List of top Mathematics Questions asked in GATE TF

Two vertical poles of height 6 m and 18 m are 10 m apart on a flat ground. A string needs to be connected from the top of one pole to a peg on the ground and then on to the top of the other pole. The minimum length (m) of the string is

The area under the curve \( y = x^2 + 2x \) between \( x = 0 \) and \( x = 4 \), using the trapezoidal rule with a step size of one, (in integer) is ____________________.

The value of \( x \) for which the inverse of the following matrix does not exist is \[ \begin{bmatrix} 1 & 3 & 0 \\ 2 & x & 4 \\ -1 & 0 & 2 \end{bmatrix} \]

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.
The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.