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 10 = $\frac{1}{2}a{t}^2...............\left(1\right)and$                        

$10+x=\frac{1}{2}a{\left(2t\right)}^2................\left(2\right)$  

$\Rightarrow X=\frac{1}{2}A\left[{\left(2t\right)}^2-t^2\right]=3\left(\frac{1}{2}a{t}^2\right)=30m$  

Let point P : (h, k)

Therefore according to question,  ${\left(h-1\right)}^2+{\left(k-2\right)}^2+{\left(h+2\right)}^2+{\left(k-1\right)}^2=14$

$\therefore$ locus of P(h, k) is $x^2+y^2+x-3y-2=0$  

Now intersection with x – axis are  $x^2+x-2=0\Rightarrow x=-2,1$  

Now intersection with y – axis are  $y^2-3y-2=0\Rightarrow y=\frac{3\pm \sqrt[]{17}}{2}$  

Therefore are of the quadrilateral ABCD is =  $\frac{1}{2}\left(\left|x_1\right|+\left|x_2\right|\right)\left(\left|y_1\right|+\left|y_2\right|\right)=\frac{1}{2}\times 3\times \sqrt[]{17}=\frac{3\sqrt[]{17}}{2}$  

Hillwoods Academy of Higher Education duration varies from course to course. The academy offers three full-time programmes at the undergraduate and postgraduate levels. Students can check out the table to know about the duration of the programmes offered at the institute:

$\frac{dy}{dx}+2ytanx=sinx,\therefore I.F.e^{{\displaystyle \int 2tanxdx}}=se{c}^{2}x$  

= cos x – 2 cos² x = $-2{\left(cosx-\frac{1}{4}\right)}^2+\frac{1}{8}\therefore y_{max}=\frac{1}{8}$

To apply for the courses offered at Hillwoods Academy of Higher Education, you can visit the official website and fill out the enquiry form available online. According to the website, you may also apply offline by going to the institute's campus. The filled in form needs to be submitted along with the documents and fees as told by Hillwoods Academy of Higher Education.

$a=\underset{n\to \infty }{lim}{\displaystyle \sum _{k=1}^n\frac{2n}{n^2+k^2}=\underset{n\to \infty }{lim}\frac{1}{n}}{\displaystyle \sum _{k=1}^n\frac{2}{1+{\left(\frac{k}{n}\right)}^2}}$

 $\therefore a={\displaystyle {\int }_0^1\frac{2}{1+x^2}dx=2ta{n}^{-1}x}]{}_0^1=\frac{\pi }{2}$

⇒ $f\text{'}\left(\frac{a}{2}\right)=\sqrt[]{2}f\left(\frac{a}{2}\right)$

Yes, you can get into Hillwoods Academy of Higher Education with 85%. The institute selects students either on an entrance or a merit basis. The minimum percentage generally ranges from 45% to 60% as per the course. But, you must note that the selection criteria is different for each programme and just securing the percentage may not be enough to get into the academy. Students can contact the admission desk of the academy to know more.

$\frac{dT}{dt}=-k\left(T-T_0\right)$  

$\frac{dT}{\left(T-T_0\right)}=-kdt$  

$\Rightarrow k=-\frac{1}{6}\mathcal{l}n\left(\frac{2}{3}\right)$             - (1)

Now $\frac{dT}{dt}=-k\left(T-T_0\right)$

t = 10.257

t₂ = 6 + 10.257 = 16.257 minutes

16.25 and or 16

$f\left(x\right)=\{\begin{array}{cc}\hfill x^3-x^2+10x-7,\hfill & \hfill x\le 1\hfill \\ \hfill -2x+lo{g}_2\left(b^2-4\right),\hfill & \hfill x>1\hfill \end{array}$  

If f(x) has maximum value at x = 1 then

$f\left(1\right)\le f\left(1\right)\Rightarrow -2+lo{g}_2\left(b^2-4\right)\le 1-1+10-7$

$\Rightarrow lo{g}_2\left(b^2-4\right)\le 5\Rightarrow 0<b^2-4\le 32$

$\Rightarrow b^2-4>0\Rightarrow b\in \left(-\infty ,-2\right)\cup \left(2,\infty \right)$         …….(i)

$And{b}^2-4\le 32\Rightarrow b\in \left[-6,6\right]$                      …….(ii)

From (i) and (ii) we get  $b\in [-6,-2)\cup (2,6]$  

$Q=\Delta \upsilon +w\Rightarrow nC\Delta T=n{C}_v\Delta T=\frac{nC\Delta T}{4}=\frac{3}{4}nC\Delta T=n{C}_v\Delta T$

$C=\frac{4}{3}{C}_v=\frac{4}{3}\times \frac{3}{2}R=2R$

$f\left(x\right)=\{\begin{array}{cc}\hfill x+a,\hfill & \hfill x?0\hfill \\ \hfill \left|x?4\right|,\hfill & \hfill x>0\hfill \end{array}\text{?}\text{?}\text{?}\text{?}and\text{?}\text{?}\text{?}g\left(x\right)=\{\begin{array}{cc}\hfill x+1,\hfill & \hfill x<0\hfill \\ \hfill {\left(x?4\right)}^2+b,\hfill & \hfill x?0\hfill \end{array}$

$?$    f (x) and g (x) are continuous on R $?$  a = 4 and b = 1 – 16 = 15

then (gof) (2) + (fog) (-2) = g (2) + f (-1) = -11 + 3 = -8

The reporting time for the CUET PG exam depends on the exam center and the shift allotted to the candidates. There are 3 shifts which start at:

1. 8.30 AM

2. 12.30 PM

3. 3.00 PM

Please arrive 1 hour before your exam.

To get admission in Hillwoods Academy of Higher Education, you need to go through the steps listed below:

Step 1: Check the eligibility criteria and then apply online or offline.

Step 2: Go through the selection rounds. This may include profile score, submission of entrance test scores, personal interview, qualifying exam marks, etc.

Step 3: Pay the fees to complete the process.

given N = 1000 turns

A = 1m²

$\omega =1rev/sec$

$=1\times 2\pi rad/sec$

$V=\frac{-d{?}_B}{dt}=\frac{-d}{dt}\left(NBAcos\omega t\right)$  

=  $140\times \frac{22}{7}$  

= 20 × 22

= 440 volts

$f\left(x\right)=\{\begin{array}{l}\frac{lo{g}_e\left(1-x+x^2\right)+lo{g}_e\left(1+x+x^2\right)}{secx-cosx},x\in \left(\frac{-\pi }{2},\frac{\pi }{2}\right)-\left\{0\right\}\\ k,x=0\end{array}$ for continuity at x = 0

      $\underset{x\to 0}{lim}f\left(x\right)=k\therefore k=\underset{x\to 0}{lim}\frac{lo{g}_e\left(1+x^2+x^4\right)}{secx-cosx}\left(\frac{0}{0}form\right)=\underset{x\to 0}{lim}\frac{cosxlo{g}_e\left(1+x^2+x^4\right)}{si{n}^{2}x}=1$  

Given G.P’s 2, 2², 2³, …60 term and 4, 4², 4³, … of 60

Now G.M. =  ${\left(2\right)}^{\frac{225}{8}}\Rightarrow {\left(2,2^2,2^3,....\right)}^{\frac{1}{60+n}}={\left(2\right)}^{\frac{225}{8}}\Rightarrow n=\frac{57}{8},20son=20$

$\therefore {\displaystyle \sum _{k=1}^{n}k(n-k)}20\times \frac{20\times 21}{2}-\frac{20\times 21\times 41}{6}=1330$  

Hillwoods Academy of Higher Education admissions are both entrance and merit-based. If you want to join the PGDM programme offered at the institute, then you must provide score secured in any of the accepted national-level exams or appear for the institute-level test. The institute accepts CAT/ XAT/ MAT/ GMAT/ ATMA scorecards for shortlisting.

The CUET (Common University Entrance Test) for postgraduate (PG) programs typically included specific time slots or schedules for different courses or disciplines.

Time slots vary according to the different courses so please check on this please.