Class 12th

The magnetizing force applied to a material is called the Magnetic intensity (H) and the total magnetic effect inside a material is called the magnetic field (B), it includes both the applied magnetic field and the material's response (magnetization).
Following is the formula showing the relation:
B =? (H + M)
Where? is the permeability of free space and M is magnetization.

This is a True or False Type questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}False.\\ Letustakeanexample:f\left(x\right)=sinxandg\left(x\right)=cotx\\ \therefore f\left(x\right).g\left(x\right)=sinx.cotx=sinx.\frac{cosx}{sinx}=cosxwhichiscontinuousatx=0butcotxisnot\\ continuousatx=0.\end{array}$

This is a True or False Type questions as classified in NCERT Exemplar

Sol: $True.$

This is a True or False Type questions as classified in NCERT Exemplar

Sol: $True.Weknowthatthesumanddifferenceoftwoormorefunctionsisalwayscontinuous.$

This is a True or False Type questions as classified in NCERT Exemplar

Sol: $True.Weknowthatthefunctioniscontinuousfunctiononitsdomain.$

This is a True or False Type questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}False.Giventhatf\left(x\right)=\left|x-1\right|in\left[0,2\right]\\ Weknowthatthefunctionisnotdifferentiable.So.itisfalse.\end{array}$

This is a Fill in the Blanks Type questions as classified in NCERT Exemplar

Sol:

This is a Fill in the Blanks Type questions as classified in NCERT Exemplar

Sol:

This is a Fill in the Blanks Type questions as classified in NCERT Exemplar

Sol:

This is a Fill in the Blanks Type questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhaty=x^{2}andt=x^3\\ Differentiatingbothfunctionsw.r.t.x\\ \Rightarrow \frac{dy}{dx}=2xand\frac{dt}{dx}=3x^2\\ \therefore \frac{dy}{dt}=\frac{dy/dx}{dt/dx}=\frac{2x}{3x^2}=\frac{2}{3x}\\ So,thederivativeof{x}^{2}w.r.t.x^{3}is\frac{2}{3x}\end{array}$