Find the dimensions of a' and 'b' in the following equation:
`(P + a//V^2) (V - b) = RT`

Find the equations of the following circle : Centre (- a, -b) and radius sqrt(a^2-b^2) .

Show that the straight lines whose direction cosines are given by the equations a l+b m+c n=0 and u l^2+z m^2=v n^2+w n^2=0 are parallel or perpendicular as (a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.

If V is the volume of a cuboid of dimensions a,b,c and S is its surface area, then prove that 1/V=2/S(1/a+1/b+1/c)

The velocity of a body is given by the equation v = b/t + c^2 + d The dimenstional formula of b is :

Find out which of the following sequences are A.P. for those which are A.P., find out the common difference. ,- a + b, (a + 1) + b, (a + 1) + (b + 1), (a+ 2) + (b + 1), (a + 2) + {b + 2), ....

In the graph between sqrt(v) and Z for the Mosley's equation sqrt(v) =a(Z-b), the intercept OX is -1 on sqrt(v) axis. What is the frequency when atomic number (Z) is 51?

Let the sides of a parallelogram be U=a, U=b,V=a' and V=b', where U=lx+my+n, V=l'x+m'y+n'. Show that the equation of the diagonal through the point of intersection of U=a, V=a' and U=b, V=b' " is given by " |{:(U,V,1),(a,a',1),(b,b',1):}| =0.