If the tangents on the ellipse 4x² + y² = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a² is equal to :

If $$f(x) = {{2 - x\cos x} \over {2 + x\cos x}}$$ and g(x) = log_ex, (x > 0) then the value of integral

$$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {g\left( {f\left( x \right)} \right)dx{\rm{ }}} $$ is

If S₁ and S₂ are respectively the sets of local minimum and local maximum points of the function,

ƒ(x) = 9x⁴ + 12x³ – 36x² + 25, x $$ \in $$ R, then :

Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of $$\Delta $$AOP is 4, is :