Mathematics Mock Test - 6

Find the area of the parallelogram whose adjacent sides are given by the vectors $(3,1,4)$ and $(1,-1,1)$.

The solution of linear inequalities $x+y\ge 5$ and $x-y\le 3$ lies:

The system of equations:$\alpha x+y+z=\alpha -1$$x+\alpha y+z=\alpha -1$$x+y+\alpha z=\alpha -1$ has no solution, if $\alpha$ is:

If the curve $y=a\sqrt{x}+bx$ passes through the point $(1,2)$ and the area bounded by the curve, the line $x=4$, and the x-axis is $8$ sq. units, then:

Evaluate $\int \frac{{\sec }^2(\ln x)}{x}dx$.