Quadratic Equation (One Variable)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #71

If 5 times of a positive whole number is 3 less than 2 times of its square, then find the number.

Question No: #72

Divide 16 into two parts such that twice the square of the larger part is 164 more than the square of the smaller part.
Ans: 10, 6
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Question No: #73

If the price of pens is reduced by Rs 6 per dozen, 3 more pens are available at Rs 30. Determine the cost per dozen pens before price reduction.

Question No: #74

A man bought `y` pencils at Rs. `x`. If the price of each pencil be `1` rupee less, then he could get `1` more pencil for the same price. Prove that, `2y = \sqrt{1+4x} - 1`.

Question No: #75

A train travels a distance of 200 km at constant speed. If the speed of the train is increased by 5 km/hour, then the journey would have taken 2 hours less. Find the original speed of the train.
Ans: 20 km / hour
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Question No: #76

If the speed of a boat in still water is 8 km/h, the boat travels 15 km downstream and 22 km upstream in 5 hours, find the speed of the current.

Question No: #77

If the difference between a positive proper fraction and its reciprocal is `9/20`, then find the fraction.
Ans: `4/5`
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Question No: #78

Solve: `x/a + a/x = x/b + b/x` (where, `x \ne 0`)
Ans: `x = \pm \sqrt{ab}`
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Question No: #79

Solve: `(\frac{x+4}{x-4})^2 - 5(\frac{x+4}{x-4}) + 6 = 0` [`x \ne 4`]

Question No: #80

Solve: `\frac{x+2}{x-2} + 6 (\frac{x-2}{x+2}) = 5` (where, `x \ne \pm 2`)
Ans: `x = 4, 6`
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