Verified Solution • 2025–26 Session moderate

QJEEM20Mab1fd: JEE Main 2020 Mathematics - Class 11 JEEM20Mab1fd Solution: Consider the two sets : A = {m ∈ R : both the roots of x 2 – (m …

Consider the two sets :
A = {m ∈ R : both the roots of
x2 – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?

Multiple Choice Options

  • A A ∩ B = {–3}
  • B B – A = (–3, 5)
  • C A ∪ B = R
  • D A - B = (−∝, −3) ∪ (5, ∝)

Step-by-Step Verified Solution

As roots are real so, D≥0

(m+1)2−4(m+4)≥0

⇒m2−2m−15≥0

⇒ (m−5)(m+3)≥0

m∈(−∝, −3] ∪ [5, ∝)

A=(−∝, −3] ∪ [5, ∝)

Given B = [−3, 5)

Now, let's examine the options.

Option A : A ∩ B = {–3} The intersection of sets A and B would be the set of elements common to both sets. In this case, the only common element is -3. So, option A is true.

Option B : B – A = (–3, 5) The subtraction (or difference) of sets A from B is the set of elements that are in B but not in A. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting A from B would leave an open interval (-3, 5), not including -3 and 5. So, option B is also true.

Option C : A ∪ B = R The union of sets A and B is the set of elements that are in A, or B, or both. Here, A U B would cover all real numbers. So, option C is true.

Option D : A - B = (-∞, -3) ∪ (5, ∞) The subtraction (or difference) of set B from A is the set of elements that are in A but not in B. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting B from A would leave (-∞, -3) U [5, ∞), not including -3 and 5. But according to the convention for writing intervals, it should be (-∞, -3) U (5, ∞). So, option D is not true.

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