Corrosion of pure iron takes place in an acidic electrolyte by forming \( {Fe}^{2+} \) ions at ambient condition. The corrosion current density is measured to be \( 2 \times 10^{-4} \, {A cm}^{-2} \). The corrosion rate (in mm per year) of iron is (rounded off to one decimal place) ............
An aluminum transmission line of 7 km length is designed to carry 100 A current with no more than 2 MW power loss. The required minimum diameter (in mm) of the transmission line is (rounded to the two decimal places) ...........
On applying 10 V across the two ends of a 100 cm long copper wire, the average drift velocity (in cm s\(^{-1}\)) in the wire is (rounded off to two decimal places).............
For a pure element with a BCC crystal structure, the surface energies per unit area of \( \{100\} \) and \( \{110\} \) free surfaces are \( S_{100} \) and \( S_{110} \), respectively. The ratio, \( \frac{S_{100}}{S_{110}} \), is (rounded off to one decimal place):
A diffraction pattern is obtained from a powdered sample of a pure element, which has FCC crystal structure. If \( x \) and \( y \) are the Bragg angles of the first and the third peaks, respectively, then the ratio, \( \frac{\sin y}{\sin x} \), is (rounded off to one decimal place)...........
Let \( f(x) = x^3 - \frac{9}{2}x^2 + 6x - 2 \) be a function defined on the closed interval [0, 3]. Then, the global maximum value of \( f(x) \) is _______
Given that the value of the integral \[ \int_1^9 (x^2 - 2)\, dx \] calculated using the Simpson's 1/3 rule with four uniform subintervals over the interval [1,9] is given by \[ f(1) + \alpha^2 + \frac{8}{3}, \] then the possible value of \( \alpha \) is _______
If the system of linear equations $x + 2y + z = 5, 2x + \lambda y + 4z = 12, 4x + 8y + 12z = 2\mu$ have infinite number of solutions, then the values of $\lambda$ and $\mu$ are ________?