AIEEE 2006 Mock Test

$ABC$ is a triangle, right-angled at $A$. The resultant of the forces acting along $AB$ and $AC$ with magnitudes $\frac{1}{AB}$ and $\frac{1}{AC}$ respectively is a force along $AD$, where $D$ is the foot of the perpendicular from $A$ onto $BC$. The magnitude of the resultant is:

Suppose a population $A$ has $100$ observations $101,102,\dots ,200$, and another population $B$ has $100$ observations $151,152,\dots ,250$. If $V_A$ and $V_B$ represent the variances of the two populations, respectively, then $\frac{V_A}{V_B}$ is:

If the roots of the quadratic equation $x^2+px+q=0$ are $\tan 30^{\circ }$ and $\tan 15^{\circ }$, respectively, then the value of $2+q-p$ is:

The value of the integral ${\int }_3^6\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dx$ is:

The number of values of $x$ in the interval $[0,3\pi ]$ satisfying the equation $2{\sin }^{2}x+5\sin x-3=0$ is: