CBSE 2026–27 Most Important Questions: Class 10 & 12 Mathematics, Science & English with Model Answers
CBSE 2026–27 Most Important Questions: Class 10 & 12 Mathematics, Science & English with Model Answers
This guide compiles the questions that appear most consistently in CBSE board exams, with model answers aligned to the CBSE marking scheme. Whether you are preparing for the 2026–27 board exams or looking for high-value practice material, this resource covers the topics and question formats that carry the most marks.
How This List Was Built
These questions were identified by analysing CBSE board papers from 2020 to 2026, official CBSE Sample Question Papers 2025–26, CBSE Marking Scheme documents, and chapters flagged as "high priority" in CBSE curriculum documents. Questions that appear in 3 or more of the last 6 years are included.
Class 10 Mathematics — Most Important Questions
Chapter: Real Numbers
Q: Prove that √2 is irrational.
Model Answer (3 marks):
Assume √2 is rational. Then √2 = p/q where p and q are integers with HCF(p, q) = 1.
Squaring: 2 = p²/q² → p² = 2q²
Therefore p² is even, which means p is even. Let p = 2m.
Then: (2m)² = 2q² → 4m² = 2q² → q² = 2m²
Therefore q² is even, which means q is even.
But this contradicts our assumption that HCF(p, q) = 1.
Therefore √2 is irrational. ∎
Examiner Note: 1 mark for the assumption, 1 mark for the contradictory deduction, 1 mark for the conclusion.
Q: Find the HCF and LCM of 96 and 120 using the prime factorisation method.
Model Answer (3 marks):
96 = 2⁵ × 3
120 = 2³ × 3 × 5
HCF = 2³ × 3 = 24
LCM = 2⁵ × 3 × 5 = 480
Verification: HCF × LCM = 24 × 480 = 11520 = 96 × 120 ✓
Chapter: Triangles
Q: State and prove the Basic Proportionality Theorem (Thales' Theorem).
Model Answer (5 marks):
Statement: If a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides them in the same ratio.
Given: In △ABC, DE ∥ BC where D is on AB and E is on AC.
To Prove: AD/DB = AE/EC
Construction: Draw DM ⊥ AC and EN ⊥ AB. Join BE and CD.
Proof:
ar(△ADE) / ar(△BDE) = AD/DB ... (i)
ar(△ADE) / ar(△CDE) = AE/EC ... (ii)
Since △BDE and △CDE are on the same base DE and between the same parallels DE and BC:
ar(△BDE) = ar(△CDE) ... (iii)
From (i), (ii), and (iii): AD/DB = AE/EC ∎
Chapter: Quadratic Equations
Q: A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream. Find the speed of the stream.
Model Answer (4 marks):
Let speed of stream = x km/h
24/(18 − x) − 24/(18 + x) = 1
24(18 + x) − 24(18 − x) = (18 − x)(18 + x)
48x = 324 − x²
x² + 48x − 324 = 0 → (x + 54)(x − 6) = 0
Speed of the stream = 6 km/h
Chapter: Statistics
Q: Find the mean daily wage from the following distribution of 50 workers:
| Daily Wages (₹) | Workers |
|---|---|
| 100–120 | 12 |
| 120–140 | 14 |
| 140–160 | 8 |
| 160–180 | 6 |
| 180–200 | 10 |
Model Answer (3 marks):
Mean = Σfi × xi / Σfi = 7260 / 50 = ₹145.20
(xi values: 110, 130, 150, 170, 190; fi × xi: 1320, 1820, 1200, 1020, 1900; Total: 7260)
Chapter: Circles
Q: Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Model Answer (4 marks):
Given: Circle with centre O, tangent AB at point P.
Proof: For any point Q on AB other than P, OQ > OR = OP (where R is on the circle). Therefore OP is the shortest distance from O to AB. The shortest distance from a point to a line is perpendicular.
Therefore OP ⊥ AB ∎
Class 10 Science — Most Important Questions
Biology: Life Processes
Q: Draw a well-labelled diagram of the human excretory system and explain the process of urine formation.
Model Answer (5 marks):
*(Labelled diagram: Kidneys, ureters, urinary bladder, urethra — 2 marks)*
Urine Formation:
1. Glomerular Filtration: Blood is filtered under pressure in the glomerulus. Water, glucose, amino acids, urea, salts pass into Bowman's capsule. Primary urine: ~180 L/day.
2. Selective Reabsorption: Useful substances (glucose, amino acids, water, salts) are reabsorbed back into blood. Volume reduces to ~1.5–2 L/day.
3. Tubular Secretion: Additional waste (excess ions) secreted from blood into the filtrate.
Concentrated filtrate passes: collecting duct → renal pelvis → ureter → urinary bladder → urethra.
Chemistry: Chemical Reactions
Q: What is a displacement reaction? Give one example and contrast with double displacement.
Model Answer (3 marks):
A more reactive element displaces a less reactive element from its compound.
Example: Fe + CuSO₄ → FeSO₄ + Cu
Difference: Displacement — one element replaces another. Double displacement — two compounds exchange ions (e.g., NaCl + AgNO₃ → AgCl↓ + NaNO₃).
Physics: Electricity
Q: Three resistors of 2Ω, 3Ω, and 6Ω are connected in parallel to a 6V battery. Find: (a) total resistance, (b) total current, (c) current through each resistor.
Model Answer (5 marks):
(a) 1/R = 1/2 + 1/3 + 1/6 = 1 → R = 1Ω
(b) I = V/R = 6/1 = 6 A
(c) I₁ = 6/2 = 3 A; I₂ = 6/3 = 2 A; I₃ = 6/6 = 1 A ✓
Class 12 Mathematics — Most Important Questions
Calculus: Derivatives
Q: Find the maximum and minimum values of f(x) = 2x³ − 15x² + 36x + 10.
Model Answer (5 marks):
f'(x) = 6x² − 30x + 36 = 6(x − 2)(x − 3)
Critical points: x = 2, x = 3
f''(x) = 12x − 30
At x = 2: f''(2) = −6 < 0 → Local Maximum = 38
At x = 3: f''(3) = 6 > 0 → Local Minimum = 37
Integrals
Q: Evaluate ∫(x + 1)/√(2x + 1) dx.
Model Answer (4 marks):
Let 2x + 1 = t² → dx = t dt, x + 1 = (t² + 1)/2
∫ = (1/2)∫(t² + 1) dt = t³/6 + t/2 + C
= (2x + 1)^(3/2)/6 + √(2x + 1)/2 + C
Probability
Q: P(A) = 0.4, P(B) = 0.6, A and B independent. Find P(A∩B), P(A∪B), P(A|B).
Model Answer (3 marks):
P(A∩B) = 0.4 × 0.6 = 0.24
P(A∪B) = 0.4 + 0.6 − 0.24 = 0.76
P(A|B) = 0.24/0.6 = 0.4 *(equals P(A) since independent)*
Class 12 Physics — Most Important Questions
Electrostatics
Q: State Gauss's Law and derive the electric field due to an infinitely long charged wire.
Model Answer (5 marks):
Gauss's Law: ∮ E⃗ · dA⃗ = Q_enclosed / ε₀
Derivation: Cylindrical Gaussian surface of radius r, length L. By symmetry, field is radial with uniform magnitude on curved surface.
E × 2πrL = λL/ε₀
E = λ/(2πε₀r) (field decreases as 1/r)
Electromagnetic Induction
Q: State Faraday's Laws. A 100-turn coil in a field changing from 0.2 T to 0.8 T in 0.5 s (area = 0.04 m²). Find induced EMF.
Model Answer (4 marks):
Faraday's First Law: Change in flux induces EMF.
Faraday's Second Law: e = −N × dΦ/dt
ΔΦ = (0.8 − 0.2) × 0.04 = 0.024 Wb
EMF = 100 × 0.024/0.5 = 4.8 V
Class 12 Chemistry — Most Important Questions
Electrochemistry
Q: Define standard electrode potential. Calculate EMF of cell: Zn|Zn²⁺(0.1M)||Cu²⁺(0.01M)|Cu. E°(Zn²⁺/Zn) = −0.76V, E°(Cu²⁺/Cu) = +0.34V.
Model Answer (5 marks):
E°cell = E°cathode − E°anode = +0.34 − (−0.76) = +1.10 V
Using Nernst equation (n = 2):
E = 1.10 − (0.0591/2) × log(0.1/0.01) = 1.10 − 0.02955 = 1.07 V
Class 12 English — Model Answer Templates
Formal Complaint Letter
Q: Write a formal letter to the Municipal Commissioner about poor road conditions in your locality.
12 Lakeview Road, Pune – 411001
June 3, 2026
The Municipal Commissioner, Pune Municipal Corporation
Subject: Complaint Regarding Dilapidated Road Condition in Lakeview Area
Dear Sir/Madam,
I am writing to bring to your urgent attention the severely deteriorated condition of roads in the Lakeview area. Despite repeated complaints over the past six months, no remedial action has been taken.
The roads are riddled with large potholes that have caused accidents. During monsoon, waterlogging compounds the problem significantly.
I sincerely request that an inspection team be deputed at the earliest and repair work commenced before the onset of the monsoon season.
Yours faithfully, Arjun
Article Writing
Q: Write an article (150–200 words) on "The Role of Technology in Modern Education."
The Role of Technology in Modern Education
*By a Student, Class XII*
Technology has redefined the boundaries of learning in the twenty-first century. What once required physical libraries can now be accessed from a smartphone — transforming education into a continuous, global process.
Digital platforms offer personalised learning pathways, allowing students to progress at their own pace. Interactive simulations bring abstract concepts in Physics and Chemistry to life. AI-powered tools identify knowledge gaps and tailor practice accordingly.
However, technology is a tool, not a teacher. Over-reliance on screens can diminish critical thinking and reduce meaningful human interaction. Students who use technology purposefully — for research, practice, and collaboration — benefit most.
The future of education lies in balance: embracing digital tools while preserving the depth and rigour of traditional learning. Schools that achieve this balance will produce graduates who are not only digitally fluent but genuinely educated.
*(Word count: ~155)*
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