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Questions › DSE › DSE 2016 › Q18
0 marksMathematics › Vector spaces, rank and eigenvalues › Linear independence, span and basisVery Hardabout 4 min

DSE 2016 Question 18: Vector spaces, rank and eigenvalues

A school with nnn students has mmm clubs to which they can belong, and students are allowed to be members of multiple clubs. It is known that (I) Each club has an odd number of members (II) Every pair of clubs has an even number of common members (including 000). Then it must be that:

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A school with n students has m clubs to which they can belong, and students are allowed to be members of multiple clubs. It is known that (I) Each club has an odd number of members (II) Every pair of clubs has an even number of common members (including 0). Then it must be that: (A) m≥ n (B) m≤ n (C) m and n can each be larger than the other, but m≠ n (D) m=n

Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.

What this question tests

This question is on Linear independence, span and basis, part of Vector spaces, rank and eigenvalues in Mathematics.

Whether vectors depend on each other, what they span and when they form a basis.

TestStop has 13 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q20Let W be the subspace of ℝ³ spanned by (0, -1, 2) and (2, -1, 0). Which one of the following vectors lies in…
  • IIT JAM 2022 · Q6Let W be a subspace of a vector space ℝ³. Then which of the following sets of vectors forms a basis of W?
Practise Vector spaces, rank and eigenvaluesMore on Linear independence, span and basis

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Question from the DSE 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.