The coefficient of x¹⁸ in the product
(1 + x) (1 – x)¹⁰ (1 + x + x²)⁹ is :

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90^o, then the length (in cm) of their common chord is :

Consider the differential equation, $${y^2}dx + \left( {x - {1 \over y}} \right)dy = 0$$, If value of y is 1 when x = 1, then the value of x for which y = 2, is :

If the area (in sq. units) of the region {(x, y) : y² $$ \le $$ 4x, x + y $$ \le $$ 1, x $$ \ge $$ 0, y $$ \ge $$ 0} is a $$\sqrt 2 $$ + b, then a – b is equal to :