### IIT Maths Sample Paper 1- Algebra

1. Let x be a real number with 0

18. When 0

x C r n-1 C r n-1 C r-1

x+1 C r n C r n C r-1

x+2 C r n+2 C r n+2 C r-1

= 0

21. Let p be a prime and m a positive integer. By mathematical induction on m, or otherwise, prove that whenever r is an integer such that p does not divide r, p divides mp C r .

22. Let a and b be real numbers for which the equation x 4 + ax 3 + bx 2 + ax + 1 = 0 has at least 1 real solution. For all such pairs (a,b), find the minimum value of a 2 +b 2 .

23. Prove that:

2/(x 2 – 1) + 4/(x 2 – 4) + 6/(x 2 – 9) + … + 20/(x 2 – 100) =

11/((x – 1)(x + 10)) + 11/((x – 2)(x + 9)) + … + 11/((x – 10)(x + 1))

24. Find all real p, q, a, b such that we have (2x-1) 20 – (ax+b) 20 = (x 2 +px+q) 10 for all x.

where cn i get da forms from>>>>>

what cn i do to get in IIT

where can i get answers for this sample questions

Iit