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only reflexive!! since for a set of integers |a-b|<1 iff a=b

Just by observation it is clear that A=pi/2 and B=-pi/6 would satisfy both conditions.

Hence 3A + B = 3pi/2 - pi/6 = 4pi/3 

q) A 10cm long rod is cut into 3 pieces whose lengths are integral multiples of 1cm. Find the the total ways in which it could be cut so that the 3 pieces form a triangle.

q) There are tickets numbered from 0000 to 9999 , if the sum of the first 2 digits is equal to the sum of the last two digits then the ticket is said to be lucky. Find the probability tht a ticket drawn at random would be lucky.

Point after reflection about y=x is A(1,4)

After translating 2 units along the x axis the co-ordinates are : B(3,4)

|OB| = 5 ; and the slope of the line OB = 4/3 ;and if the angle made by OB with the pos x axis=@ then tan@ = 4/3

if OB is rotated pi/4 in the counterclockwise dir. B point would become

5cos(pi/4+@),5sin(pi/4+@)

= (-1/root2 , 7/root2)....(ans)