Quantitative an...

If Φ is the acute angle between the two straight lines represented by 3y = 9x + 5 and 3y = 7x + 9, then what is value of tanΦ ?

The sum of the areas of two circles, which touch each other externally, is 153π. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.

A 180-metre-long train crosses a platform of equal length in 18 seconds. What is the speed of the train?

Find the equation of the line parallel to the line passing through (5, 7) and (2, 3) and having x intercept as -4.

What is the equation of a straight line passing through the points A (-2, 6) and B (4, -3)?

The respective ratio between the speed of the boat downstream and the speed of the boat upstream is 27: 17. By what percent is the speed of the boat downstream more than the speed of the boat in still water?

If (2 + 4 + 6 + ... 50^th  terms)/(1 + 3 + 5 + ... n^th terms) = 51/2, then find the value of n.

What is the equation of tangent to the circle x² + y² = 625 at point P (24, -7)?

If 2x² - 15x + 28 = 0 and 2y² - 21y + 54 = 0, then which of the following is true?