If `V` be the volume of a tetrahedron and `V '` be the volume of another tetrahedran formed by the centroids of faces of the previous tetrahedron and `V=K V^(prime),t h e nK` is equal to a. `9` b. `12` c. `27` d. `81`

The volume of a tetrahedron formed by the coterminous edges vec a , vec b ,a n d vec c is 3. Then the volume of the parallelepiped formed by the coterminous edges vec a+ vec b , vec b+ vec ca n d vec c+ vec a is 6 b. 18 c. 36 d. 9

Let G_1, G_2a n dG_3 be the centroids of the triangular faces O B C ,O C Aa n dO A B , respectively, of a tetrahedron O A B Cdot If V_1 denotes the volumes of the tetrahedron O A B Ca n dV_2 that of the parallelepiped with O G_1,O G_2a n dO G_3 as three concurrent edges, then prove that 4V_1=9V_2dot

If three edges of a cuboid be a, b, c units volume be v cubic units and total surface areas be s sq-units, then what is the value of 1/v ?

If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec G C is equal to a. vec0 b. 3 vec G A c. 3 vec G B d. 3 vec G C

If the height , curved surface area and volume of a right circular cone be h, c and v respectively , then that 3pi vh^3-c^2h^2+9v^2=0 .

If the length, breadth, height, total surface area and volume of a cuboid are l, b, h, s, v respectively, then the relation between l, b, h, s, v is

Equal volumes of two monoatomic gases, A and B, at same temperature and pressure are mixed. The ratio of specific heals (C_p / C_v) of the mixture will be

Two equally charged soap bubbles of equal volume are joined together to form a larger bubble . If each bubble had a potential V, find the potential of the resultant bubble.