11.Represent the following problem situations in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
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12.
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
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Short Answer Type
13.Find the roots of the following quadratic equations by factorisation method: x2 – 3x – 10 = 0
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14.Find the roots of the following quadratic equations by factorisation method: 2x2 + x – 6 = 0
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15.Find the roots of the following quadratic equations by factorisation method:
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16.Find the roots of the following quadratic equations by factorisation method:
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17.Find the roots of the following quadratic equations by factorisation method:
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Long Answer Type
18.John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
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19.A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production was Rs. 750. We would like to find out the number of toys produced on that day.
20.Find two numbers whose sum is 27, and product is 182.
Let the first number be x so, second number = 27 - x. According to question, x(27 – x) = 182 ⇒ 27x – x2 = 182 ⇒ x2 – 27x + 182 = 0 ⇒ x2 – 14x – 13x + 182 = 0 ⇒ x(x – 14) – 13 (x– 14) = 0 ⇒ (x – 13) (x – 14) = 0 Either x – 13 = 0 or x – 14 = 0 ⇒ x = 13 or x = 14 If x = 13 then other number = 21 – x = 27 – 13 = 14 If x = 14 then other number = 27 - x = 27 – 14 = 13 Hence, required two numbers are 13 and 14.
Long Answer Type
Short Answer Type
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