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For admission to the BSc course at Bunts Sangha's Ramanath Payyade College of Hospitality Management Studies, students need to fulfil the minimum eligibility criteria in the first place. The selection criteria for this course is Written Examination, Group discussion and Personal Interview and candidates must pass Class 12 with a 45% aggregate. The duration of the course is three years.

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhaty=log\left(\frac{1-x^2}{1+x^2}\right)\\ \Rightarrow y=log\left(1-x^2\right)-log\left(1+x^2\right)\left[?log\frac{x}{y}=logx-logy\right]\\ Differentiatingbothsidesw.r.t.x\\ \Rightarrow \frac{dy}{dx}=\frac{1}{1-x^2}.\frac{d}{dx}\left(1-x^2\right)-\frac{1}{1+x^2}.\frac{d}{dx}\left(1+x^2\right)\\ \Rightarrow =\frac{-2x}{1-x^2}-\frac{2x}{1+x^2}=\frac{-2x-2x^3-2x+2x^3}{\left(1-x^2\right)\left(1+x^2\right)}=\frac{-4x}{\left(1-x^4\right)}\\ Hence,thecorrectoptionis\left(b\right)\end{array}$

If you want to teach in a government school then yes you'll need to clear the following exams:

• CTET (Central Teacher Eligibility Test)
• State TET (like UPTET, HTET, BTET, etc.)

But if you are planning to work in private schools, preschools or even in tuition centers then PTT is enough to get you started. Many people also gain experience and then appear for CTET later.

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=\left|sinx\right|\\ Letg\left(x\right)=\left|sinx\right|andt\left(x\right)=\left|x\right|\\ \therefore f\left(x\right)=tog\left(x\right)=t\left[g\left(x\right)\right]=t\left(sinx\right)=\left|sinx\right|\\ whereg\left(x\right)andt\left(x\right)botharecontinuous.\\ \therefore f\left(x\right)=got\left(x\right)iscontinuousbutt\left(x\right)isnotdifferentiableatx=0.\\ So,f\left(x\right)isnotcontinuousatsinx=0\Rightarrow x=n\pi ,n\in Z.\\ Hence,thecorrectoptionis\left(b\right)\end{array}$

 Both of the institutions, IISER Pune and IISER Bhopal offer BS+MS courses for the duration of five years. This integrated programme is different from BSc courses as it focuses more on research papers. Now, to identify which is better, below is the comparison of Shiksha ratings of both institutes on different parameters such as course-specific, placements, infrastructure, etc. 

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=\{\begin{array}{cc}\hfill mx+1,\hfill & \hfill x\le \frac{\pi }{2}\hfill \\ \hfill sinx+n,\hfill & \hfill x>\frac{\pi }{2}\hfill \end{array}iscontinuousatx=\frac{\pi }{2}\\ R.H.L.=\underset{x\to {\frac{\pi }{2}}^{+}}{lim}\left(sinx+n\right)=\underset{h\to 0}{lim}\left[sin\left(\frac{\pi }{2}+h\right)+n\right]\\ =\underset{h\to 0}{lim}cosh+n=1+n\\ Also,L.H.L.=\underset{x\to {\frac{\pi }{2}}^{-}}{lim}\left(mx+1\right)=\underset{h\to 0}{lim}\left[m\left(\frac{\pi }{2}-h\right)+1\right]\\ =\frac{m\pi }{2}+1\\ Whenf\left(x\right)iscontinuousatx=\frac{\pi }{2}.\\ \therefore L.H.L.=R.H.L.\\ \frac{m\pi }{2}+1=1+n\Rightarrow n=\frac{m\pi }{2}\\ Hence,thecorrectoptionis\left(c\right)\end{array}$

The total tuition fee to pursue a BCom at Takshashila University ranges from INR 1.5 Lacs to INR 1.8 lakh. This fee is provided in a range because the tuition fee for a few courses is different than others. Students must note that the aforementioned fees is as per the official admission brochure. However, it is subject to change.

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=x^{2}sin\frac{1}{x}wherex\ne 0.\\ So,theValueofthefunctionfatx=0,sothatf\left(x\right)iscontinuousis0.\\ Hence,thecorrectoptionis\left(a\right)\end{array}$

Takshashila University admits students to its BCom course based on fulfilment of eligibility and selection criteria. As per the eligibility requirements, students who are interested in taking admission must have completed Class 12 from a recognised board of India. Students note that only fulfilling the eligibility criteria does not guarantee admission.

Candidates seeking course admission at Bunts Sangha's Ramanath Payyade College of Hospitality Management Studies cannot enrol for direct admission. The college admits students based on Written Examination, Group discussion and Personal Interview. Candidates looking for course admission must complete Class 12 as the basic educational qualification. Apart from the UG courses, the college also offers Diploma/ Certificate/Honours courses.

Here's a quick comparison:

Note: This information is sourced from the official website of the institute and may vary.

If you want to work in government primary schools  then D.El.Ed. + CTET is often preferred. But for private schools, PTT and NTT are widely accepted.

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=e^{\left|x\right|}\\ Weknowthatmodulusfunctioniscontinuousbutnotdifferentiableinitsdomain.\\ Letg\left(x\right)=\left|x\right|andt\left(x\right)=e^{\left|x\right|}\\ \therefore f\left(x\right)=got\left(x\right)=g\left[t\left(x\right)\right]=e^{\left|x\right|}\\ Sinceg\left(x\right)andt\left(x\right)botharecontinuousatx=0butf\left(x\right)isnotdifferentiableatx=0.\\ Hence,thecorrectoptionis\left(a\right)\end{array}$

The Institute of Cost Accountants of India (ICMAI) facilitates the CMA Final admission window throughout the year. The enrolment window for candidates who wish to appear for the CMA Final exam in June will be open until July 31. ICMAI might change the deadline for the enrolment process.

Students who wish to appear in the December term must complete their registration within this window. Candidates failing to enrol to the course before the deadline can still fill the admission form and appear for the next exam term.

1. $\frac{dq}{dt}=t=20t+8t^2$

$\Rightarrow {\displaystyle \underset{0}{\overset{q}{\int }}dq={\displaystyle \underset{0}{\overset{15}{\int }}\left(20t+8t^2\right)dt}}$

$\Rightarrow q=20\times \frac{15^2}{2}+8.\frac{15^3}{3}=11250C$

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=cotx\\ \Rightarrow f\left(x\right)=\frac{cosx}{sinx}\\ Weknowthatsinx=0iff\left(x\right)isdiscontinuous.\\ \therefore Ifsinx=0\\ \therefore x=n\pi ,n\in n\pi .\\ So,thegivenfunctionf\left(x\right)isdiscontinuousontheset\left\{x=n\pi ;n\in Z\right\}.\\ Hence,thecorrectoptionis\left(a\right)\end{array}$

The admission process includes Written Examination, Group discussion and Personal Interview for course admission at Bunts Sangha's Ramanath Payyade College of Hospitality Management Studies. The college offers BSc and BA programmes. Candidates looking for course admission must complete class 12 with a 45% aggregate.

Admission dates are important for the prospective students for admission purpose. These dealines gives students the time to submit and register themselves for the desired course at the University. Students should be regularly visit the official website and check for the new updates so as to stay informed.