Question
The ratio of the length of two trains P and Q is 5:6 and
the ratio of the time taken by both trains to cross a man standing on a platform is 2:3. If the speed of the train P is 25 km/h, then find the speed of the train Q in m/s.Solution
Let the length of train P = 5a , time = 2b Speed = 5a/2b Let the length of train Q = 6a , time = 3b Speed = 6a/3b Ratio of the speed = (5a/ 2b)/ (6a/ 3b) => 5/4 Speed of train Q = (25/5) × 4 = 20 km/h in m/s = 20 × (5/18) = 50/9 m/s
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 24x + 143 = 0
Equation 2: y² - 20y + 96 = 0
l. 3x2 + 17x + 24 = 0
II. 2y2 + 15y + 27 = 0
I. x2 – 3(x + 5) = -11
II. y2 – 4(y + 2) = -2y
I. 8a2 – 22a+ 15 = 0
II. 12b2 - 47b + 40=0
If α, β are the roots of the equation x² – px + q = 0, then the value of α2+β2+2αβ is
...I. 2y2 + 11y + 15 = 0
II. 3x2 + 4x - 4= 0
I. 3p² + 13p + 14 = 0
II. 8q² + 26q + 21 = 0
- Suppose both the roots of q² + kq + 49 = 0 are real and equal, then determine the value of 'k'.
I. x2 – 18x + 81 = 0
II. y2 – 3y - 28 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 34x + 285 = 0
Equation 2: y² - 26y + 165 = 0
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