AIEEE 2008 PYQ Mock Test

The value of $\int \frac{\sin x}{\sin (x-\pi /4)}dx$ is:

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

Let $a,b,c$ be any real numbers. Suppose that there are real numbers $x,y,z$ not all zero such that $x=cy+bz$, $y=az+cx$ and $z=bx+ay$. Then $a^2+b^2+c^2+2abc$ is equal to:

Let $A$ be a square matrix all of whose entries are integers. Then which one of the following is true?

The quadratic equations $x^2-6x+a=0$ and $x^2-cx+6=0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4:3$. Then the common root is: