IIT-JEE Exam

Let an denote the number of all n digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = the number of such n digit integers ending with digit 1 and cn = the number of such n digit integers ending with digit 0.
The value of b^6 is??

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IIT-JEE Other Question

Consider the statements:
P : There exists some x such that f(x) + 2x = 2(1 + x2)
Q : There exists some x  such that 2f(x) + 1 = 2x(1 + x)
For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2 2, then
option
A. a+b-c>0
B. a+b-c<0
C. a-b-c=0
D. None of these