Sample Papers for IIT JEE

Hi I would like to have the previous year question paper for the sample paper for the IIT JEE examination required for preparation?

[pawan]

The previous year question paper for the sample paper for the IIT JEE examination required for preparation is as follows:

1. Let g(x) be a continuous function such that 0ò1 g(t) dt = 2. Let f(x) = 1/2 0òx (x-t)2 g(t) dt then find f �(x) and hence evaluate f "(x).
2. Find area of region bounded by the curve y=[sinx+cosx] between x=0 to x=2p.
3. Solve: [3Öxy + 4y - 7Öy]dx + [4x - 7Öxy + 5Öx]dy = 0.
4. f(x+y) = f(x) + f(y) + 2xy - 1 " x,y. f is differentiable and f �(0) = cos a. Prove that f(x) > 0 " x Î R.
5. Show that 0òp q3 ln sin q dq = 3p/2 0òp q2 ln [Ö2 sin q] dq.
6. A function f : R® R satisfies f(x+y) = f(x) + f(y) for all x,y Î R and is continuous throughout the domain. If I1 + I2 + I3 + I4 + I5 = 450, where In = n.0òn f(x) dx. Find f(x).
7. Evaluate 0òx [x] dx .
8. Let f(x) be a real valued function not identically equal to zero such that f(x+yn)=f(x)+(f(y))n; y is real, n is odd and n >1 and f �(0) ³ 0. Find out the value of f �(10) and f(5).
9. Evaluate: 0ò11/{ (5+2x-2x2)(1+e(2-4x)) } dx
10. If f(x) is a monotonically increasing function " x Î R, f "(x) > 0 and f -1(x) exists, then prove that å{f -1(xi)/3} < f -1({x1+x2+x3}/3), i=1,2,3
11. Let P(x)= Õ (x-ai), where i=1 to n. and all ai�s are real. Prove that the derivatives P �(x) and P "(x) satisfy the inequality P�(x)2 ³ P(x)P"(x) for all real numbers x.
12. Determine the value of 0ò1 xa-1.(ln x)n dx where a Î {2, 3, ...} and n Î N.
13. Evaluate ò sinx dx/[sin(x-p/6).sin(x+p/6)]
14. Discuss the applicability of Rolle�s theorem to f(x)=log[x2+ab/{(a+b)x}] in the interval [a,b].
15. Find the polynomial function f(x) of degree 6 which satisfies : Lim(x®0)[1 + f(x)/x3]1/x = e2 and has local maxima at x=1 and local minima at x=0,2.
16. Find all the values of a (a¹ 0) for which: 0òx (t2-8t+13) dt = x sin(a/x). Find that solution.
17. Suppose that the cubic polynomial h(x)=x3 - 3bx2 + 3cx + d has a local maximum A(x1,y1) and a local minimum at B(x2,y2). Prove that the point of inflection of h is at the midpoint of the line segment AB.
18. y = f(x) be a curve passing through (1,1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area 2. Form the differential equation and determine all such possible curves.