If a₁ (> 0), a₂, a₃, a₄, a₅ are in a G.P., a₂ + a₄ = 2a₃ + 1 and 3a₂ + a₃ = 2a₄, then a₂ + a₄ + 2a₅ is equal to ___________.

The integral $${{24} \over \pi }\int_0^{\sqrt 2 } {{{(2 - {x^2})dx} \over {(2 + {x^2})\sqrt {4 + {x^4}} }}} $$ is equal to ____________.

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.

The dimension of mutual inductance is :