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JEE Advanced Paper 1 2024 Paper

SECTION 2

• This section contains THREE (03) questions.
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s).

Question : 7

Total: 51

Let ℝ3 denote the three-dimensional space. Take two points P=(1,2,3) and Q=(4,2,7). Let dist(X,Y) denote the distance between two points X and Y in ℝ3. Let
S={X∈ℝ3:(dist(X,P))2−(dist(X,Q))2=50} and
T={Y∈ℝ3:(dist(Y,Q))2−(dist(Y,P))2=50}.
Then which of the following statements is (are) TRUE?

There is a triangle whose area is 1 and all of whose vertices are from S.
There are two distinct points L and M in T such that each point on the line segment LM is also in T.
There are infinitely many rectangles of perimeter 48 , two of whose vertices are from S and the other two vertices are from T.
There is a square of perimeter 48 , two of whose vertices are from S and the other two vertices are from T.

Validate

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