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Sets and Functions Preparation Hub

Master Sets and Functions with coaching-grade theory notes, verified video lectures, and 10 interactive MCQs with instant mistake analysis. Continue with 500+ adaptive questions inside the Exam Sprinter app.

πŸ“˜ Theory Notes✍️ Interactive Practice⏱️ CBT Simulator

What is Sets and Functions?

Sets and Functions covers the essential principles and concepts required for NDA.

πŸ’‘ Why Study Sets and Functions?

Highly important, frequently tested in NDA.

ParameterDetails / Relevance
Target ExamNDA
Subject CategoryMathematics
Estimated Study Duration10 Hours
Expected Questions2 Questions
Difficulty IndexHard
Interactive Solved MCQs10 Questions with AI Diagnostics
Adaptive App Practice500+ Questions & Real-Time AI Tutor

⚠️ Common Pitfalls to Avoid

  • Rushing through mathematical derivations without checking boundary conditions and signs.
  • Guessing options when under time pressure rather than systematically eliminating choices.
  • Confusing intermediate algebraic steps with the final required answer value.
βœ“ COACHING-GRADE CLASSROOM NOTES

Sets and Functions Theory & Derivations

Browse All Notes Library β€Ί

Access comprehensive classroom-grade derivations and NCERT micro-extracts for Sets and Functions. Features step-by-step proofs and standard assumptions.

Important Formulas & Cheat Sheet

✍️ STEP 3: PRACTICE & ANALYZE

Sets and Functions Interactive Practice

⏱️ Take Chapter CBT Test

Solve these 10 standard exam-level questions. The system tracks your response time, detects rapid guessing via Cognitive Reading Thresholds, and outputs your post-session diagnosis.

Interactive Practice Progress:0 / 10 Answered
Q1Sets & Operations
Expected: 90sMedium

Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?

Q2Relations & Functions
Expected: 90sMedium

If f(x) = 4x + 3, then what is f o f o f(-1) equal to?

Q3Composition of Functions
Expected: 90sMedium

What is f(Ο€4)f\left(\frac{\pi}{4}\right) equal to ?

Q4Sets & Operations
Expected: 90sMedium

Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if x2 - 5xy + 4y2 = 0 : 1. R is reflexive 2. R is symmetric 3. R is transitive Which of the above statements is /are correct ?

Q5Relations & Functions
Expected: 90sMedium

A, B, C and D are four sets such that A ∩\cap B = C ∩\cap D = Ο•\phi. Consider the following 1. A βˆͺ\cup C and B βˆͺ\cup D are always disjoint. 2. A ∩\cap and B ∩\cap D are always disjoint. Which of the above statements is/are correct?

Q6Composition of Functions
Expected: 90sMedium

Let R be a relation from A = {1, 2, 3, 4} to B= {1, 3, 5} such that R = {(a, b) : a βˆ’-1 equal to?

Q7Sets & Operations
Expected: 90sMedium

Let f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?

Q8Relations & Functions
Expected: 90sMedium

Let f(n)=[14+n1000]f(n) = \left[ {{1 \over 4} + {n \over {1000}}} \right], where [x] denote the integral part of x. Then the value of βˆ‘n=11000f(n)\sum\limits_{n = 1}^{1000} {f(n)} is

Q9Composition of Functions
Expected: 90sMedium

What is (1βˆ’x)f(x)+xf(x+1) (1-x)f(\sqrt{x})+xf(\sqrt{x}+1) equal to?

Q10Sets & Operations
Expected: 90sMedium

Which one of the following is correct in respect of f(x)=1∣xβˆ£βˆ’xf(x) = \frac{1}{\sqrt{|x| - x}} and g(x)=1xβˆ’βˆ£x∣g(x) = \frac{1}{\sqrt{x - |x|}}?

πŸ—ΊοΈ Recommended Learning Sequence

Probabilityβž”Sets and Functions (Current)βž”Complex Numbers

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