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$\frac{1}{x\left(x^n+1\right)}=\frac{x^{n-1}}{x^{n-1}\cdot x\left(x^n+1\right)}=\frac{x^{n-1}}{x^n\left(x^n+1\right)}$

Putting xⁿ = t Þ n x^{n- 1}dx = dt

$\begin{array}{l}\therefore {\displaystyle \int \frac{dx}{x\left(x^n+1\right)}}={\displaystyle \int \frac{x^{n-1}dx}{x^n\left(x^n+1\right)}}=\frac{1}{n}{\displaystyle \int \frac{dt}{t(t+1)}}\\ =\frac{1}{n}{\displaystyle \int \frac{(t+1-t)}{t(t+1)}}dt\\ =\frac{1}{n}{\displaystyle \int \left\{\frac{t+1}{t(t+1)}-\frac{t}{t(t+1)}\right\}}dt.\\ =\frac{1}{n}\left\{{\displaystyle \int \frac{dt}{t}}-{\displaystyle \int \frac{dt}{t+1}}\right\}\\ =\frac{1}{n}\{logt-log(t+1)\}+C.\\ =\frac{1}{n}log?\frac{t}{t+1}+\; C\\ =\frac{1}{n}log\left|\frac{x^n}{x^n+1}\right|+C.\end{array}$

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer – (c)

Explanation – R/S= (l₁/100-l₁)= 100 (2.9/100-2.9)= 100/97.1=2.98ohm

So he should change S to almost 3 ohm and repeat the experiment.

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$\begin{array}{l}\Rightarrow A=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\\ Andfrom\left(1\right)weget,-\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\\ \therefore {\displaystyle \int \frac{dx}{y^2-1}}=\frac{1}{2}{\displaystyle \int \frac{dx}{y-1}}-\frac{1}{2}{\displaystyle \int \frac{dx}{y+1}}\\ =\frac{1}{2}{\displaystyle \int \frac{dx}{x^2-1}}-\frac{1}{2}{\displaystyle \int \frac{dx}{x^2-1}}\left\{y=x^2\right\}\\ =\frac{1}{2}\times \frac{1}{2\cdot 1}log\left|\frac{x-1}{x+1}\right|-\frac{1}{2}ta{n}^{-1}x+\; C\\ =\frac{1}{4}log\left|\frac{x-1}{x+1}\right|-\frac{1}{2}ta{n}^{-1}x+\; C\end{array}$

Some of the most common Figures of Speech are as follows:

·       Simile

·       Metaphor

·       Personification

·       Hyperbole.

This is not the exact or absolute list, but are among the commonly used Figures of Speech. 

Yes, candidates with a  45% aggregate marks in Class 12 from a recognised board are eligible to apply for the BCom programme at NCAS. Having 40% marks meets the eligibility requirement, allowing students to proceed with the application process.

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This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (a)

Explanation- eeq= $\frac{e_2{r}_{1+}{e}_2{r}_1}{r_1+r_2}$

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Admission to the BCom programme at Nazareth College of Arts and Science is determined purely by merit. Selection is based on the students' Class 12 academic results, with no entrance examination needed. The college assesses applications by examining academic performance and releases merit lists to finalise the admission process.

Figures of Speech are literary devices which add value to a sentence by providing an imagery, special effect and contrasts to create a vivid impact, drama element and improve the reader engagement. Figures of Speech is widely used in literature such as poems, drama or plays, novels, short stories, etc. Apart from that, Figures of Speech are also used in day to day lives and commercial purposes such as advertisement campaigns.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (b)

Explanation- as we know that J=E, and current density is directly proportional to electric field, so electric field produced by charges accumulated on the surface of wire.

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This is a long answer type question as classified in NCERT Exemplar

Given volume V = 1m³

area = 0.01mm²

= 8.01 $\times {10}^{-6}$ m²= ${10}^{-8}$ m²

Temperature both inside and outside are equal

So initial pressure inside the box = 1.50atm

Final pressure inside the box= 0.1atm

Assuming V_x= speed of nitrogen molecule in x direction

n_i = number of molecules per unit volume in a time interval of $?T$

Let area of the wall, number of particles colliding in time

$?t$ = $\frac{1}{2}n$ _i (v_{x $?t$} )A , here we use ½ because particle moves both in positive and negative direction.

V_x²+ V_y²+ V_z²= V_rms²

V_x²= V_rms²/3 if all three velocities are equal.

½ mv_rms²= 3/2K_BT/m

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This is a Short Answer Type Questions as classified in NCERT Exemplar

Explanation- according to ohms law

I= $\frac{V_{eff}}{R_{eff}+R}$

If voltage and resistance increase

V'= nVeff, R'= nReff

I'= $\frac{\mathrm{n}\mathrm{V}\mathrm{e}\mathrm{f}\mathrm{f}}{\mathrm{n}\mathrm{R}\mathrm{e}\mathrm{f}\mathrm{f}+\mathrm{n}\mathrm{R}}=$ $\frac{V_{eff}}{R_{eff}+R}$ =

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