IIT Maths Sample Paper 1- Algebra

1. Let x be a real number with 00 then AC-B 2 £ 0.
18. When 0 1
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.

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4 Comments


  1. vipasha gh@ngor!a says:

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

  2. vaibhav atray says:

    what cn i do to get in IIT

  3. naveen says:

    where can i get answers for this sample questions

  4. Taranjitsingh4 says:

    Iit

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