An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If $$\mu$$ is the average marks of girls and $$\sigma$$² is the variance of marks of 50 candidates, then $$\mu$$ + $$\sigma$$² is equal to ________________.

If $$\int {{{2{e^x} + 3{e^{ - x}}} \over {4{e^x} + 7{e^{ - x}}}}dx = {1 \over {14}}(ux + v{{\log }_e}(4{e^x} + 7{e^{ - x}})) + C} $$, where C is a constant of integration, then u + v is equal to _____________.

Curved surfaces of a plano-convex lens of refractive index $$\mu$$₁ and a plano-concave lens of refractive index $$\mu$$₂ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s²)