concept practice

Mixed questions

Advanced rarely tests one chapter alone. Each item shows which knowledge terms join, the bridge between them, and what to practise.

Showing 35 of 35 mixed stems

Mathematics2026 · Paper 2 · Q15–Q16linked-numerical

Exponential curves + area

Calculus – Curves+Definite Integration – Area+Trigonometric equations

Knowledge bridge

Step 1: set y = e^{-x} equal to y = e^{-x}(sin x + cos x) and cancel the common exponential to get a trig equation for intersection abscissae α_i. Step 2: order those roots and set up the definite integral of the difference of the two curves between α_1 and α_4 for the enclosed area β. Step 3: simplify the given log expression in β to a clean numerical value.

Why it feels hard

The stem hides trig solving inside an exponential envelope; students often integrate before finding exact limits.

What to practise

Drill ‘cancel common positive factor → trig roots → area integral’ as one reflex chain.

Open 2026 year review →
Mathematics2026 · Paper 2 · Q17–Q18linked-numerical

Ellipse intersection + angle + common area

Coordinate Geometry – Ellipse+Tangents & angle between curves+Area of common region

Knowledge bridge

Step 1: solve the two ellipse equations simultaneously for the first-quadrant intersection P. Step 2: differentiate implicitly to get slopes of both tangents at P; convert the angle formula into 4 tan θ. Step 3: for the common area, set up the integral (or standard ellipse-sector form) of the overlapping region and read cot α from that area.

Why it feels hard

Two different asks on one geometry figure — angle then area — under numerical fatigue.

What to practise

For two conics, always compute intersection → slopes → area in that fixed order.

Open 2026 year review →
Mathematics2026 · Paper 2 · Q8multi-correct

DE solution + extrema + intersections

Differential Equations+Functions / AOD+Curve intersections

Knowledge bridge

Step 1: solve x y' = y − x³ (homogeneous/linear in y/x) to get the family y = Cx − x³/2. Step 2: impose the given condition to fix C, then use y' = 0 to locate the local max. Step 3: compare monotonicity on (1,2) and count positive roots of f = g.

Why it feels hard

Multi-correct options test DE, calculus and graph reading together; one sign error in the DE kills several options.

What to practise

After every DE, immediately ask: extrema? monotonicity? intersections with a given g?

Open 2026 year review →
Mathematics2026 · Paper 1 · Q2single-correct

Parabola points + circumcircle + ellipse

Coordinate Geometry – Parabola+Circle (circumradius)+Ellipse conditions

Knowledge bridge

Step 1: recover points P, Q, R from the slope/tangent conditions on the parabola. Step 2: find the circumcircle of triangle PQR (perpendicular bisectors). Step 3: read the required radius / relation that also ties to an ellipse option.

Why it feels hard

Geometry hops across three curve types in one SC item.

What to practise

Practise ‘points on parabola → circle through them → conic check’ as a single drill.

Open 2026 year review →
Mathematics2026 · Paper 1 · Q16matching

Matching across circle / parabola / ellipse / hyperbola

Circle+Parabola+Ellipse+Hyperbola

Knowledge bridge

Step 1: for each List-I geometric condition, reduce to a standard conic equation or point. Step 2: match coordinates/parameters in List-II without mixing ellipse and hyperbola templates. Step 3: verify one substituted point per match to avoid swap errors.

Why it feels hard

Matching lists punish template mix-ups under time pressure.

What to practise

Keep a one-page conics identity sheet and practise full matching sets weekly.

Open 2026 year review →
Physics2026 · Paper 1 · Q1single-correct

Rolling disks + relative rotation on a large disk

Mechanics – Rotation+Rolling without slipping+Relative angular motion

Knowledge bridge

Step 1: relate arc lengths so the small disks roll without slipping on the large circumference (geometry of contact). Step 2: convert path radius R+r into orbital and spin rates (ω/51-type ratios). Step 3: close the remaining angular gap 2π − Δθ to get the meeting time τ.

Why it feels hard

Easy to use the wrong Δθ (2/51 vs 4/51) if relative rolling sense is mishandled.

What to practise

Always draw contact velocities and write v = ωr for every rolling interface before algebra.

Open 2026 year review →
Physics2026 · Paper 1 · Q2single-correct

Mutual inductance + LC resonance

EMI – Mutual inductance+AC / LC circuits+Effective inductance

Knowledge bridge

Step 1: read the coupling M = L/2 and series inductance to form L_eff. Step 2: replace the network by one equivalent L_eff (here 3L/4). Step 3: apply ω₀ = 1/√(L_eff C) to get 2/√(3LC).

Why it feels hard

Students remember ω=1/√(LC) but forget to rebuild L_eff from mutual terms.

What to practise

For every coupled-inductor problem, compute L_eff first, then resonate.

Open 2026 year review →
Physics2026 · Paper 2 · Q15–Q16linked-numerical

Fluid flow between chambers + changing capacitance

Fluids – level vs time+Electrostatics – Capacitance+Dielectric / liquid between plates

Knowledge bridge

Step 1: from the linked fluid setup, find liquid height in the left chamber at t = 500 s. Step 2: translate that height (or remaining liquid fraction) into the dielectric fill between capacitor plates. Step 3: compute ΔC = (8−n)ε₀ and extract n.

Why it feels hard

Two chapters share one clock variable t; errors in height propagate into capacitance.

What to practise

Practise fluid+capacitor linked numericals where the same h(t) feeds both answers.

Open 2026 year review →
Physics2026 · Paper 2 · Q17–Q18linked-numerical

Disk collision + rotation about pivot + energy loss

Mechanics – Collision+Rotation about a fixed point+Energy & angular momentum

Knowledge bridge

Step 1: apply angular impulse about the pivot C for the particle–disk collision. Step 2: convert post-collision ω into maximum rise of centre O (energy after collision). Step 3: compare mechanical energy before vs after to get the collision energy loss.

Why it feels hard

Choosing the wrong axis or mixing linear KE with rotational KE about C breaks both answers.

What to practise

Linked collision–rotation: conserve angular momentum about the eventual pivot, then energy separately.

Open 2026 year review →
Physics2026 · Paper 1 · Q3single-correct

Cylinder rolling off a vertical edge

Rigid body rotation+Loss of contact+Energy conservation

Knowledge bridge

Step 1: use energy to relate ω and θ as the cylinder rolls on the edge. Step 2: write radial (centripetal) condition with normal → 0 at loss of contact. Step 3: solve for v = √(5gR/7) (or the option equivalent).

Why it feels hard

Combines rolling constraint, energy and N=0 in one geometric setting.

What to practise

Memorise the ‘energy + N=0’ template for bodies leaving curved/edge surfaces.

Open 2026 year review →
Chemistry2026 · Paper 1 · Q8multi-correct

Multi-step organic synthesis + functional tests

Organic reaction sequence+Heterocycles+Tollens / qualitative tests

Knowledge bridge

Step 1: push each reagent in order to get intermediates Q, R, S, T. Step 2: recognise the heterocyclic closure in T. Step 3: apply Tollens (and related tests) only to the structure that still has the oxidisable group (S).

Why it feels hard

Mechanism memory plus lab-test logic in one multi-correct/sequence item.

What to practise

After every synthesis map, annotate which intermediates pass Tollens/Fehling/iodoform.

Open 2026 year review →
Chemistry2026 · Paper 2 · Q15–Q16linked-numerical

Ideal solution molar volumes + vapour mole fraction

Solutions – colligative / ideal+Raoult’s law+Vapour–liquid composition

Knowledge bridge

Step 1: from the linked ideal-solution data, compute the vapour-to-liquid molar volume ratio for pure B. Step 2: find liquid mole fractions (e.g. from molality). Step 3: apply Raoult to get y_B in the vapour (numerical ~0.16 style).

Why it feels hard

Two numericals share solution data; unit slips (molality vs mole fraction) are common.

What to practise

Convert every molality stem to x_i before touching vapour pressures.

Open 2026 year review →
Chemistry2026 · Paper 2 · Q17–Q18linked-numerical

Kjeldahl nitrogen + Carius sulphur on related organics

Organic practical – Kjeldahl+Organic practical – Carius+Stoichiometric estimation

Knowledge bridge

Step 1: from structure/formula of L, count N and convert mass to moles of NH₃, then to mL of 1 M H₂SO₄. Step 2: from M, count S and convert to grams of BaSO₄ via Carius stoichiometry. Step 3: keep atomic masses consistent across both linked estimation asks.

Why it feels hard

NCERT ‘end chapter’ methods under numerical pressure; easy arithmetic slips.

What to practise

Treat Kjeldahl/Carius as fixed stoichiometry templates — practise until automatic.

Open 2026 year review →
Chemistry2026 · Paper 2 · Q3–Q4multi-concept

Polymer ozonolysis + biomolecule sweetener

Polymers – natural rubber+Ozonolysis / functional tests+Biomolecules – disaccharide

Knowledge bridge

Step 1: ozonolyse the rubber repeating unit to carbonyl fragments; apply iodoform/Tollens to identify Y. Step 2: read the chlorinated disaccharide sweetener as linked galactose+fructose-type units. Step 3: connect ‘polymer degradation products’ thinking with biomolecule structure reading.

Why it feels hard

Students often skip polymers/biomolecules until too late; stems assume NCERT fluency.

What to practise

Schedule polymers + carbohydrates every fortnight with one Adv-style product ID set.

Open 2026 year review →
Mathematics2025 · Paper 2 · Q1–Q2multi-concept

Limit/derivative structure + area inequalities

Calculus – Limits / AOD+Definite Integration – Area+Inequalities of regions

Knowledge bridge

Step 1: analyse the given limit expression to identify the correct f(x) / derivative behaviour. Step 2: on a related (or following) stem, sketch the region defined by inequalities. Step 3: integrate carefully (logs appear from 1/x-type boundaries).

Why it feels hard

Back-to-back calculus depth: analytic limit then geometric area.

What to practise

Pair every limit/AOD drill with one area-of-region numerical the same day.

Open 2025 year review →
Mathematics2025 · Paper 1 · Q13numerical

Parabola numerical with algebraic constraints

Coordinate Geometry – Parabola+Algebraic parameters+Numerical answer

Knowledge bridge

Step 1: write the parabola in standard form and express the geometric condition algebraically. Step 2: reduce to an equation in the unknown parameter. Step 3: extract the required integer/decimal for the NUM grid.

Why it feels hard

Conic geometry collapses into algebra; diagram alone is not enough.

What to practise

Translate every parabola condition into an equation before computing.

Open 2025 year review →
Physics2025 · Paper 1 · Q2–Q3single-correct

Back-to-back rotation SC pair

Rotation+Rigid body dynamics+Energy / torque

Knowledge bridge

Step 1: identify axis and moment of inertia for each stem. Step 2: apply torque = Iα or energy+constraint as needed. Step 3: refuse to reuse numbers from Q2 in Q3 without re-deriving.

Why it feels hard

Similar-looking rotation stems invite copy-paste mistakes.

What to practise

Reset the free-body and axis choice on every new rotation question.

Open 2025 year review →
Physics2025 · Paper 1 · Q5multi-correct

EMI/AC multi-correct

Electromagnetic induction+AC circuits+Phase / amplitude

Knowledge bridge

Step 1: write induced emf from flux change. Step 2: place that source in the AC network (reactances). Step 3: test each option for amplitude, phase and limiting behaviour separately.

Why it feels hard

MC options mix Faraday facts with circuit phasors.

What to practise

Separate ‘induction law’ checks from ‘impedance algebra’ checks on paper.

Open 2025 year review →
Chemistry2025 · Paper 1 · Q12–Q13multi-concept

Polymers numerical + named organic reactions

Polymers+Named reactions+Stoichiometry of products

Knowledge bridge

Step 1: identify the polymer/monomer relation and compute the asked count or mass. Step 2: on the next item, map the named-reaction sequence to the major product. Step 3: connect functional-group changes across both questions if reagents overlap thematically.

Why it feels hard

End-chapter Organic + mechanism memory in numerical/SC mix.

What to practise

Never isolate polymers from GOC week — Advanced joins them in spirit.

Open 2025 year review →
Mathematics2024 · Paper 1 · Q4single-correct

Ellipse single-correct with parametric depth

Ellipse+Tangents / chords+Algebraic conditions

Knowledge bridge

Step 1: place the ellipse in standard form and introduce eccentric angle or slope form. Step 2: impose the geometric condition (tangent/chord/focus). Step 3: match the simplified relation to the correct option.

Why it feels hard

Parametric slips create attractive wrong options.

What to practise

Keep both slope and parametric forms of ellipse tangents fluent.

Open 2024 year review →
Physics2024 · Paper 1 · Q9–Q10numerical

Rotation numerical beside wave optics

Mechanics – Rotation+Wave optics+Numerical accuracy

Knowledge bridge

Step 1: finish the rotation NUM with a clear MOI/energy chain. Step 2: switch mental model to interference/diffraction for the next NUM. Step 3: protect calculator/decimal hygiene across both.

Why it feels hard

Topic switch mid-numerical section drains working memory.

What to practise

In NUM blocks, write a one-line topic label before each solve.

Open 2024 year review →
Physics2024 · Paper 1 · Q6–Q7multi-correct

Waves multi-correct + ray optics multi-correct

Waves / Sound+Ray optics+Multi-correct option logic

Knowledge bridge

Step 1: for waves, check superposition/phase options individually. Step 2: for optics, ray-trace each claim (TIR, magnification, mirror/lens sign). Step 3: never assume ‘exactly two correct’ — mark only proven options.

Why it feels hard

Two consecutive MC items amplify partial-marking risk.

What to practise

Practise MC pairs under a strict ‘prove or leave’ rule.

Open 2024 year review →
Chemistry2024 · Paper 1 · Q10–Q14numerical

Practical organic + coordination + electrochem stretch

Organic practical/analysis+Coordination compounds+Electrochemistry

Knowledge bridge

Step 1: decode the practical/analysis NUM (tests, equivalents). Step 2: count coordination isomers / geometry carefully. Step 3: finish with electrochem NUM using consistent electron/ Faraday stoichiometry.

Why it feels hard

A long NUM corridor mixes three Chem branches.

What to practise

Build a ‘mixed Chem NUM’ set: 1 practical + 1 coordination + 1 electrochem.

Open 2024 year review →
Mathematics2023 · Paper 1 · Q7–Q9multi-concept

Parabola/ellipse tangents + area numerical

Conics – common tangents+Calculus – Area+Trigonometric equations

Knowledge bridge

Step 1: for the ellipse–parabola common-tangent MC, write both tangent conditions and compare. Step 2: later area NUM — find intersection limits first. Step 3: integrate difference of functions; keep trig-equation NUM technique nearby for neighbouring items.

Why it feels hard

Classic Advanced join: geometry conditions feeding calculus numerics in the same paper.

What to practise

Any week you revise conics, end with one area-between-curves NUM.

Open 2023 year review →
Physics2023 · Paper 1 · Q8–Q10numerical

Modern Physics NUM + ray optics NUM chain

Modern Physics+Ray optics+Linked-style numericals

Knowledge bridge

Step 1: finish photoelectric/nuclear arithmetic cleanly. Step 2: switch to ray-optics formulae (mirror/lens/prism) without reusing constants wrongly. Step 3: track significant figures as required by the grid.

Why it feels hard

Formula-dense corridor; one wrong sign convention costs two questions.

What to practise

Keep a tiny optics sign-convention sticky note on your desk during NUM practice.

Open 2023 year review →
Chemistry2023 · Paper 1 · Q5–Q6single-correct

Electrochemistry + chemical equilibrium SC pair

Electrochemistry+Chemical equilibrium+Thermodynamic links

Knowledge bridge

Step 1: relate E_cell / Nernst quantities carefully. Step 2: on equilibrium, write K in terms of activities and compare options. Step 3: note shared thermo language (ΔG, K, E) across both stems.

Why it feels hard

Conceptual overlap tempts overthinking simple algebra.

What to practise

Drill ΔG° = −nFE° = −RT ln K until the three forms feel identical.

Open 2023 year review →
Mathematics2022 · Paper 1 · Q1–Q2numerical

Inverse trig NUM + trig equation NUM

Inverse trigonometry+Trigonometric equations+Numerical answers

Knowledge bridge

Step 1: reduce inverse-trig expressions with principal-value care. Step 2: solve the neighbouring trig equation in the stated interval. Step 3: enter integers carefully — range mistakes are common.

Why it feels hard

Heavy NUM opening stresses accuracy before you are warm.

What to practise

Start Math mocks with a 10-minute trig warm-up when the paper is NUM-heavy.

Open 2022 year review →
Physics2022 · Paper 1 · Q7numerical

EMI/AC numerical among mechanics NUMs

EMI/AC+Mechanics context switching+Numerical

Knowledge bridge

Step 1: isolate the electromagnetic law needed (flux/induced emf/impedance). Step 2: compute the asked scalar. Step 3: consciously leave rotation kinematics behind so constants are not mixed.

Why it feels hard

Topic island inside a Mechanics-heavy NUM sea.

What to practise

Underline the chapter keywords in each NUM stem before writing equations.

Open 2022 year review →
Chemistry2022 · Paper 1 · Q6–Q8numerical

Organic practical + named-reaction NUM burst

Organic practical/analysis+Named reactions+Physical mixed NUM nearby

Knowledge bridge

Step 1: decode practical/analysis data into a count or identification. Step 2: push named-reaction reagents to the major product / stoichiometric ask. Step 3: keep Physical mixed NUMs mentally separate so Organic logic is not diluted.

Why it feels hard

Organic numericals feel unfamiliar if you only practised MCQ mechanisms.

What to practise

Convert two named reactions per week into a numerical ask (moles, isomers, mass).

Open 2022 year review →
Mathematics2021 · Paper 1 · Q8–Q10linked-numerical

Straight-line linked numerical stem

Coordinate Geometry – Straight line+Linked numerical stems+Distance / intercept algebra

Knowledge bridge

Step 1: extract all shared geometric data from the paragraph once. Step 2: answer the first NUM (slope/intercept/distance). Step 3: reuse intermediates for the linked follow-ups without re-deriving from scratch.

Why it feels hard

Early example of Advanced’s linked-stem tax on organisation.

What to practise

Box shared quantities at the top of linked stems — treat them as a mini formula sheet.

Open 2021 year review →
Physics2021 · Paper 1 · Q6–Q9linked-numerical

Capacitance/field linked numerical chain

Electrostatics – Capacitance+Electric field+Linked numericals

Knowledge bridge

Step 1: draw the capacitor/field configuration and label charge/potential. Step 2: solve the first NUM for a base quantity (C, E, V). Step 3: propagate that value through linked asks (energy, force, series/parallel changes).

Why it feels hard

Long electrostatic chains amplify one early algebra mistake.

What to practise

In linked EM stems, verify units of the first answer before continuing.

Open 2021 year review →
Chemistry2021 · Paper 1 · Q5–Q9linked-numerical

Organic linked NUM + Physical thermo/mixed

Organic named/reactions (linked)+Physical thermodynamics+Metallurgy / mixed Physical

Knowledge bridge

Step 1: resolve the Organic linked numerical using reaction stoichiometry. Step 2: switch to thermo/mixed Physical NUMs with fresh variables. Step 3: keep metallurgy facts (if present) as recall, not calculation, items.

Why it feels hard

Branch switching inside one NUM section.

What to practise

Label each Chem NUM as Org/Phy/Inorg in the margin before solving.

Open 2021 year review →
Mathematics2020 · Paper 1 · Q3–Q4single-correct

Area calculus beside parabola geometry

Calculus – Area+Coordinate Geometry – Parabola+Single-correct pair

Knowledge bridge

Step 1: for the area item, find intersection limits and integrate. Step 2: for the parabola item, apply focus–directrix or tangent properties. Step 3: notice how often Advanced seats Calculus and Conics as neighbours — train that adjacency.

Why it feels hard

2020’s Calculus weight makes area items feel easy until limits are wrong.

What to practise

Always find limits from geometry before writing ∫.

Open 2020 year review →
Physics2020 · Paper 1 · Q2–Q4single-correct

Rotation triple in opening SC block

Rotation+Rigid body+Angular kinematics

Knowledge bridge

Step 1: assign I and axis for each stem independently. Step 2: use rolling/energy/torque as appropriate. Step 3: compare answers only after each FBD is complete — similarity is a trap.

Why it feels hard

Three rotation SCs in a row reward method, not memory of a single formula.

What to practise

Build a rotation checklist: axis → I → constraint → energy/torque.

Open 2020 year review →
Chemistry2020 · Paper 1 · Q16–Q17numerical

Physical mixed numerical pair

Physical – Mixed+Mole / gas / thermo blend+Numerical

Knowledge bridge

Step 1: parse which Physical sub-ideas are fused (mole + thermo, gas + equilibrium, etc.). Step 2: write governing equations for each piece. Step 3: combine numerically without dropping stoichiometric factors.

Why it feels hard

‘Mixed’ Physical tags mean the stem will not stay in one textbook chapter.

What to practise

Practise deliberately cross-chapter Physical sets (thermo×gases×equilibrium).

Open 2020 year review →