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Concept & Question of the Day

One short concept or multiple-choice question every day for B.Sc Mathematics students, with the answer and solution. Tap an option to check yourself.

Question of the Day 18 Oct 2026

Where does Rolle's theorem hold for f(x) = x² − 4x + 3 on [1, 3]?

4th SemesterReal Analysis-II

f(x) = x² − 4x + 3 is continuous on [1, 3], differentiable on (1, 3) and f(1) = f(3) = 0. Find the point c in (1, 3) given by Rolle's theorem.

Concept of the Day 17 Oct 2026

Rank–Nullity Theorem

3rd SemesterLinear Algebra

For a linear map T : V → W where V is finite-dimensional, dim V = rank(T) + nullity(T). Here rank(T) = dim of the range of T and nullity(T) = dim of the kernel of T.

Example

T : ℝ³ → ℝ², T(x, y, z) = (x, y). The range is all of ℝ², so rank = 2. The kernel is the z-axis {(0, 0, z)}, so nullity = 1. Check: 3 = 2 + 1.

Concept & Question of the Day

Where does Rolle's theorem hold for f(x) = x² − 4x + 3 on [1, 3]?

Solution

Rank–Nullity Theorem

Example

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