Let `a, b.c.d,e, f` be positive integers such that `a/b lt c/d lt e/f`. Suppose `af-be =-1`. Show that `d geq b+f`

Let a,b,c,d,e, be real numbers such that a+b lt c+d , b+c lt d+e, c+d lt e+a, d+e lt a+b . Then

If a,b,c,d,e, f are A. M's between 2 and 12 , then find a + b + c +d + e +f.

The number of 7 digit integers abcdefg, where a lt b lt c lt d gt e gt f gt g such that a, b, c, d, e, f, g in {1,2,3,…..,9} . Are

The number of 7 digit integers abcdefg, where a lt b lt c lt d gt e gt f gt g such that a, b, c, d, e, f, g in {1,2,3,…..,9} . Are

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

A B C D is a parallelogram in which B C is produced to E such that C E=B C. A E intersects C D\ at F . Prove that a r\ (\ A D F)=\ a r\ (\ E C F) . If the area of \ D F B=3\ c m^2, find the area of ABCD.

If A B C and D E F are similar triangles such that 2\ A B=D E and B C=8c m , then E F=

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E .