Academia Aeternum
तमसो मा ज्योतिर्गमय
Wisdom · Knowledge · Eternity
MCQ Practice Arena
Decode Every Relation — Master One-One, Onto and Invertible Functions
Relations & Functions opens Class XII by extending Class XI groundwork into proof-style objective questions. CBSE boards frequently test equivalence relations and bijection proofs as assertion-reason MCQs, while JEE Main asks 1–2 direct questions on invertibility and composition every year. This bank mirrors that mix so you build both proof intuition and calculation speed.
Recall these cold before attempting MCQs — they appear in >70% of questions.
For relation MCQs, check all three properties one at a time and disprove with a single counterexample the moment one fails — don't verify every pair once you've found a break. For function-type questions, test one-one algebraically by assuming f(x₁)=f(x₂) and solving for x₁=x₂, and test onto by solving y=f(x) for x and confirming it lies in the domain. Invertibility MCQs almost always reduce to a bijectivity check first.
Work through each rung in order — do not jump to Hard before mastering Easy.
Identify relation properties from a given set, evaluate f(x) and gof(x)
Prove a relation is an equivalence relation, verify one-one/onto algebraically
Composition of piecewise functions, invertibility proofs with domain restrictions
JEE Main — equivalence classes and bijection counts; CBSE — assertion-reason proofs