Find the equation of the plane which contains the line of intersection of the planes $x+2 y+3 z-4=0,2 x+y-z+5=0$ and which is perpendicular to the plane $5 x+3 y-6 z+8=0$.
The probability of a shooter hitting a target is $\frac{3}{4}$. How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99 ?
Solve the following linear programming problem graphically. Minimise and Maximise $Z =3 x+9 y$ Subject to constraints : $x+3 y \leq 60, x+y \geq 10, x \leq y, x \geq 0, y \geq 0$.
Find the vector equation of the line passing through the point $(1,2,-4)$ and perpendicular to the two lines $\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}$ and $\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5}$.
$A = R -\{3\}, B = R -\{1\}$ consider the function $f: A \rightarrow B$ defined by $f(x)=\frac{x-2}{x-3}$. Is $f$ bijective? If yes then find Inverse function of $f$.