Mathematics · 2025
JEE Main · 29 January 2025, Shift 2 · Q1
If the domain of the function log_5(18 x-x^2-77) is (α, β) and the domain of the function log_(x-1)((2 x^2+3 x-2)/(x^2-3 x-4)) is (γ, δ), then…
If the domain of the function $\displaystyle \log _5\left(18 x-x^2-77\right)$ is $\displaystyle (\alpha, \beta)$ and the domain of the function $\displaystyle \log _{(x-1)}\left(\frac{2 x^2+3 x-2}{x^2-3 x-4}\right)$ is $\displaystyle (\gamma, \delta)$, then $\displaystyle \alpha^2+\beta^2+\gamma^2$ is equal to:
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 186$
More from Relations and Functions
- Let for some α ∈ R, f: R → R be a function satisfying f(x+y)=f(x)+2 y^2+y+α x y for all x, y ∈ R. If f(0)=-1 and f(1)=2, then the value of…2026
- Consider two sets A={x ∈ Z:|(|x-3|-3)| ≤ 1} and B={x ∈ R-{1,2}: ((x-2)(x-4))/(x-1) log_e(|x-2|)=0}. Then the number of onto functions f: A → B is…2026
- Let f: R-{0} → R be a function such that f(x)-6 f(1/x)=35/(3 x)-5/2. If the lim_x → 0(1/(α x)+f(x))=β; α, β ∈ R, then α+2 β is equal to2025
- The function f:(-∞, ∞) →(-∞, 1), defined by f(x)=(2^x-2^-x)/(2^x+2^-x) is:2025
- Let f:[0,3] → A be defined by f(x)=2 x^3-15 x^2+36 x+7 and g:[0, ∞) → B be defined by g(x)=(x^2025)/(x^2025+1). If both the functions are onto and…2025
- The number of relations, defined on the set \{a, b, c, d\}, which are both reflexive and symmetric, is equal to:2026
- For the function f:[1, ∞) →[1, ∞) defined by f(x)=(x-1)^4+1, among the two statements: (I) The set S={x ∈[1, ∞): f(x)=f^-1(x)} contains exactly two…2026
- Let R={(x, y) ∈ N × N: log_e(x+y) ≤ 2}. Then the minimum number of elements, required to be added in R to make it a transitive relation, is ____.2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.