Mathematics Tes...

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r is equal to

If a³ + b⁶ = 2, then the maximum value of the term independent of x in the expansion of (ax^1/3 + bx^-1/6)⁹ (a > 0, b > 0) is

The co-ordinates of the point which divides the line segment joining the points (5,4, 2) and (−1,−2, 4) in the ratio 2 : 3 externally is

The area of an expanding rectangle is increasing at the rate of 48 cm²/sec. The length of the rectangle is always equal to the square of the breadth. At the instant when the breadth is 4.5 cm, The length is increasing at the rate of

If ⁿP_r = 1680 and ⁿC_r = 70, then 69 n + r! is equal to

Consider the straight line ax + by = c, where a, b, c ∈ R⁺ this line meets the coordinate axes at A and B respectively. If the area of the ΔOAB, O being origin, is always a constant equal to half, then

If for a ΔABC, cot A⋅cot B⋅cot C>0 then the triangle is

The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x² + y² = 9 is

 be two perpendicular unit vectors such that