Statement (I) : The set of solutions of |x| 2 – 4|x| + 3 5 then x2 – 8x + 15 > 0. Which of the above statements is (are) true?

(A) Statement I is true, but Statement II is false

(C) Both Statement I and Statement II are true

(D) Both Statement I and Statement II are false

TS EAMCET · Maths · Basic of Mathematics

Statement (I) : The set of solutions of |x| 2 – 4|x| + 3 < 0 is the interval (–3, 3). Statement (II) : If x < 3 or x > 5 then x2 – 8x + 15 > 0. Which of the above statements is (are) true?

A Statement I is true, but Statement II is false
B Statement II is true, but Statement I is false
C Both Statement I and Statement II are true
D Both Statement I and Statement II are false

Verified Solution

Answer & Solution

Correct Answer

(B) Statement II is true, but Statement I is false

Step-by-step Solution

Detailed explanation

\(\mathrm{I} \rightarrow|\mathrm{x}|^2-4|\mathrm{x}|+3 5\) then it satisfy the given in equality \(\mathrm{x}^2-8 \mathrm{x}+15>0\) \(\Rightarrow\) Statement II \({ }^{\text {nd }}\) is correct.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app