$Assertion (A)$: van der Waals' forces are responsible for chemisorption. $Reason (R)$: High temperature is favourable for chemisorption. The correct answer is

When a wave traverses a medium,the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$,where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

Perlon is

Which of the following statements are true regarding Bohr's model of the hydrogen atom?
$(I)$ Orbiting speed of the electron decreases as it shifts to discrete orbits away from the nucleus.
$(II)$ Radii of allowed orbits of the electron are proportional to the principal quantum number.
$(III)$ Frequency with which electrons orbit around the nucleus in discrete orbits is inversely proportional to the cube of the principal quantum number.
$(IV)$ Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits.
Select the correct answer using the codes given below.

At a given instant of time,the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is:

The lengths of tangent,subtangent,normal,and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$,and $D$ respectively. Then their increasing order is: