(1)The HCF and LCM of two nos. are equal when they are equal .

(2) e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity

(2a) 2 < e < 3

(3) log(1+x) = x – (x^2)/2 + (x^3)/3 – (x^4)/4 ………to infinity [ Note the alternating sign . .Also note that the ogarithm is with respect to base e ]

(4) In a GP the product of any two terms equidistant from a term is always constant .

(5) Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1

( |a|+|b| = |a+b| if a*b>=0

else |a|+|b| >= |a+b|

(6) ANy function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y) .