Amit M Agarwal Solutions for Chapter: Graphical Transformations, Exercise 1: Proficiency in 'Graphical Transformations' Exercise 1

The number of integral roots of the equation $x^2=1-\left|x-5\right|$

The number of real solutions of the equation $1-x=\left[\cos x\right]$ is:

The number of solutions of $[\sin x+\cos x]=3+[-\sin x]+[-\cos x]$ in the interval $[0,2\mathrm{\pi }]$ is (where $[ . ]$ denotes the greatest integer function.)

The equation $2^{\left|x^2-12\right|}=\sqrt{e^{\left|x\right|\log 4}}$ has:

Remark: Base of logarithm is $e$.

The number of real roots of the equation $x^2+x+3+2\sin x=0, x\in [-\mathrm{\pi },\mathrm{\pi }]$ is:

The number of roots of the equation $x^3+x^2+2x+\sin x=0$ in $[-2\mathrm{\pi },2\mathrm{\pi }]$ is:

The number of roots of the equation $1+3^{\frac{x}{2}}=2^x$ is:

The equation $x^2-2=\left[\sin x\right]$, where $[ . ]$ denotes the greatest integer function, has: