A train moving with constant acceleration takes t seconds to pass a certain fixed point and the front and back end of the train pass the fixed point with velocities u and v respectively. Show that the length of the train is .
Show that, for a positive integer n, the coefficient of xk, () in the expansion of 1 + (1 + x) + (1 + x) + ... + (1 + x)n is
Find the values of 'a' for which the expression x2 - (3a - 1)x + 2a2 + 2a - 11 is always positive
Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex.
Given curve is, y2 = ax.
Put y = a, a2 = ax
⇒ x = a
So, coordinates of A and B are (a, a) and (a, - a).
Now, slope of OA = a/a = 1 = m1
slope of OA = -a/a = - 1 = m2
Here, m1m2 = - 1
Hence, the angle subtended by the double ordinate to its vertex is π/2
The equation to the pairs of opposite sides of a parallelogram are x2 - 5x + 6 = 0 and y2 - 6y + 5. Find the equations its diagonals.