In the figure given below,a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles. What is the perimeter of each of the smaller rectangles?

The diagonals of a parallelogram $PQRS$ are along the lines $x + 3y = 4$ and $6x - 2y = 7$. Then $PQRS$ must be a

Let $A(\alpha, -2)$,$B(\alpha, 6)$,and $C\left(\frac{\alpha}{4}, -2\right)$ be the vertices of a $\triangle ABC$. If $\left(5, \frac{\alpha}{4}\right)$ is the circumcentre of $\triangle ABC$,then which of the following is $NOT$ correct about $\triangle ABC$?

The area of the triangle formed by the line $x \sin \alpha + y \cos \alpha = \sin 2\alpha$ and the coordinate axes is

Let $A(h, k)$,$B(1, 1)$,and $C(2, 1)$ be the vertices of a right-angled triangle with $AC$ as its hypotenuse. If the area of the triangle is $1$ square unit,then the set of values which $k$ can take is given by

If $(0, 1), (1, 1)$ and $(1, 0)$ are the midpoints of the sides of a triangle,find its incentre.