Consider the following inequalities.

(i) 2x $$-$$ 1 > 7

(ii) 2x $$-$$ 9 < 1

Which one of the following expressions below satisfies the above two inequalities?

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.

Let X, Y and Z represent the following operations :

X : rotation of the square by 180 degree with respect to the S-Q axis.

Y : rotation of the square by 180 degree with respect to the P-R axis.

Z : rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.

Consider the following three distinct sequences of operation (which are applied in the left to right order).

(1) XYZZ

(2) XY

(3) ZZZZ

Which one of the following statements is correct as per the information provided above?

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex to the area of the original equilateral triangle is

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in