CSIR NET Part C
One statement at a time
Part C looks like a multiple-choice question, but it is really four separate true/false calls — and the marking scheme gives you nothing unless every one of them is right. So practise them the way they are actually marked. When you slip, you get the counterexample and, more usefully, the kind of mistake it was.
No account needed. Press T or F to answer, ↵ to continue.
Drilling Standard counterexample only — drill everything instead
The mistakes it is testing for
Every statement here is built on one of these 13 reasoning slips. Getting one wrong tells you which — that is the whole point of drilling statements rather than whole questions.
- Execution slip — The idea was right. The computation was not.
- Hypothesis dropped — A theorem applied without checking one of its preconditions.
- Boundary and endpoint — The statement turns at the edge of the interval, the domain, or the parameter range.
- Standard counterexample — There is a canonical object that settles this. Recognising it is the whole question.
- Converse assumed — The theorem runs one way. You used it in the other.
- Invariants don't determine — Two objects sharing an invariant were treated as the same object.
- Limit assumed to exist — Reasoning with a limit before establishing there is one. limsup is not lim.
- Property not inherited — A property assumed to pass to subobjects, quotients, or through a chain. It does not.
- Pointwise vs uniform — The mode of convergence — or of continuity — was the wrong one.
- Base field or ring — The answer changes with the field or ring you are working over.
- Dependence misread — Independence, pairwise vs mutual, or correlation vs dependence.
- Moments and tails — A moment assumed to exist, or tail behaviour assumed to be tame.
- Existence vs uniqueness — A theorem giving one was read as giving both.