CAT Exam Logical Reasoning Cryptography

The degree of each term of a polynomial P(x) is odd. When P(x) is divided by (x-3),the remainder is 6. What is the remainder when P(x) is divided by (x^2– 9) ?

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CAT Other Question

A car runs on four tyres and has one extra tyre. If each tyre lasts for 10,000 km then what is the maximum distance (in km) that the car can travel using the five tyres? How many integral values of 'x' are possible for which (2^70 + 2^1039 + 2^x) equals the square of a whole number?