The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is

If $$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4$$, then $$\frac{d y}{d x}=$$

If $$x \cos \theta+y \sin \theta=5, x \sin \theta-y \cos \theta=3$$, then the value of $$x^2+y^2=$$

The area of the region bounded by the curve $$y=4 x^3-6 x^2+4 x+1$$ and the lines $$x=1, x=5$$ and $$X$$-axis is