Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Mathematics
Chapter
Application of Derivatives

JEE Advanced 2007 · Paper 2 · Mathematics · Application of Derivatives

Let f(x)=(x^2-6 x+5)/(x^2-5 x+6) .

Let f(x)=x2−6x+5x2−5x+6f(x)=\frac{x^2-6 x+5}{x^2-5 x+6}. Let f(x)=(x^2-6 x+5)/(x^2-5 x+6) .

Options

  1. AA-p; B-q; C-q; D-p
  2. BA-r; B-s; C-q; D-r
  3. CA-s; B-p; C-q; D-p
  4. DA-r; B-q; C-p; D-r

Correct answer

A. A-p; B-q; C-q; D-p

Step-by-step solution

f(x)=(x−1)(x−5)(x−2)(x−3)\frac{(x-1)(x-5)}{(x-2)(x-3)}The graph of f(x)f(x) is shown <imgsrc="/api/proxy−image?url=https<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_advanced%252Fwvp0nANowQRUUqEKwDE04wK9eFTqRImRXTt4B2hjHOM.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2Fwvp0nANowQRUUqEKwDE04wK9eFTqRImRXTt4B2hjHOM.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2Fwvp0nANowQRUUqEKwDE04wK9eFTqRImRXTt4B2hjHOM.original.fullsize.png?alt=media"> \\ (A)If−1<x<1⇒0<f(x)<1If -1 \lt x \lt 1 \Rightarrow 0 \lt f(x) \lt 1 (B)If1<x<2⇒f(x)<0If 1 \lt x \lt 2 \Rightarrow f(x) \lt 0 (C)If3<x<5⇒f(x)<0If 3 \lt x \lt 5 \Rightarrow f(x) \lt 0 (D)Ifx>5⇒0<f(x)<1If x \gt 5 \Rightarrow 0 \lt f(x) \lt 1
Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the function f: (0, ∞) arrow (-∞, ∞) given by f(x) = x \, _e(x) - x + 1 . Then… JEE Advanced 2026Let P be the point on the parabola y = x^2 such that the slope of the tangent to the… JEE Advanced 2026Let f: ℝ arrow ℝ be a differentiable function such that f((x+y)/(3)) = (f(x) + f(y))/(3)… JEE Main 2026_ 0 ≤ x ≤ π (16 ((x)/(2)) ^3((x)/(2))) is equal to: JEE Main 2026Let f(x) be a polynomial of degree 5 , and have extrema at x = 1 and x = -1 . If _ x → 0… JEE Main 2026The number of critical points of the function f(x) = cases |( x)/(x)|, & x ≠ 0 1, & x = 0… JEE Main 2026Let f be a differentiable function satisfying f(x)=1-2 x+∫_ 0 ^ x e^ (x-t) f(t) dt, x ∈ R… JEE Main 2026Consider the following three statements for the function f:(0, ∞) arrow ℝ defined by… JEE Main 2026Let (2 α, α) be the largest interval in which the function f(t)= |t+1| t^ 2 , t 2 , is… JEE Main 2026Let f(x)=x^ 2025 -x^ 2000 , x ∈[0,1] and the minimum value of the function f(x) in the… JEE Main 2026Let f: ℝ → ℝ be a twice differentiable function such that f''(x) > 0 for all x ∈ ℝ and… JEE Main 2026Let f: R arrow R be a twice differentiable function such that the quadratic equation f(x)… JEE Main 2026Let ℝ denote the set of all real numbers. Define the function f: R arrow R by f(x)=\… JEE Advanced 2025Let ℝ denote the set of all real numbers. For a real number x , let [x] denote the… JEE Advanced 2025Let ℝ denote the set of all real numbers. Let f: ℝ arrow ℝ be defined by f(x)= cases (6… JEE Advanced 2025Let the function f(x)=(x)/(3)+(3)/(x)+3, x ≠ 0 be strictly increasing in (-∞, α_1) U(α_2… JEE Main 2025 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs