JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023If the domain of the function f(x)=loge(4x2+11x+6)+sin−1(4x+3)+cos−1(310x+6) is (α,β], then 36∣α+β∣ is equal to:
Choose the correct answer:
- A.
72
- B.
63
- C.
45
(Correct Answer) - D.
54
45
Explanation
Solution:
Domain nikalne ke liye teeno conditions ko satisfy karna hoga:
-
log ke liye: 4x^2 + 11x + 6 > 0 \implies (4x+3)(x+2) > 0 \implies x \in (-\infty, -2) \cup (-3/4, \infty).
-
sin−1 ke liye: −1≤4x+3≤1⟹−4≤4x≤−2⟹x∈[−1,−1/2].
-
cos−1 ke liye: −1≤310x+6≤1⟹−3≤10x+6≤3⟹−9≤10x≤−3⟹x∈[−0.9,−0.3].
-
Teeno ka intersection lene par domain (−0.75,−0.5] aata hai.
-
Isliye α=−0.75 aur β=−0.5.
-
36∣α+β∣=36∣−0.75−0.5∣=36×1.25=45
Correct Option: (3)
Explanation
Solution:
Domain nikalne ke liye teeno conditions ko satisfy karna hoga:
-
log ke liye: 4x^2 + 11x + 6 > 0 \implies (4x+3)(x+2) > 0 \implies x \in (-\infty, -2) \cup (-3/4, \infty).
-
sin−1 ke liye: −1≤4x+3≤1⟹−4≤4x≤−2⟹x∈[−1,−1/2].
-
cos−1 ke liye: −1≤310x+6≤1⟹−3≤10x+6≤3⟹−9≤10x≤−3⟹x∈[−0.9,−0.3].
-
Teeno ka intersection lene par domain (−0.75,−0.5] aata hai.
-
Isliye α=−0.75 aur β=−0.5.
-
36∣α+β∣=36∣−0.75−0.5∣=36×1.25=45
Correct Option: (3)