The diagram below shows a river system consisting of 7 segments, marked $P, Q, R$, $\mathrm{S}, \mathrm{T}, \mathrm{U}$, and V . It splits the land into 5 zones, marked $\mathrm{Z} 1, Z 2, Z 3, Z 4$, and $Z 5$. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?
Note: The figure shown is representative.
A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?
Note: The figures shown are representative.
A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.
The minimum number of such cuts required is
In the $4 \times 4$ array shown below, each cell of the first three rows has either a cross (X) or a number.
The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is