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Chouksey Engineering College accepts students based on PET/JEE Main entrance exam scores. Students seeking to join the college need to meet the course-specific admission criteria. Hence, direct admissions may not be possible. Students can however, visit the college's official website and connect with the college via either email or phone to get more information about the admission chances of the college.

This is a Short answer type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}LetI={\displaystyle \int \frac{1+cosx}{x+sinx}}dx\\ Putx+sinx=t\Rightarrow \left(1+cosx\right)dx=dt\\ \therefore I={\displaystyle \int \frac{dt}{t}}=log\left|t\right|=log\left|x+sinx\right|+C\\ Hence,therequiredsolutionislog\left|x+sinx\right|+C.\end{array}$

This is a Short answer type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}LetI={\displaystyle \int \frac{e^{6logx}-e^{5logx}}{e^{4logx}-e^{3logx}}}dx\\ \therefore I={\displaystyle \int \frac{e^{log{x}^6}-e^{log{x}^5}}{e^{log{x}^4}-e^{log{x}^3}}}dx\\ ={\displaystyle \int \frac{x^6-x^5}{x^4-x^3}dx}={\displaystyle \int \frac{x^2\left(x^4-x^3\right)}{x^4-x^3}dx}={\displaystyle \int x^{2}dx}\\ =\frac{1}{3}{x}^3+C\\ Hence,therequiredsolutionis\frac{1}{3}{x}^3+C.\end{array}$

This is a Short answer type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}LetI={\displaystyle \int \frac{\left(x^2+2\right)}{x+1}}dx\\ \therefore I={\displaystyle \int \left[\left(x-1\right)+\frac{3}{x+1}\right]}dx\\ ={\displaystyle \int \left(x-1\right)dx}+3{\displaystyle \int \frac{1}{x+1}dx}\\ =\frac{x^2}{2}-x+3log\left|x+1\right|+C\\ Hence,therequiredsolutionis\frac{x^2}{2}-x+3log\left|x+1\right|+C.\end{array}$

The admission in the MBA score is subject to merit scored. The accepted entrance exams are CAT, MAT, etc. Fee structure for Gangadhar Meher University courses includes various components, such as facility fees, tuition fees, student welfare funds, etc. As per the overall structure, the total tuition fee for MBA is INR 90,000. The mentioned fee is as per the official website/sanctioning body. However, it is subject to change. Hence, is indicative. Given below are the key highlights for the Gangadhar Meher University MBA courses:

This is a Short answer type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}L.H.S.={\displaystyle \int \frac{2x+3}{x^2+3x}}dx\\ Put{x}^2+3x=t\\ \therefore \left(2x+3\right)dx=dt\\ \Rightarrow {\displaystyle \int \frac{dt}{t}}=log\left|t\right|\Rightarrow log\left|x^2+3x\right|+C=R.H.S.\\ L.H.S.=R.H.S.\\ Hence,proved.\end{array}$

DYPIET Pune tuition fee for the B.Tech courses ranges from INR 1.7 Lacs to INR 3.6 Lacs. The one-time fee is INR 13,500 and may be included in the total fee structure, which also comprises tuition fees, hostel fees, and other charges. Check out the following BTech fee breakup:

NOTE: The mentioned fee is taken from the official website/sanctioning body. It is still subject to change and, hence, is indicative.

Yes, Chouksey Engineering College accept Class 12th marks for admission. The basic eligibility for course admission is to pass Class 12. Chouksey Engineering College offers BTech, MTech, and MBA under two streams, i.e., Management and Engineering. Apart from the UG and PG courses, the college also offers PhD courses. 

This is a Short answer type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}L.H.S.={\displaystyle \int \frac{2x-1}{2x+3}}dx\\ \Rightarrow {\displaystyle \int \left(1-\frac{4}{2x+3}\right)}dx\left[Dividingthenumeratorbythe\text{\hspace{0.17em}denominator}\right]\\ \Rightarrow {\displaystyle \int 1.}dx-4{\displaystyle \int \frac{1}{2x+3}dx}\Rightarrow {\displaystyle \int 1.}dx-\frac{4}{2}{\displaystyle \int \frac{1}{x+\frac{3}{2}}dx}\\ \Rightarrow {\displaystyle \int 1.}dx-2{\displaystyle \int \frac{1}{x+\frac{3}{2}}dx}\Rightarrow x-2log\left|x+\frac{3}{2}\right|+C\\ \Rightarrow x-2log\left|\frac{2x+3}{2}\right|+C\Rightarrow x-log\left|{\left(\frac{2x+3}{2}\right)}^2\right|+C\\ \left[?nlogm=log{m}^n\right]\\ \Rightarrow x-log\left|{\left(2x+3\right)}^2\right|-log{2}^2+C\\ \Rightarrow x-log\left|{\left(2x+3\right)}^2\right|+C_1=R.H.S.\left[where{C}_1=C-log{2}^2\right]\\ L.H.S.=R.H.S.\\ Hence,proved.\end{array}$

In order to get enrollment in the MBA programme at the Gangadhar Meher Unievrsity, students need to fulfill the set eligibility criteria. It is important to develop further understanding of the knowlege. The below table gives idea about the eligibility criteria and the accepted exams.

Chouksey Engineering College admissions are currently open for all courses. Candidates are selected for courses based on entrance-exam scores. Aspirants can apply online on the official website of the institute. The applications are open for various courses. Interested candidates meeting the eligibility criteria can fill out the form.

This is a Long answer type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}LetI={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|sinx+cosx\right|dx}\dots \left(i\right)\\ ={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|sin\left(\frac{\pi }{4}-\frac{\pi }{4}-x\right)+cos\left(\frac{\pi }{4}-\frac{\pi }{4}-x\right)\right|dx}\left[Using{\displaystyle \underset{a}{\overset{b}{\int }}f\left(x\right)dx={\displaystyle \underset{a}{\overset{b}{\int }}f\left(a+b-x\right)dx}}\right]\\ ={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|sin\left(-x\right)+cosx\right|dx}\\ ={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|cosx-sinx\right|dx}\dots \left(ii\right)\\ Adding\left(i\right)and\left(ii\right)\\ 2I={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|cosx+sinx\right|dx}+{\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|cosx-sinx\right|dx}\\ 2I={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|\left(cosx+sinx\right)\left(cosx-sinx\right)\right|dx}\\ 2I={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}log\left|co{s}^{2}x-si{n}^{2}x\right|dx}\\ \therefore 2I={\displaystyle \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}logcos2xdx}\\ 2I=2{\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}logcos2xdx}\left[?{\displaystyle \underset{-a}{\overset{a}{\int }}f\left(x\right)dx=2{\displaystyle \underset{0}{\overset{a}{\int }}f\left(x\right)dxiff\left(-x\right)=f\left(x\right)}}\right]\\ \therefore I=\pi {\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}logcos2xdx}\\ Put2x=tdx=\frac{dt}{2}\\ Whenx=0\therefore t=0;whenx=\frac{\pi }{4}\therefore t=\frac{\pi }{2}\\ I=\frac{1}{2}{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}logcostdt}\text{\&thi}\end{array}$

$\begin{array}{l}Onadding\left(iii\right)and\left(iv\right),weget\\ 2I=\frac{1}{2}{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\left(logcost+logsint\right)dt}\\ 2I=\frac{1}{2}{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}logsintcostdt}\\ 2I=\frac{1}{2}{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{log2sintcostdt}{2}}\\ 2I=\frac{1}{2}{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\left(logsin2t-log2\right)dt}\\ 4I={\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}logsin2tdt}-{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}log2dt}\\ Put2t=u\Rightarrow 2dt=du\Rightarrow dt=\frac{du}{2}\\ \therefore 4I=\frac{1}{2}{\displaystyle \underset{0}{\overset{\pi }{\int }}logsinudu}-{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}log2dt}\left[Changingthelimit\right]\\ 4I=\frac{1}{2}\times 2{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}logsinudu}-log2{\left[t\right]}_0^{\frac{\pi }{2}}\\ 4I={\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}logsinudu}-log2.\frac{\pi }{2}\\ 4I=2I-\frac{\pi }{2}.log2\end{array}$

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

Both prontosil and Salvarsan and antibacterial drugs (antimicrobials) discovered by Paul Ehrlich. Salvarsan is also known as arsphenamine. It is an organoarsenic molecule and has -As = As- double bond.

Salvarsan and prontosil show similarity in their structure. Both of these drugs are antimicrobials. Salvarsan contains -As = As- linkage whereas prontosil has -N = N- linkage.