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Ram and Raj travel along a straight line from X to Y with different unifrom speeds. Ram started from X and reaches the place Y in t s. if Raj travels half of the total distance between X and Y in 2t s, determine the ratio of speevds of Ram and Raj.

A long taut string is plucked at its centre. The pulse travelling on it can be described as y (x, t) = e^(-(x+2t)^(2))+e^(-(x-2t)^(2)) . Draw the shape of the string at time t=0 , a short time after t=0 and a long time after t=0 .

Read the following information carefully and answer the question that follow: (i) Five friends P, Q, R, Sand T travelled to five different cities of Chennai, Kolkata, Delhi, Bangalore and Hyderabad by different modes of transport of Bus, Train, Aeroplane, Car and Boat from Mumbai. (ii) The person who travelled to Delhi did not travel by boat. (iii) R went to Bangalore by car and Q went to Kolkata by aeroplane. (iv) S travelled by boat whereas T travelled by train. (v) Mumbai is not connected by bus to Delhi and Chennai. Which of the following combinations of place and mode is not correct?