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Linear mass density,  $\lambda ={\lambda }_0\left(1-\frac{x^2}{L^2}\right)kg/m$

$M={\displaystyle \int \lambda dx}={\displaystyle \underset{0}{\overset{L}{\int }}{\lambda }_0\left(1-\frac{x^2}{L^2}\right)dx}$

$={\lambda }_0\left(L-\frac{L^3}{3L^2}\right)=\frac{2L{\lambda }_0}{3}$

$As,x_C=\frac{3L}{\alpha }=\frac{9}{8}L.\Rightarrow \alpha =\frac{3\times 8}{9}=8/3$

BCom course at Indus College is a three-year undergraduate programme divided into six semesters. It combines academic knowledge with practical insights, making it ideal for students aiming to enter the commerce field. The structured curriculum helps students build a strong foundation in business concepts, preparing them for various career opportunities or further studies.

Krea University offers courses at UG, PG and doctoral levels IFMR Graduate School of Business and School of Interwoven Arts and Sciences (SIAS). The university offers BA/ BA (Hons), BSc/ BSc (Hons) and Integrated BBA at UG level. The university offers a two-year MBA programme at the PG level. Admission to all the offered programmes is entrance-based.

h = 39.2 + 19.6 = 58.8 m

Height above tower

$h\text{'}=\frac{u^2}{2g}=\frac{19.6\times 19.6}{2\times 9.8}$

= 19.6

$As,\frac{k}{5}=78.4\Rightarrow k=392$

IHM Meerut offers admission to various UG level courses on the basis of merit and accepted entrance exam. For courses such as BHMCT, candidates must secure a minimum aggregate in Class 12 and must secure valid scores in CUET UG exam, as suggested by the IHM Meerut. Candidates must analyse previous year trend to understand the probability of seeking admission at IHM Meerut for BHMCT.

$x\left(1-x^2\right)\frac{dy}{dx}+\left(3x^{2}y-y-4x^3\right)=0$

$\Rightarrow x\left(1-x^2\right)\frac{dy}{dx}+\left(3x^2-1\right)y=4x^3$

$\Rightarrow y=2x-1\left(x^3-x\right)\therefore y\left(3\right)=-18$

ISB&M College of Commerce admissions are based on merit and entrance exams. The college considers scores in MAH-CET for admission. To get online admission to ISB&M Institute,  candidates must check the official website of the institute. For offline ISB&M admission, candidates can download the application form from the website or they can also collect the same from ISB&M College of Commerce campus. 

Yes, candidates need to have a valid score in any of the accepted entrance exams for admission at Krea University. The university accepts scores in CUET-UG, ACT or SAT for admission in BA/ BA (Hons) programme. Aspirants without score in any of the accepted entrance tests can appear for KREA Aptitude Test for admission. Selected aspirants are further required to pass a personal interview round for final admission.

f = 20 kHz

Deviation ratio = 10

NIT Puducherry offers BTech and M.Tech programmes as it popular programmes. The university offers these programmes to students at the UG and PG levels. The university is mainly concerned with streams such as Engineering and Science. Further, the university offerfs a BTech programme to students for a duration of 4 years and M.Tech for a duration of 2 years. 

ISB&M College of Commerce is ranked one of the top commerce colleges. The college is ranked by various prominent ranking agencies such as IIRF, Times B-Schools, GHRDC BBA College Survey, and others. Some of the recent ISB&M College of Commerce rankings 2025 are tabulated below:

$\left[\frac{x}{\sqrt[]{x^2-y^2}}+e^{y/x}\right]x\frac{dy}{dx}=x+\left[\frac{x}{\sqrt[]{x^2-y^2}}+e^{y/x}\right]y$

$\Rightarrow e^{y/x}\left[xdy-ydx\right]=xdx+\frac{x}{\sqrt[]{x^2-y^2}}\left(ydx-xdy\right)$

$\Rightarrow e^{y/x}d\left(y/x\right)=\frac{dx}{x}-\frac{d\left(y/x\right)}{\sqrt[]{1-{\left(y/x\right)}^2}}$

Integrating

$e^{y/x}=\mathcal{l}nx-si{n}^{-1}\left(\frac{y}{x}\right)+c$

Passes (1, 0)

1 = c

$\Rightarrow \alpha =\frac{1}{2}exp\left(\sqrt[]{e}-1+\frac{\pi }{6}\right)$

Candidates who have passed Class 12 can apply for the BA/ BA (Hons) programme at Krea University. Applicant should be less than 21 years of age as of August 1 of that year. 

n.p.m. transistor current gain B = 100

As, B = $\frac{I_C}{I_B}Voltagegain,\frac{V_{out}}{V_{in}}=\left(\frac{I_C}{I_B}\right)\frac{R_2}{R_i}$

$V_{out}=\frac{B{R}_2}{R_{in}}Vin$

$\frac{10^3}{10^3}V=1v$

For admission to IHM Meerut, candidates must visit the official website of the Institute to fill out the application form. After a successful application submission, candidates will be shortlisted based on the provided eligiblity criteria. Furthermore, candidates must meet the cutoff of the entrance exams to be shortlisted. For final admission, shortlisted candidates must pay the fees and confirm the seat. 

 $\frac{1}{{\lambda }_{\text{min}}}=R\left[\frac{1}{1}-\frac{1}{\mathrm{\infty }}\right]=R\mathrm{}[n=\mathrm{\infty }\to n=1]$

$\frac{1}{{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}}=\mathrm{R}\left[\frac{1}{1}-\frac{1}{4}\right]=\frac{3\mathrm{R}}{4}\mathrm{}[\mathrm{n}=2\to \mathrm{n}=1]$

$\Rightarrow \mathrm{\Delta }\lambda \Rightarrow \frac{4}{3R}-\frac{1}{R}\mathrm{}\Rightarrow \mathrm{}\frac{1}{3R}=340$

For Paschan $\Rightarrow \frac{1}{{\lambda }_{\text{min}}}=R\left[\frac{1}{9}\right]\mathrm{}[\mathrm{n}=\mathrm{\infty }\to \mathrm{h}=3]$

$\Rightarrow \frac{1}{{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}}=\mathrm{R}\left[\frac{1}{9}-\frac{1}{16}\right]=\frac{7\mathrm{R}}{144}$

$\Rightarrow \mathrm{\Delta }\lambda =\frac{81}{7\mathrm{R}}$

ISB&M College of Commerce has an experienced faculty with PhD holders and individuals with higher degrees. The faculty are experienced with several years of teaching. It focuses on theoretical and practical knowledge for the students. The faculty engages the students with the latest activities and innovative teaching, and quality research. ISB&M COC also invites guest faculty for guest lectures and offers the opportunity for students to interact with some of the best personalities.