JEE Main 2005 Mathematics — Questions with Solutions

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…

If the angle θ between the line (x+1)/(1)=(y-1)/(2)=(z-2)/(2) and the plane 2 x-y+√(λ) z+4= 0 is such that θ=(1)/(3) th…

The plane x+2 y-z=4 cuts the sphere x²+y²+z²-x+z-2=0 in a circle of radius