TIFR CSE 2013 | Part B | Question: 2

Question

Consider polynomials in a single variable $x$ of degree $d$. Suppose $d < n/2$. For such a polynomial $p(x)$, let $C_{p}$ denote the $n$-tuple $(P\left ( i \right ))_{1 \leq i \leq n}$. For any two such distinct polynomials $p, q,$ the number of coordinates where the tuples $C_{p}, C_{q}$ differ is.

• A. At most $d$
• B. At most $n - d$
• C. Between $d$ and $n - d$
• D. At least $n - d$
• E. None of the above.

Comments

@Pragy Agarwal 

sir, i couldn't find any info related " n-tuple" polynomial. What is is basically ?  Any hint to approach this question ?

Answer 1

let p(x)=x and q(x)=2x-1 these are two polynomials of degree 1 suppose n=4 so n/2=2 so d<n/2 both these polynomials are satisfying these relation of degree if we put different values p(1) will be same for both the polynomials but p(2), p(3),p(4) will be different for both the polynomials hence 3 different values 1 same value hence i can say that n-d that 4-1=3 differ values. Hence option d is the answer.