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When connected in series, equivalent capacitance,

$C_1=\frac{C*C}{C+C}=\frac{C}{2}$            

When connected in parallel, equivalent capacitance

C₂ = C + C = 2C

$\frac{C_1}{C_2}=\frac{C/2}{2C}=\frac{1}{4}$            

$P{A}^2+P{B}^2=co{s}^2\theta +{\left(sin\theta -3\right)}^2+co{s}^2\theta +{\left(sin\theta +6\right)}^2$

= 2 cos² θ + 2 sin² θ + 6 sin q + 45

= 6 sin θ + 47

for maximum of PA² + PB², sin θ = 1

then P (1, 2)

Hence P, A & B will lie on a straight line.

Students should compare aspects like available specialisations, faculty experience, practical training opportunities, placement support, infrastructure, and industry exposure. Additionally, factors such as seat intake, college reputation, location, and student reviews can help determine whether ITM Institute of Hotel Management offers a better fit than other institutions for the BBA programme.

The Columbia University cost of attendance, varies, depending on the choice of the course and the type of accommodation, a student opts for. The average cost of undergraduate courses at Columbia ranges between USD 58,689-USD 67,481 (INR 51.5 L-INR 59.1 L), while that of graduate courses ranges between USD 23,064-USD 140,443 (INR 20.2 L-INR 1.23 Cr) per year.  While the annual cost of attendance is around USD 22,247 (INR 19.5 L) per year. 

Students can estimate the 4 year tuition cost, from the costs mentioned above. 

Given

$\left(x\right)=\{\begin{array}{l}2sin\left(\frac{-\pi x}{2}\right),x<-1\\ \left|a{x}^2+x+b\right|,-1\le x\le 1\\ sin\pi x,x>1\end{array}$

If f (x) is continuous for all $x\in R$ then it should be continuous at x = 1 & x = -1

At x = -1, L.H.L = R.H.L. Þ 2 = |a + b - 1|

=>a + b – 3 = 0  OR  a + b + 1 = 0 . (i)

=>a + b + 1 = 0 . (ii)

           (i) & (ii), a + b =-1

The total tuition fee for the MBBS course at Kerala University of Health Sciences ranges from INR 1.1 Lacs to INR 5.4 lakh. Additionally, the total tuition fee for MBBS at BFUHS ranges from INR 7.8 Lacs to INR 33 lakh. 

The institute offers a BTech, MTech, BBA and BCA courses. Candidates must complete Class 12 as the basic eligibility criteria. Students can check the points mentioned below to know the course stream:

• Business & Management Studies
• Engineering
• IT & Software

Yes, the India Today 2024 rankings for Hotel/Hospitality Management included the BBA programme offered by ITM Institute of Hotel Management, placing the institute at the 53rd spot nationally. This recognition from a reputable ranking body reinforces the programme’s credibility and the institute’s dedication to delivering high-quality education in the hospitality and management fields.

Given f(X) = ${\displaystyle {\int }_1^x\frac{lo{g}_{e}t}{\left(1+t\right)}dt............\left(i\right)}$  

So  $f\left(\frac{1}{x}\right)={\displaystyle {\int }_1^{1/x}\frac{\lambda lo{g}_{e}t}{1+t}dt}............\left(ii\right)$

put $t=\frac{1}{z}thendt=-\frac{1}{z^2}dz$

$f\left(\frac{1}{x}\right)={\displaystyle {\int }_1^x\frac{lo{g}_{e}t}{t\left(1+t\right)}}dt............\left(iii\right)$    

(i) + (iii), f(x) + $f\left(\frac{1}{x}\right)={\displaystyle {\int }_1^x\left(\frac{lo{g}_{e}t}{1+t}+\frac{lo{g}_{e}t}{t\left(1+t\right)}\right)dt}$

$={\left[\frac{{\left(lo{g}_{e}t\right)}^2}{2}\right]}_1^x=\frac{{\left(lo{g}_{x}x\right)}^2}{2}$  

Hence f(e) + $f\left(\frac{1}{e}\right)=\frac{1}{2}$

In 2024, the BBA programme at ITM Institute of Hotel Management contributed to the institute securing the 53rd position in the India Today rankings for Hotel/Hospitality Management. This ranking highlights the programme's quality, strong curriculum, and industry relevance, reflecting ITM's commitment to preparing students for successful careers in the competitive hospitality sector.

$i=\frac{6-4}{2+8}=0.2A$

$V_x+4+0.2\times 8=V_Y$

$\Rightarrow V_Y-V_X=5.6V$

The final step for securing admission to the BBA programme at ITM Institute of Hotel Management involves confirming selection by submitting all required documents and completing the tuition fee payment of INR 6.9 Lacs - INR 12 Lakh. Candidates will be officially notified of their selection through the college website or via their registered contact details.

For admission to the BBA programme at ITM Institute of Hotel Management, students need to provide Class 12 mark sheets, proof of identity, recent passport-size photographs, and any other documents requested by the institute. These documents are necessary for verification and must be submitted along with the completed application during the admission process.

Yes, final year candidates can apply for GATE (even if their results are not declared). Candidates must mention complete and correct details regarding their educational qualifications while filling out the application form. 

NOTE: Your final results are not required at the time of filling out the application form. Candidates must provide only the documents prescribed by the GATE authorities. 

However, make sure to keep a provisional certificate or a certificate from your Head of Department confirming your current enrollment, as it will be required at the time of admission or PSU recruitment. 

For line of intersection of two planes

put z = $\lambda$ then

$x+2y=6-\lambda \&y=4-2\lambda \Rightarrow x+2\left(4-2\lambda \right)=6-\lambda$           

=> $x=3\lambda -2$

Now $\overrightarrow{a}.\overrightarrow{PQ}=0gives9\lambda -15+4\lambda -4+\lambda -1=0$

$So,P\left(\frac{16}{7},\frac{8}{7},\frac{10}{7}\right)=P\left(\alpha ,\beta ,\gamma \right)$

$\Rightarrow 21\left(\alpha +\beta +\gamma \right)=21\times \frac{34}{7}=102$

The institute offers various courses such as BTech, MTech, BBA and BCA. The selection criteria are a mix of entrance exams and merit-based as per the respective courses.  Students can check the table below to know some of the course tuition fees at DPGITM:

Note: This information is sourced from official website/ sanctioning body and is subject to change.

$p=\frac{h}{\lambda }$  

So, two photons having equal linear momenta have equal wavelength. As wavelength decreases, momentum and energy of photon increases.

Given x + 2y – 3z = a

2x + 6y – 11z = b

x – 2y + 7z = c

Here $\begin{array}{cc}\hfill \hfill & \hfill \hfill \\ \hfill \hfill & \hfill \hfill \\ \hfill \hfill & \hfill \hfill \end{array}\begin{array}{cc}\hfill \begin{array}{l}\\ \end{array}\hfill & \hfill \hfill \end{array}$

$\Delta =\left|\begin{array}{ccc}\hfill 1\hfill & \hfill 2\hfill & \hfill -3\hfill \\ \hfill 2\hfill & \hfill 6\hfill & \hfill -11\hfill \\ \hfill 1\hfill & \hfill -2\hfill & \hfill 7\hfill \end{array}\right|\begin{array}{cc}\hfill \begin{array}{l}=\left(42-22\right)-2\left(14+11\right)-3\left(-4-6\right)\\ \end{array}\hfill & \hfill =20-50+30=0\hfill \end{array}$

For infinite solution ${}_{}{}_{}{}_{}$

20a – 8b – 4c = 0 5a = 2b + c

Yes, applications are open at DPG Institute of Technology and Management for various courses. The mode of application is online. Aspirants need to apply at the official website for admission to the various programme. Candidates can fill out the application form on the institute's official website.

The Columbia University MS in CS fees, for international students is around USD 64,800 or INR 56.75 L for the first year. The cost is the same for all graduate engineering programs with 12 points per semester, and tends to typically increase by 2-7% from second year onwards.

The overall Columbia University cost of attendance for international students, enrolled in graduate engineering courses, with 12 points or more per semester, is USD 103,304 or INR 90.5 L.