It is often said that the world is witnessing now a second industrial revolution, which will transform the society as radically as did the first. List some key contemporary areas of science and technology, which are responsible for this revolution.

The electric current in a charging R-C circuit is given by where R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.

The length and the radius of a cylinder measured with a slide calipers are found to be 4.54 cm and 1.75 cm respectively. Calculate the volume of the cylinder.

A meter scale is graduated at every millimeter. How many significant digits will be there in a length measurement with this scale?

Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.

The length of the string of a simple pendulum is measured with a meter scale to be 90.0 cm. The radius of the bob plus the length of the hook is calculated to be 2.13 cm using measurements with a slide callipers. What is the effective length of the pendulum? (The effective length is defined as the distance between the point of suspension and the center of the bob.)

Though the statement quoted above may be disputed, most physicists do have a feeling that the great laws of physics are at once simple and beautiful. Some of the notable physicists, besides Dirac, who have articulated this feeling, are Einstein, Bohr, Heisenberg, Chandrasekhar, and Feynman. You are urged to make special efforts to get access to the general books and writings by these and other great masters of physics.

(See the Bibliography at the end of this book.) Their writings are truly inspiring!

Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y = 2x² and the slope of tangent is

x 1 2 3 4 5 6 7 8 9 10

y 2 8 18 32 50 72 98 128 162 200

Find the area bounded by the curve y = e^-x, the X-axis and the Y-axis.