Yes sure, here I am sharing the IIT JEE Last year papers for mathematics:

Algebra
1. Simplify the expression (a > 0, a  0) : (a-x/ 5)[2a2x-ax(2ax-1)] {1-(5ax/2ax-1)-2}-1/2 [(ax+2)2-5]-(a2x+4)[a2x+4(1-ax)]-1/2+4ax[1+(ax+2)(a2x-4ax+4)-1/2]{ax+2+(a2x-4ax+4)1/2}-1 and determine for which values of x this expression is equal to 1.
2. Prve that log418 is an irrational number.
3. Determine all such integers a and b for which one of the roots of 3x3+ax2+bx+12=0 is equal to 1 + 3.
4. Solve in terms of complex numbers: z3 + (7)*=0; z5.11 = 1. (* indicates conjugate).
5. Prove that if a > 0, b > 0 then for any x and y the following inequality holds true: a.2x+b.3y+1 (4x+9y+1)(a2+b2+1)
6. Prove the inequality nn+1 > (n+1)n, n  3, n  N.
7. Prove that
(b+c)2 a2 a2
b2 (c+a)2 b2
c2 c2 (a+b)2
= 2abc(a+b+c)3
8. (Without expanding)
9. Sum the series: 1 + 4x + 9x2 + ...
10. The eqns ax2 + bx + c=0 and x3=k have a common root. Prove that
a b c
b c ak
c ak bk
= 0
11. If  is a root of x4=1 then Show that a + b + c2 + d3 is a factor of
a b c d
b c d a
c d a b
d a b c
12. Hence Show that the det is equal to -(a+b+c+d)(a-b+c-d){(a-c)2+(b-d)2}.
13. Find the coefficient of x4 in (1 + 2x + 3x2)5.
14. The sum of squares of 3 terms of a GP is S2. If their sum is S, Prove that 2  (1/3,1)  (1,3).
15. Find the sum to n terms: 0!/5! + 1!/6! + 2!/7! + ...
16. If f(x)=ax/(ax + a) (a > 0), evaluate r=12n-1 f(r/2n).





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Attached Files

IIT JEE Last year papers for mathematics(1).pdf (1.41 MB, 47 views)