Mathematics Tes...

If the coefficients of (2r + 1)^th term and (r + 2)^th terms in the expansion of (1 + x)⁴³ are equal then r is equal to ______.

The minimum distance of a point on the curve y = x² - 4 from the origin is

At any point on a curve, the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point. If the curve passes through (0, 1), then the equation of the curve is

By rotating the coordinate axes in the positive direction about the origin by an angle α, if the point (1, 2) is transformed to  in new coordinate system then

The equation of the base of an equilateral triangle is 12x + 5y - 65 = 0. If one of its vertices is (2, 3), then the length of the side is

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is ______.

The equation of a common tangent to the curves, y² = 16x and xy = -4, is