AIEEE 2010 PYQ Mock Test

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is:

Consider the system of linear equations:$x_1+2x_2+x_3=3$$2x_1+3x_2+x_3=3$$3x_1+5x_2+2x_3=1$ The system has:

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is:

For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is:

The circle $x^2+y^2=4x+8y+5$ intersects the line $3x-4y=m$ at two distinct points if: