Two persons A and B agree to meet at a place between 11 to 12 noon. The first one to arrive waits for 20 minutes and then leave. if the time of their arrival be independent and at random, then the probabity that A and B meet is:

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is

Suppose that the number of telephone calls coming into a telephone exchange between 10 A.M. and 11 A.M., say, X_(1) is a random variable with possion distribution with parameter 2. Similarly the number of calls arriving between 11 A.M. and 12 noon, say X_(2) also follows a poisson distribution with parameter 6. If X_(1) and X_(2) are independent, what is the probability that more than 5 calls come in between 10 A.M. and 12 noon.

places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find the speed of the cars.

Places A and B are 100 km apart on a highway. One car starts from A and another from b at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars

Places A and B are 100 km apart on a highway. One car starts from A and another from b at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars

Two point sources of sound are kept at a separation of 10 cm. They vibrate in phase to produce waves of wavelength 5.0 cm. What would be the phase difference between the two waves arriving at a point 20 cm from one source (a) on the line joining the sources and (b) on the perpendicular bisector of the line joining the sources ?

A situation is shown in which two objects A and B start their motion from same point in same direction. The graph of their velocities against time is drawn. u_A and u_B are the initial velocities of A and B respectively. T is the time at which their velocities become equal after start of motion. You cannot use the data of one question while solving another question of the same set. So all the questions are independent of each other. 6. Let v_A and v_B be the velocities of the particles A and B respectively at the moment A and B meet after start of the motion. If u_A = 5 ms^-1 and u_B = 15 ms^-1, then the magnitude of the difference of velocities v_A and v_B is

A situation is shown in which two objects A and B start their motion from same point in same direction. The graph of their velocities against time is drawn. u_A and u_B are the initial velocities of A and B respectively. T is the time at which their velocities become equal after start of motion. You cannot use the data of one question while solving another question of the same set. So all the questions are independent of each other. 5. If the value of T is 4 s, then the time after which A will meet B is

Two persons stand near a railway line separated by a distance 2 km. A detonator is exploded by the first person. The second person 2 km away hears two sounds, one from the sound that has travelling through the rail and the other through the air. What is the interval between them? Given Young's modulus of steel = 2 xx 10^11 N//m^2. Density of steel = 8000 kg/m ""^3. Density of air = 1.29 kg/m ""^3. Atmospheric pressure =1 xx 10^(2) N//m^2. y for air = 1.4