IIT-JEE Exam

The number of distinct real roots of x^4 - 4x^3 + 12x^2 + x - 1 = 0 is

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IIT-JEE Other Question
Let a = -ˆi - kˆ , b = -ˆi + j
 
and c = ˆi + 2ˆj+ 3kˆ 
be three given vectors. If r

is a vector such that r ´ b = c´ b
   
and r × a = 0  
, then the value of r × b
 
is A charge Q is uniformly distributed over a long rod
AB of length L as shown in the figure. The electric
potential at the point O lying at a distance L from
the end A is -