Mathematics Tes...

Let f be a twice differentiable function on (1, 6). If f(2) = 8, f'(2) = 5, f'(x) ≥ 1 and f''(x) ≥ 4, for all x ∈ (1, 6), then

If the function f(x)=   is twice differentiable, then the ordered pair (k₁, k₂) is equal to

 is equal to

If f(x) = min 

Let y = y(x) be the solution of the differential equation 

If y(0) = 0, then y (1/2) is equal to

Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :

If a circle C passing through the point (4,0) touches the circle x² + y² + 4x – 6y = 12 externally at the point (1, –1), then the radius of C is :

The equation of a tangent to the hyperbola 4x² – 5y² = 20 parallel to the line x–y = 2 is :

The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of the following points ?