Question
Ramesh rows in still water at the speed of 8 kmph to go
a certain place and come back. Find his average speed for the whole journey if the river is flowing at a speed of 4kmph?Solution
Ramesh’s speed upstream = 8 – 4 = 4kmph Ramesh’s speed downstream = 8 + 4 = 12kmph Let the distance be x km. ∴ Time taken upstream = x/4 kmph And time taken downstream = x/12 kmph ∴ Average speed = 2x/(x/4+ x/12) = 6 kmph Alternate method: Average speed during whole journey = (U^2-V^2)/U= (8^2-4^2)/8=(64-16)/8=48/8=6kmph
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 26x + 168 = 0
Equation 2: y² - 23y + 132 = 0
I. 3q² -29q +18 = 0
II. 9p² - 4 = 0
I. 12x2 - 55x + 63 = 0
II. 10y2 - 47y + 55 = 0
(i) 2x² + 14x - 16 = 0
(ii) y² – y – 12 = 0
If x + 1/x = 3, find x² + 1/x².
I. 15b2 + 26b + 8 = 0
II. 20a2 + 7a - 6 = 0
For what values of k does the equation x² – (k+1)x + k = 0 have two distinct real roots, both greater than 1?
I. 63x2 + 148x + 77 = 0
II. 21y2 + 89y + 88 = 0
I. 8x² + 2x – 3 = 0
II. 6y² + 11y + 4 = 0
I. 9x2 + 45x + 26 = 0
II. 7y2 – 59y − 36 = 0
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