At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t2/4 minutes. Find t.
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see Fig.]. Find the length and breadth of the pond.
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
Find whether the equations have real roots. If real roots exist, find them
5x2 – 2x – 10 = 0
Find whether the equations have real roots. If real roots exist, find them.
-2x2 + 3x + 2 = 0
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