There are two paths that one can choose to go from Sarah's house to James house. One way is to take C street, and the other way requires to take A street and then B street. How much shorter is the direct path along C street ? (Using figure).

Consider Galileo's method of measuring the speed of light using two lanterns. To get an accuracy of about 10%, the time taken by the experimenter in closing or opening the shutter should be about one tenth of the time taken by the light in going from one experimenter to the other. Assume that it takes 1/100 second for an experimenter to close or open the shutter. How far should the two experimenters be to get a 10% accuracy ? What are the difficulties in having this separation ?

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is^(2n)C_n-1.

Sound waves from a loudspeaker spread nearly uniformly in all directions if the wavelength of the sound is much larger than the diameter of the loudspeaker. (a) Calculate the frequency for which the wavelength of sound in air is ten times the diameter of the speaker if the diameter is 20 cm. (b) Sound is essentially transmitted in the forward direction if the wavelength is much shorter than the diameter of the speaker. Calculate the frequency at which the wavelength of the sound is one tenth of the diameter of the speaker described above. Take the speed of sound to be 340 m s^-1 .

Two rectangular blocks A and B of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of A is 100°C and that of B at the other end is 0°C. If the ratio of their thermal conductivity is 1 : 3, then under steady state, the temperature of the junction in contact will be

Take three different colour sheets , place one over the other and draw a triangle on the top sheet. Cut the sheets to get triangles of different colour which are identical. Mark the vertices and the angles as shown. Place the interior angles angle1,angle2 and angle3 on a straight line, adjacent to each other, without leaving any gap. What can you say about the total measure of the three angles angle1,angle2 and angle3 ? Can you use the same figure to explain the ''Exterior angle property'' of a triangle ? If a side of a triangle is stretched, the exterior angle so formed is equal to the sum of the two remote interior angles.

In each of the following questions, there are two statements. One is assertion (A) and other is reasoning (R) Mark the correct answer as a. A and R correct, R is the correct explanating of A. b A and R are correct but R is not the correct explanatin of A c. A is correct R is false d. Both A and R are false. Assertion: MTP is a voluntary or intentional termination of pregnancy in a surgical way Reason : Government of India legalized MTP without any restrictions.

An organization plans to plant saplings is 25 streets in a town in such a way that one sapling for the first street, three for the seconds, nine for the third and so on. How many sapling are needed to complete the work?

Figure shows the elipticla path of a planet about the sun. The two shaded parts have equal area. If t_1 and t_2 be the tim taken by the planet to go from a to b and from c to d respectively

A question paper has two parts A and B. Part A has 4 questions and B has 3 questions. One question from either part has to be selected. In how many different ways can this selection be made?

A charge of 1.0 C is placed at the top of your college building and another equal charge at the top of your house. Take the separaton between the two charges to be 2.0 km. Find the force exerted by the charges on each other. How many time of your weight is this force?