JEE Main 2025 PYQ: f(x) satisfies f(x)+6f(1/x)=35/(3x)-7/2. If lim(x→0)[1/(αx)+f(x)] exists finitely and equals β, find α-2β by first solving for f(x).
JEE Main 2021 PYQ: for f(x)=5^x/(5^x+5), find the sum f(1/20)+f(2/20)+…+f(39/20) using the pairing identity f(x)+f(2-x)=1.
Find the range [a,b] of f(x)=1/(2+sin3x+cos3x), then find α/β where α, β are the AM and GM of a and b, using the fact that sin3x+cos3x ranges over [−√2,√2].
Consider f:R→R defined by f(x)=2x/√(1+9x²). If (f∘f∘⋯∘f, 10 times)(x)=2^10x/√(1+9αx²), find the value of √(3α+1).
If the domain of log5(18x−x²−77) is (α,β) and the domain of log(x−1)[(2x²+3x−2)/(x²−3x−4)] is (γ,δ), then α²+β²+γ² is: A)195 B)179 C)186 D)174.