How many circles can be drawn that pass(es) through two fixed points?

The graph of y = 4x – 5 passes through which point?

If $$(1 + x)^n = \sum_{r=0}^{n} C_r x^r,$$​ then $$\left(1 + \frac{C_1}{C_0}\right)\left(1 + \frac{C_2}{C_1}\right)\left(1 + \frac{C_3}{C_2}\right)\cdots\left(1 + \frac{C_n}{C_{n-1}}\right)$$ is equal to:

The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16, cm is:

The ratio in which the line segment joining the points (5, -2) and  (0, 7) is divided by the point $$\left( \frac{5}{3}, 4 \right)$$​ is:

If  P  and Q are the points with coordinates  (-3, 4) and (2, 1) respectively, then the coordinates of the point  R on  PQ produced such that PR = 2QR  are:

One root of the quadratic equation x² + ax + 1 = 0 lies inside a unit circle with center at origin. Then the other root:

​Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9):​

A (x, 5), B (3, – 4) and C (– 6, y) are the three vertices of a triangle ABC. If (3.5, 4.5) is the centroid of the triangle, find the point (x + 3, y – 4).

If (3, 2) are coordinates of the centroid of a triangle, whose vertices are (0, 4), (-2, 0) and (p, 2), then find the value of p.

Find the relation between x and y such that the point (x, y) is equidistant from (6, 2) and (4, 6).