Summary of "CUET Maths 2026 PYQ | Top 100 Most Important Previous Year Questions | CUET Science Preparation"

Overview

This was a live-class revision (Part 2) covering the remaining ~50 of the top ~100 previous-year MCQs for CUET Maths. The session focused on rapid problem-solving, common PYQ question types, and exam strategy. Part 1 covered the first set of questions.

Topics covered

Representative list of topics discussed in the class:

Limits, continuity and points of discontinuity (including piecewise definitions and modulus/absolute-value functions)
Differentiability and derivatives:
- First and second derivatives; chain rule; product/quotient rules
- Examples with trigonometric, exponential and logarithmic functions
Tests for increasing/decreasing using f′(x) and completing the square
Graph ideas: V-shaped graphs (|x|), even/odd functions, sign of derivatives from graphs
Integrals and definite integrals:
- Standard forms and identities (e.g., cos²x = (1 + cos2x)/2)
- Symmetry arguments (odd/even functions over [-a, a])
- Integrals involving modulus (split domain at breakpoints)
- Area under curves and area between curves; switching to dy when convenient
- Basic substitution and evaluation tricks
Applications: rate of change (e.g., area of circle w.r.t radius), volume of sphere/balloon with variable diameter
Coordinate geometry and vectors:
- Dot product, cross product, unit vectors, direction cosines, projections
Differential equations:
- Order and degree, linear vs non-linear classification
- Integrating factor method for first-order linear ODEs; separation of variables
Linear programming (LPP): feasible region sketching, corner points and objective evaluation
Basic probability: conditional probability P(A|B) = P(A ∩ B)/P(B), independence, complements
Quick exam-oriented problem types: modulus integrals, definite integrals with substitution, area between curves, vector algebra and projection, LPP corner evaluation

Methodologies / Step-by-step procedures

Key procedures and techniques emphasized in the class:

Checking continuity for piecewise functions

Identify potential breakpoints from the piecewise definition.
Compute left-hand limit (LHL) and right-hand limit (RHL) at the point.
Evaluate f at the point (if defined).
If LHL = RHL = f(point) → continuous; otherwise mark as a point of discontinuity.

Handling modulus (|·|) in integrals and expressions

Find points where the inside of |·| changes sign.
Split the integral/expression into intervals determined by those points.
Replace |expression| with its ± form on each interval and integrate piecewise.
Sum the results across intervals.

Determining increasing / decreasing intervals

Compute f′(x).
Solve f′(x) > 0 for increasing regions, f′(x) < 0 for decreasing.
For quadratics/polynomials, use completing the square to determine sign of f′(x).
For trigonometric derivatives, consider critical points where derivative = 0 or undefined within the interval.

Finding second derivatives (example with chain rule)

Apply chain rule and product rule stepwise: differentiate inner functions, then outer functions.
For d²y/dx², differentiate y′ carefully and simplify, keeping track of products and nested chains.

Definite integrals using identities or symmetry

Use trig identities to simplify integrands (e.g., cos²x → (1 + cos2x)/2).
For integrals from −a to a: odd integrand → 0; even integrand → 2·∫0^a.
Use substitutions like x → a − x or x → 1 − x to exploit symmetry (e.g., ∫ f(x) + f(1 − x)).

Area between curves

Sketch or determine intersection points.
Use vertical slices: ∫(top − bottom) dx between x-limits.
If symmetry or convenience dictates, use horizontal slices: ∫ x dy and multiply by 2 if symmetric.

Volume and rate problems

Express radius r from diameter or given relation.
Use V = (4/3)π r³ for spheres; differentiate to get dV/dt or dV/dx using chain rule.

Vectors

Dot product: a · b = ax bx + ay by + az bz.
Magnitude: |a| = sqrt(sum of squares).
Unit vector: â = a / |a|.
Vector of magnitude m in direction of a: m · (a / |a|).
Cross product yields a vector perpendicular to two given vectors (direction ratios).
Projection formulas: scalar projection (a·b)/|b| and vector projection ( (a·b)/|b|^2 ) b.

Solving first-order linear ODEs

Write in standard form: dy/dx + P(x) y = Q(x).
Integrating factor: IF = e^{∫P(x) dx}.
Multiply equation by IF, integrate both sides, then apply initial condition to find constant.

LPP (linear programming) strategy

Sketch the feasible region from inequalities (careful with quadrant restrictions).
Identify corner points (vertices) of the feasible region.
Evaluate the objective function at each corner point; extrema occur at vertices.
Note bounded vs unbounded feasible regions and exam-specific section rules (core vs applied).

Exam & study practical instructions and tips

Use the Careers Adda app:
- Install via the link in the video description.
- Download PPTs/PDFs from the class (instructor provides PDFs on the app).
- Take teacher-recommended mock tests on the app to simulate exam conditions, identify weak areas, and observe negative-marking effects.
- Coupon code NS10 for discounts on Pratigya 2.0 / Pratigya Plus 2.0 courses.
CUET paper attempt strategy:
- Attempt Questions 1–15 (Section A) — all students must attempt these.
- Verify whether your paper is Core or Applied (B1 / B2 labels) and attempt the appropriate section accordingly.
Practice approach:
- Regularly solve PYQs and timed mock tests to build speed and accuracy.
- For modulus/piecewise problems, sketch a small number line to determine subinterval forms before integrating or taking limits.
- For continuity/differentiability problems, explicitly compute LHL, RHL and f(point) at suspect points.
Additional logistics:
- Join the teacher’s Telegram channel and Google Meet sessions for doubt-clearing.
- Watch Part 1 PDF (available on the app) if you missed the first class.

Tip: In modulus problems watch the sign carefully when splitting intervals; common mistakes are wrong signs or forgetting to split at all breakpoints.

Examples / notable problem-types demonstrated

Continuity of piecewise functions at specified points (e.g., find a − b using equality of LHL and RHL).
Monotonicity intervals by factorizing derivatives and completing the square.
Differentiation of y = ln(sin(x²/3 − 1)) and computing the second derivative.
Definite integrals involving |x − a| with breakpoints at 1, 2, 4 — evaluate piecewise.
Area between parabola y = x² and line y = 4 (use symmetry; integrate in x or y).
Volume rate for a balloon whose diameter varies linearly with x.
Vector cross product to find direction ratios perpendicular to two lines.
LPP corner-point evaluation for objective function maxima/minima.
Probability questions involving P(A ∩ B), conditional probability P(A|B), and complements.

Classroom style and other notes

Interactive class: students submitted answers in chat; presenter corrected mistakes and encouraged participation.
Strong emphasis on aiming high (full marks in math) through persistent practice.
Repeated recommendation to take mock tests and consider structured paid/free batches (Pratigya courses).
Instructor highlighted common pitfalls: wrong sign when splitting modulus intervals, forgetting symmetry, and mixing up core/applied sections on the paper.

Speakers / sources

Presenter: Neha — Math educator (Science Adda channel)
Platforms referenced: Science Adda (YouTube livestream), Careers Adda app (PPTs, PDFs, mock tests), Pratigya 2.0 / Pratigya Plus (paid course references)
Chat participants (examples, listed as participants not speakers): Saksham, Sukhman (Sukhman Gill), Ramesh, Kaushik, Manoj, Dharmendra, Satyam, Soham, Shreya, Bhumi, Anjali, Priyanshu, Samarth, Rani, Aditya, Deeksha, Akshay, Pragati, Movies Max, Tech Insta, Boss, Geetanjali, Manik, Ujjwal, Jaspreet, Kuldeep, Ranjan, and many others.

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