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Christukula mission higher secondary school, CLASS X, INTERIM III, MATHEMATICS, Total Marks: 20, , Time: 40 MIN, , Question 1, Prove that, cosec6θ = cot6θ + 3cot2θ cosec2θ + 1, , [2], , Question 2, An integer is chosen at random from the first two hundreds digit. What is the probability, that the integer chosen is divisible by 6 or 8., , [2], , Question 3, ], , [2], , Question 4, Thirty women were examined in a hospital by a doctor and the number of heartbeats per, minute was recorded and summarised as follows. Find the mean heartbeats per minute, for these women, choosing a suitable method., Number of heart beats per minute, , 65-68, , 68-71, , 71-74, , 74-77, , 77-80, , 80-83, , 83-86, , Number of women, , 2, , 4, , 3, , 8, , 7, , 4, , 2, , [3], Question 5

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A student noted the number of cars passing through a spot on a road for 100, periods each of 3 minutes and summarised it in the table given below. Find the, mode, of the data by drawing a histogram, , Number of cars, , Frequency, , 0-9, , 7, , 10-19, , 14, , 20-29, , 13, , 30-39, , 12, , 40-49, , 20, , 50-59, , 11, , [3], , Question 6, The angle of elevation of an aeroplane from a point A on the ground is 60°., After a flight of 15 seconds, the angle of elevation changes to 30°. If the, aeroplane is flying at a constant height of 1500√3 m, find the speed of the, plane in km/hr., [3], , Question 7, Draw an Ogive for the following frequency distribution by less than the, method and also find, [5],  the median

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 the inter quartile range,  the number of students who obtained more than 75% marks, From, your ogive, , Number of, Students, , 0 – 10, , 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60, , 7, , 10, , 23, , 51, , 6, , 3