Matching exercise choose the correct one out of the alternatives $$A, B, C, D$$

Group $$-$$ $${\rm I}$$
$$P.$$ $${2^{nd}}$$ order differential equations
$$Q.$$ Non-linear algebraic equations
$$R.$$ Linear algebraic equations
$$S.$$ Numerical integration

Group $$-$$ $${\rm II}$$
$$(1)$$ Runge $$-$$ Kutta method
$$(2)$$ Newton $$-$$ Raphson method
$$(3)$$ Gauss Elimination
$$(4)$$ Simpson's Rule

A long glass cylinder of inner diameter $$=0.03m$$ and outer diameter $$=0.05m$$ carries hot fluid inside. If the thermal conductivity of glass $$=1.05$$ $$W/mK,$$ the thermal resistance $$(K/W)$$ per unit length of the cylinder is

The $$DC$$ power source for arc welding has the characteristic $$3V + 1 = 240,$$ where $$V=$$ Voltage and $${\rm I}\,\, = $$ current in amp. For maximum arc power at the electrode, voltage should be set at

In an orthogonal cutting test, the following observations were made
Cutting force $$=1200N ;$$ Thrust force $$=500N$$
Tool rake angle $$=zero ;$$ Cutting speed $$=1$$ $$m/s,$$
Depth of cut $$=0.8mm;$$
Chip thickness $$=1.5$$ $$mm$$

Friction angle during machining will be