AIEEE 2012 PYQ Mock Test

If the integral $\int \frac{5\tan x}{\tan x-2}dx=x+a\ln |\sin x-2\cos x|+k$, then $a$ is equal to:

Statement 1: An equation of a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$ is $y=2x+2\sqrt{3}$.Statement 2: If the line $y=mx+\frac{4\sqrt{3}}{m},(m\ne 0)$ is a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$, then $m$ satisfies $m^4+2m^2=24$.

Let $A=\left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 3& 2& 1\end{array}\right]$. If $u_1$ and $u_2$ are column matrices such that $A{u}_1=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$ and $A{u}_2=\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]$, then $u_1+u_2$ is equal to:

If $n$ is a positive integer, then $(\sqrt{3}+1{)}^{2n}-(\sqrt{3}-1{)}^{2n}$ is:

If 100 times the 100th term of an AP with non-zero common difference equals 50 times its 50th term, then the 150th term of this AP is: