AIEEE 2011 PYQ Mock Test

$\frac{d^{2}x}{d{y}^2}$ equals:

If $\frac{dy}{dx}=y+3>0$ and $y(0)=2$, then $y(\ln 2)$ is equal to:

Let $\mathbb{R}$ be the set of real numbers.Statement-1 : $A=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x-y\text{ is an integer}\}$ is an equivalence relation on $\mathbb{R}$.Statement-2 : $B=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x=\alpha y\text{ for some rational number }\alpha \}$ is an equivalence relation on $\mathbb{R}$.

The value of ${\int }_0^{1}8\frac{\ln (1+x)}{1+x^2}dx$ is:

Let $\alpha ,\beta$ be real and $z$ be a complex number. If $z^2+\alpha z+\beta =0$ has two distinct roots on the line $\text{Re}(z)=1$, then it is necessary that: