A speaks truth in 60% of the cases, while B is 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact ?
From a lot of 6 items containing 2 defective items, a sample of 4 items are drawn at random. Let the random variable X denote the number of defective items in the sample. If the sample is drawn without replacement, find :
(a) The probability distribution of X
(b) Mean of X
(c) Variance of X
The Cartesian equation of line is : 2x - 3 = 3y + 1 = 5 - 6z. Find the vector equation of a line passing through (7, – 5, 0) and parallel to the given line.
Water is dripping out from a conial funnel of semi-verticle angle at the uniform rate of 2 cm2/sec in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is 4 cm, find the rate of decrease of the slant height of the water.
Using matrices, solve the following system of equations :
2x - 3y + 5z = 11
3x + 2y - 4z = - 5
x + y - 2z = - 3
Given equations,
2x - 3y + 5z = 11
3x + 2y - 4z = - 5
x + y - 2z = - 3
This can be written in the form AX = B
Where,
We know, A- 1 =
= 2(- 4 + 4) + 3(- 6 + 4) + 5(3 - 2)
= 0 - 6 + 5 = - 1
Hence it is a non - singular matrix.
Let us find the (adj A) by finding the minors and cofactors
Thus, A11 = 0, A12 = 2, A13 = 1
A21 = - 1, A22 = - 9, A23 = - 5
A31 = 2, A32 = 23, A33 = 13
A- 1 =
=
We know, AX = B, then X = A– 1 B
Therefore,
Matrix multiplication can be done by multiplying the rows of matrix A with the column of matrix B.
Therefore,
Hence, x = 1, y = 2 and z = 3
A cone is inscribed in a sphere of radius 12 cm. If the volume of the cone is maximum, find its height.