यदि दो ग्रहों की त्रिज्याएँ `r_(1)` तथा `r_(2)` व घनत्व `d_(1)` और `d_(2)`, तथा गुरुत्वीय त्वरण `g_(1)` और `g_(2)` हों, तो सिद्ध कीजिए कि -
`(g_(1))/(g_(2))=(r_(1)d_(1))/(r_(2)d_(2))`

The Graham's law states that ''at constant pressure and temperature the rate of diffusion or effusion of a gas is inversely proportional to the squar root of its density Rate of diffusion prop (1)/(sqrt(d)) If r_(1) and r_(2) represent the rates of diffusion of two gases and d_(1) and d_(2) are their respective densities, then r_(1)/(r_(2))=sqrt((d_(2))/(d_(1))) r_(1)/(r_(2)) =sqrt((M_(2))/(M_(1))) xx P_(1)/(P_(2)) (V_(1)xxt_(2))/(V_(2)xxt_(1)) = sqrt((d_(2))/(d_(1))) = sqrt((M_(2))/(M_(1))) V prop n (where n is no of moles) V_(1) prop n_(1) and V_(2) prop n_(2) If some moles of O_(2) diffuse in 18 sec and same moles of other gas diffuse in 45sec then what is the molecular weight of the unknown gas ? .

The Graham's law states that ''at constant pressure and temperature the rate of diffusion or effusion of a gas is inversely proportional to the squar root of its density Rate of diffusion prop (1)/(sqrt(d)) If r_(1) and r_(2) represent the rates of diffusion of two gases and d_(1) and d_(2) are their respective densities, then r_(1)/(r_(2))=sqrt((d_(2))/(d_(1))) r_(1)/(r_(2)) =sqrt((M_(2))/(M_(1))) xx P_(1)/(P_(2)) (V_(1)xxt_(2))/(V_(2)xxt_(1)) = sqrt((d_(2))/(d_(1))) = sqrt((M_(2))/(M_(1))) V prop n (where n is no of moles) V_(1) prop n_(1) and V_(2) prop n_(2) Helium and argon monoatomic gases and their atomic weights are 4 and 40 respectively Under identical conditions helium will diffuse through a semipermeable membrane .

The Graham's law states that ''at constant pressure and temperature the rate of diffusion or effusion of a gas is inversely proportional to the squar root of its density Rate of diffusion prop (1)/(sqrt(d)) If r_(1) and r_(2) represent the rates of diffusion of two gases and d_(1) and d_(2) are their respective densities, then r_(1)/(r_(2))=sqrt((d_(2))/(d_(1))) r_(1)/(r_(2)) =sqrt((M_(2))/(M_(1))) xx P_(1)/(P_(2)) (V_(1)xxt_(2))/(V_(2)xxt_(1)) = sqrt((d_(2))/(d_(1))) = sqrt((M_(2))/(M_(1))) V prop n (where n is no of moles) V_(1) prop n_(1) and V_(2) prop n_(2) 2 g of hydrogen diffuse from a container in 10 minutes How many grams of oxygen would diffuse through the same container in the same time under similar conditions ? .

Prove that the area of the triangle with vertices (p,q),(x_(1),y_(1)) and (x_(2),y_(2)) where p,x_(1),x_(2) are in G.P. with common ratio r_(1) and q, y_(1), y_(2) and in G.P with common ratio r_(2) is (1)/(2) pq(r_(1)-1) (r_(2)-1) (r_(2)-r_(1)) sq unit.

If the circle S_(1)=0,S_(2)=0i.e,g_(1),f_(1),c_(1) and g_(2),f_(2),c_(2) touch each other than prove that [2g_(1)g_(2)+2f_(1)f_(2)-[c_(1)+c_(2))]^(2)=4r^(2)r_(1)^(2), where r_(1),r_(2) are the radia of the two circles.

If f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3 are polynomials in x such that f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3 and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| then F'(x) at x = a is ..... .

If f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3 are polynomials in x such that f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3 and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| then F'(x) at x = a is ..... .

There circle C_1,C_2 and C_3 with radii r_1 , r_2 and r_3 (where r_1 तीन वृत्त C_1,C_2 तथा C_3 जिनको त्रिज्याएँ r_1 , r_2 तथा r_3 है, (जहाँ r_1

If D_(r)=|(r,x,n(n+1)//2),(2r-1,y,n^(2)),(3r-1,z,n(3n+1)//2)| then sum_(r=1)^(n)D_(r)=

If f: R to R, g : R to R defined by f(x) = 3x-2, g(x) = x^(2)+1 , then find: (i) (gof^(-1))(2) , (ii) (gof)(x-1)