Mathematics Mock Test - 10

$I=\int \frac{\sin x}{\sin x-\cos x}dx$ is equal to:

The triangle formed by the points $A(0,7,10),B(-1,6,6)$ and $C(-4,9,6)$ is:

Let the line $\frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-3}{4}$ lie in the plane $x-y+az+b=0$. The value of $b-a$ is:

The equation of a plane passing through the line of intersection of the planes $x+2y+3z=2$ and $x-y+z=3$ and at a distance $\frac{2}{\sqrt{3}}$ from the point $(3,1,-1)$ is $ax+by+cz-17=0$. The value of $a+b+c-17$ is:

For any two events $A$ and $B$, $P(A)=P(A|B)=1/4$ and $P(B|A)=1/2$. Then which of the following is NOT correct?