Graphing inequality (Tomato subjective 90)

Graphing inequality (Tomato subjective 90)

Problem: Draw the region of points in the plane, which satisfy . Solution: region will bounded by lines , , & . Why is that? First note that \( |x| \le 1 \) implies: Similarly, if we demand \( |y| \le 1 \) (the double shaded zone). Now if we want \( |y| \le |x|...
Perpendiculars from Center (Tomato subjective 107)

Perpendiculars from Center (Tomato subjective 107)

Problem : If a, b and c are the lengths of the sides of a triangle ABC and if \( p_1 , p_2 \) and \( p_3 \) are the lengths of the perpendiculars drawn from the circumcentre onto the sides BC, CA and AB respectively, then show that . Solution : Let O be the circum...
Sum of polynomials (Tomato subjective 173)

Sum of polynomials (Tomato subjective 173)

Problem : Let be polynomials in , each having all integer coefficients, such that . Assume that is not the zero polynomial. Show that and Solution : As are integer coefficient polynomials so gives integer values at integer points. Now as is not zero polynomial for...
Round robin tournament (Tomato subjective 172)

Round robin tournament (Tomato subjective 172)

Problem : Suppose there are teams playing a round robin tournament; that is, each team plays against all the other teams and no game ends in a draw.Suppose the team loses games and wins games.Show that = Solution : Each team plays exactly one match against each other...