8 JEE Main 2005 Application of Derivatives previous-year questions with verified answers and step-by-step solutions.
These are the JEE Main 2005 previous-year questions from the Application of Derivatives chapter of Mathematics. Each links to a full solution with a verified answer key. To see the whole chapter across all years, visit the Application of Derivatives chapter hub.
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is…
Let f be differentiable for all x. If f(1)=-2 and fⁱme(x) ≥ 2 for x [1,6], then
Area of the greatest rectangle that can be inscribed in the ellipse (x²)/(a²)+(y²)/(b²)=1 is
A spherical iron ball 10 ~cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 ~c…
If x is so small that x³ and higher powers of x may be neglected, then (1+x)³ / ²- (1+(1)/(2) x )³(1-x)¹ / ²
The normal to the curve x=a( θ+θ θ), y=a( θ-θ θ) at any point ' θ ' is such that
If f is a real-valued differentiable function satisfying |f(x)-f(y)| ≤(x-y)², x, y R and f(0)=0, then f(1) equals
If the equation an xⁿ+an₋₁ xⁿ⁻¹+… …+a₁ x=0, a₁ ≠ 0, n ≥ 2, has a positive root x=α, then the equation n an xⁿ⁻¹+(n-1) a…