If two circles of radii 18 cm and 8 cm touch externally, then the length of a direct common tangent is:

$$\left({1\over cosecθ}-{1\over sinθ} \right)+{1\over {cosecθ-cotθ}} -{1\over secθ+tanθ} =?$$

If 9x² + y² = 37 and xy = 2, x, y>0, then the value of (27x³+ y³) is:

The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is

A kite in the shape of a square with a diagonal 32 cm attached to an equilateral triangle of the base 8 cm. Approximately how much paper has been used to make it? (Use √3 = 1.732)

Given that x³ + y³ = 72 and xy = 6 with x > y. Then the value of (x – y) is

If the areas of two isosceles triangles are in the ratio of X² : Y², then the ratio of their corresponding heights is:

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17cm. The length of AB and CD are 10 cm and 24 cm, respectively. The radius (in cm) of the circle is