31.In a class, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product would have been 210. Find her marks in the two subjects.
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32.The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
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33.The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
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34.A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, would have taken 1 hour less for the same journey. Find the speed of the train.
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35.Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
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36.An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.
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37.Sum of the area of the two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
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Short Answer Type
38.Find the discriminant of the following quadratic equations. If the real roots exist, find them
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Long Answer Type
39.Find the discriminant of the following quadratic equations. If the real roots exist, find them
40.Find the discriminant(or the nature of the roots) of the following quadratic equations. If the real roots exist, find them
2x2 – 6x + 3 = 0 Here, a = 2, b = –6, c = 3 Now, D = b2 – 4ac = (–6)2 – 4(2) (3) = 36 – 24 = 12 Since, D > 0 Therefore, the given quadratic equation has real and distinct roots. Now, Hence, roots are
Long Answer Type
hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Short Answer Type
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