AIEEE 2013 PYQ Mock Test

${\lim }_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to:

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$ -sided regular polygon. If $T_{n+1}-T_n=10$, then the value of $n$ is:

At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\frac{dP}{dx}=100-12\sqrt{x}$. If the firm employs $25$ more workers, then the new level of production of items is:

Statement - I: The value of the integral ${\int }_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\pi /6$.Statement - II: ${\int }_a^{b}f(x)dx={\int }_a^{b}f(a+b-x)dx$.

If $P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$ is the adjoint of a $3\times 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to: