JEE Advanced Mathematics question
In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than once.) Column I: (i) Given is divisible by 3. When is divided by 3 the remainder will be (ii) is (iii) If for all and for all then is (iv) If then equals Column II: (a) (b) (c) (d)
Answer: (2)
Solution
**(i)** Check each residue modulo 3: gives ; gives ; gives . Only works, so the remainder is → **(d)**. - **(ii)** , so
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