Maths — Mock Test

Evaluate $\lim_{x\to 0}\frac{\sin(3x)}{5x}$.

If $f(x)=\frac{x^{2}+1}{x}$, then $f'(1)$ is

If $\tan(\theta)=\frac{1}{2}$, then $\cos(2\theta)$ is

The general solution of $\cos(x)=0$ is

The perpendicular distance of the point $(2,-1)$ from the line $3x+4y-5=0$ is

The centre and radius of the circle $x^{2}+y^{2}-6x+4y-3=0$ are respectively

The focus of the parabola $y^{2}=12x$ is

The distance between the points $(1,2,3)$ and $(3,-2,0)$ is

In an arithmetic progression, the $7$th term is $20$ and the $13$th term is $38$. The $20$th term is

The coefficient of $x^{3}$ in the expansion of $(1+2x)^{5}$ is