Show that `(7!) / (4! 3!) + (7!) / (5! 2!) = (8!) / ( 5! 3!)`

(4)/(x) + (5)/(y) = 7 , (3)/(x) + (4)/(y) = 5

Show that A(-4,-7), B(-1,2), C(8,5) and D(5,-4) are the vertices of a parallelogram.

Show that A(4,-1), B(6,0), C(7,-2) and D(5,-3) are vertices of a square.

If sin 2 theta =3/4, then sin ^(3) theta + cos ^(3) theta = ............... A) (sqrt5)/( 8) B) (sqrt7)/(8) C) (sqrt11)/(8) D) (5sqrt7)/(16)

Show that C_0 + C_2 + C_4 + C_6 + C_8 = C_1 + C_3 + C_5 + C_7 = 128