A tank with a rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 4 meter and volume is 36 cubic meters. If building of the tank costs ₹ 100 per square meter for the base and ₹ 50 per square meter for the sides, then the cost of least expensive tank is

The length (in units) of the projection of the line segment, joining the points $$(5,-1,4)$$ and $$(4,-1,3)$$, on the plane $$x+y+z=7$$ is

If the volume of tetrahedron, whose vertices are $$\mathrm{A}(1,2,3), \mathrm{B}(-3,-1,1), \mathrm{C}(2,1,3)$$ and $$D(-1,2, x)$$ is $$\frac{11}{6}$$ cubic units, then the value of $$x$$ is

Let

Statement 1 : If a quadrilateral is a square, then all of its sides are equal.

Statement 2: All the sides of a quadrilateral are equal, then it is a square.