How many moles of hydrogen atoms are present in 20g ?
1g Hydrogen contains 1 mole hydrogen atom. Hence, 20g Hydrogen will contain 20 mole H-atom. Ans or, Since molar mass of H = 1g/mol Hence number of moles = mass/Molar Mass = 20/1 = 20 moles Ans
Is the function defined by f: R-> R f(x) = x-[x] differentiable ?
Let's check for continuity first. At integer points c=Z Left hand limit = x->c- Lim x-[x] = c-1 Right Hand limit - x->c+ lim x-[x] = c f(c) = c Since LHL is not equal to RHL, hence it is not continuos. For a function to be differentiable, it should be continuous first. Since this function is not continuous, hence it is not differentiable.
If y=x^2, then find the fractional error in the measurement of y given fractional error in measuring x is 10%.
Since y = x^2 => Dy/y = 2Dx/x Hence, Fractional error in y = Dy/y*100 = 2*10% = 20%