After the change of pattern with effect from the 2007 exam, the degree of difficulty of IIT-JEE has been considerably reduced, as you can judge from the following Matrix-Match Type question which appeared in the 2008 question paper:

Column I gives a list of possible set of parameters measured in some experiments The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in column I with the graphs given in column II. Indicate your answer by darkening the appropriate bubbles of the 4×4 matrix given in the ORS.

(A) Potential energy of a simple pendulum (y-axis) as a function of displacement (x-axis)

(B) Displacement (y-axis) as a function of time (x-axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x-direction

(C) Range of a projectile (y-axis) as a function of its velocity (x-axis) when projected at a fixed angle

(D) The square of the time period (y-axis) of a simple pendulum as a function of its length (x-axis)

(A) is to be matched with (p) since the potential energy (*U*) of a simple pendulum is given by

*U* = *mgh = mgℓ*(1– cos*θ*).

Here *h* is the height of the bob with respect to the mean position of the bob, *ℓ* is the length of the pendulum and *θ* is the angular displacement. *U* is thus related to *θ* non-linearly as indicated in the graph (p).

(B) is to be matched with (q) and (s). When the acceleration is zero, the velocity is constant and the displacement is directly proportional to the time as indicated in the graph (q). When the acceleration is constant, the velocity is directly proportional to the time and the displacement is non-linearly related to the time as indicated in the graph (s). [Remember *s = ut + *½* at*^{2}].

(C) is to be matched with (s) since the range *R *of a projectile is given by

*R =*(

*u*

^{2}sin2

*θ*)/

*g*where

*u*is the velocity of projection and

*θ*is the angle of projection. For fixed angle of projection, the range is directly proportional to the

*square*of the velocity of projection as indicated in graph (s).

(D) is to be matched with (q) since the time period of a simple pendulum is given by

*T = *2*π*√(*ℓ/g*) so that the *square* of the time period *T *is directly proportional to the length *ℓ* of the pendulum as indicated in graph (q).

You will have to darken the bubbles of the 4×4 matrix as shown