ISRO Scientist or Engineer Refrigeration & Air-Conditioning 2014

Hot steel sphere of diameter 40mm is immersed in oil. If the heat transfer coefficient between the sphereand oil is 300 W/sqm K , then Biot Number is:(Take $$k_{steel}$$ = 50 W/m K and $$k_{oil}$$ = 0.2 W/m K)

A metallic surface is maintained at 1000 K, the wavelength at which maximum spectral intensity occurs

Air at 293 is flowing with velocity of 3m/s over a heated flat square plate. Plate is 0.3 m wide and is maintained at 330 K. Average heat loss from the plate due to convection is (Take $$v = 16.768E-6 m^2/s, Pr = 0.7, k = 0.027 W/m K$$)

Twofluids A and B exchange heatin counterflow heat exchanger. Fluid A enters at 700 K and fluid B enters at 300 K. Mass flow rate of A & B is 1 kg/s. Specific heat of fluid A and B is 1000 J/kg K and 4000 J/kg K. Net Effectiveness of heat exchange is 75 %. Exit temperature of Fluid B is

If the following equations are consistent, then value of k is
4x - 3y + 1 = 0
kx - 8y + 10 = 0
x + y - 5 = 0

If $$\omega$$ and $$\omega^2$$ are cube roots of unity, then $$(2 - \omega + 2 \omega^2)(2 + 2 \omega - \omega^2)$$ is

Area of the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

find $$\lim_{x \rightarrow 0} \frac{1 - \cos x}{x^2}$$

Equation of the plane parallel to the x axis and passes through the point (4,6,2) and (4, -5, 3)

$$\overline{a}$$ and $$\overline{b}$$ are vectors such that $$2 \overline{a} - 4 \overline{b}$$ and $$10 \overline{a} + 8 \overline{b}$$ are perpendicular to each other. Angle between the vectors $$\overline{a}$$ and $$\overline{b}$$ is