HOTS Questions for Class X Mathematics

Questions

1.Show that square of any positive odd integer is of the form 8q+1 for some integer 'q'.2.Prove that  3+2√5  is irrational3.Find all the zeroes of the polynomial x²-5x³- 9x²+15x+18  if two of its zeroes are  √3  and '-√ 3' 4.If sin(A+B)=1 and cos(A-B)=1 then find both the angles 'A 'and 'B'.5.Find whether  51/120  and 637/7280 have terminating or non-terminating decimal expansions.

6. Prove the Pythagoras theorem and the Basic Proportionality Theorem