ISRO Scientist or Engineer Refrigeration & Air-Conditioning 2013

A composite slab has twolayers of different materials with thermal conductivities $$k_1$$ and $$k_2$$. If each layer has the same thickness , then the equivalent thermal conductivity of the slab will be

The period of the function $$\cos 3x + \sin 6x$$ is:

If $$Y = \frac{(2^x - 1)}{x^{\frac{1}{2}}}$$ then $$\lim_{x \rightarrow 0} Y$$ is:

Degree and Order of the following differential equation are:
$$\sqrt{\left\{\left[1 + \left(\frac{dy}{dx}\right)^2\right]^3\right\}} = \left[\frac{d^2y}{dx^2}\right]$$

The straight line perpendicular to the line $$-2x + 3y + 4 = 0$$ is:

The maximum value of $$f(x) = \frac{(\log x)}{(x)}$$ is $$\frac{1}{e}$$ at:

If $$y = \sec^{-1} \left[\frac{(x + 1)}{(x - 1)}\right] + \sin^{-1} \left[\frac{(x - 1)}{(x + 1)}\right]$$ then $$\left(\frac{dy}{dx}\right)$$ is equal to:

A small disc shaped earth Satellite, 1 m in diameter circles the earth at a distance of 300 km from the surface. The flat surface of the disc (with emissivity 0.3 and temperature (-) $$18^\circ C$$ is oriented tangential to the earth’s surface with view factor of 0.91. Average Earth temperature is $$~ 27^\circ C$$ while surrounding of satellite is 0 K. Net rate at which energy is leaving satellite is

Consider the following two processes:
(A). A heat source at 1200K loses 2500kJ of heat to sink at 800K
(B). A heat source at 800K loses 2000k) of heat to sink at SOOK
Which of the following statements is TRUE?

A fin has omm diameter and 100mm length. The thermal conductivity of fin material is 400 W m$$^{-1}$$ K$$^{-1}$$. One end of the fin is maintained at $$130^\circ C$$ and its remaining surface is exposed to ambient air at $$30^\circ C$$. if the convective heat transfer coefficient is 40 Wm$$^{-2}$$K$$^{-1}$$ the heat loss (in W) from the fin is