Mathematics Tes...

A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 1/4 , 1/3 and 1/12, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. The probability that he comes by bus is:​

If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A ∩B) 

A random variable X has the following probability distribution: 

Then k =?​

The equation of the plane passing through the intersection of the planes    and  and the point (1, 2, 1) is:​

The Cartesian form of the equation of the plane  is:

The length of the perpendicular from the origin to the plane 3x + 2y –6z = 21 is:​

If l, m, n are the direction cosines of the normal to the plane and p be the perpendicular distance of the plane from the origin, then the equation of the plane is:

The combined equation to two parabolas, both have their axis along x-axis, is given by  y⁴ - y²  (4x + 4 - 2 sin² 2 α) + sin² 2 α (4x + 4x + sin² 2 α) = 0. The locus of the point of intersection of tangents, one to each of the parabolas, when they include an angle of 90 ° 
is

The straight line x + y = k + 1 touches the parabola y = x(1 –x) if

Focus and vertex of the parabola that touches x-axis at (1, 0) and x = y at (1, 1) are (h, k) and (p, q) then the value of 25(p + q +h + k)