AIEEE 2003 (Maths) Mock Test

If in a triangle $ABC$, $a{\cos }^2\left(\frac{C}{2}\right)+c{\cos }^2\left(\frac{A}{2}\right)=\frac{3b}{2}$, then the sides $a,b$ and $c$:

In a triangle $ABC$, medians $AD$ and $BE$ are drawn. If $AD=4$, $\angle DAB=\frac{\pi }{6}$ and $\angle ABE=\frac{\pi }{3}$, then the area of the $\Delta ABC$ is:

The trigonometric equation ${\sin }^{-1}x=2{\sin }^{-1}a$, has a solution for:

The upper $\frac{3}{4}$ th portion of a vertical pole subtends an angle ${\tan }^{-1}\frac{3}{5}$ at point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is:

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ equal to: