Subject Experts Solutions for Chapter: Solved Paper 2017 (II), Exercise 1: PAPER I : Mathematics

If $l_1=\frac{d}{dx}\left(e^{\sin x}\right)$

$l_2=\underset{h\to 0}{\lim }\frac{e^{\sin \left(x+h\right)}-e^{\sin x}}{h}$

$l_3=\int e^{\sin x}\cos xdx$

then which one of the following is correct?

The general solution of $\frac{dy}{dx}=\frac{ax+h}{by+k}$ represents a circle only when

If $\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sin x}{x}=l$ and $\underset{x\to \infty }{\lim }\frac{\cos x}{x}=m$, then which one of the following is correct $?$

What is ${\int }_0^{2\pi }\sqrt{1+\sin \frac{x}{2}}dx$ equal to $?$

The area bounded by the curve $\left|x\right|+\left|y\right|=1$ is

If $x$ is any real number, then $\frac{x^2}{1+x^4}$ belongs to which one of the following intervals?

The left-hand derivative of $f\left(x\right)=\left[x\right]\sin \left(\pi x\right)$ at $x=k$ where $k$ is an integer and $\left[x\right]$ is the greatest integer function, is

If $f\left(x\right)=\frac{x}{2}-1$, then on the interval $\left[0,\pi \right]$ which one of the following is correct $?$