CUET Mathematics Mock Test - 4

Find the distance between the straight line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{1}$ and the plane $x-y+z-5=0$.

The minimum value of $3x+5y$ such that:$3x+5y\le 15$$4x+9y\le 18$$13x+2y\le 2$$x\ge 0,y\ge 0$ is:

What is the area of one of the loops between the curve $y=c\sin x$ and the x-axis?

Two models, $P$ and $Q$, of a product earn profits of $\text{₹}100$ and $\text{₹}80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respectively, while the total production time available is $150$ hours. For a total batch size of $40$, the objective function $Z$ is subjected to the constraints:

Find the area under the curve $y=x+2$, bounded by the x-axis and the y-axis.