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Since a is a odd natural number then $\left|{\displaystyle \underset{1}{\overset{3}{\int }}{y}^{a}dy}\right|=\frac{364}{3}\Rightarrow \left|{\left(\frac{y^{a+1}}{a+1}\right)}_1^3\right|=\frac{364}{3}\Rightarrow \frac{3^{a+1}}{a+1}=\frac{364}{3}$

a = 5

 $\frac{x^2}{{\left(\sqrt[]{\frac{5}{2}}\right)}^2}+\frac{y^2}{{\left(\sqrt[]{\frac{5}{3}}\right)}^2}=1$

Equation of tangent having slope m is

$y=mx\pm \sqrt[]{\frac{5}{3}{m}^2+\frac{5}{3}},$ which passes through (1, 3) and we get m₁ + m₂ = -4 and m₁m₂ = $\frac{44}{9}$

$\therefore$ Acute angle between the tangents is α  = tan^-1 $\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=ta{n}^{-1}\left(\frac{24}{7\sqrt[]{5}}\right)$

Rajiv Gandhi University of Knowledge Technologies Andhra Pradesh has an intake of 300 students for the BTech course. Candidates must fill the application forms online through the official website to apply for admission in the university. However, after getting selected, they need to pay RGUKT tuition fee or a certain enrolment fee to confirm admissiom and secure their seat. 

TSSM College of Engineering Pune offers postgraduate, undergraduate, and other programmes to students. These courses are provided across the Engineering and various other streams. At the UG level, the college offers BTech courses to students. At the postgraduate level, TSSM Bhivarabai College of Engineering Narhe, offers an MTech programme to students. The college also provides Diploma programmes to students.

| (A + I) (adj A + I)| = 4 |A adj A + A + Adj A + I| = 4 | (A)I + A + adj A + I|= 4|A| = 1

|A + adj A| = 4

$A=\left[\begin{array}{cc}\hfill a\hfill & \hfill b\hfill \\ \hfill c\hfill & \hfill d\hfill \end{array}\right]\Rightarrow adjA=\left[\begin{array}{cc}\hfill a\hfill & \hfill -b\hfill \\ \hfill -c\hfill & \hfill d\hfill \end{array}\right]\Rightarrow \left|\begin{array}{cc}\hfill \left(a+d\right)\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill \left(a+d\right)\hfill \end{array}\right|=4\Rightarrow a+d=\pm 2$

UI= $\frac{1}{2}c{v}^2$

$U_i=\frac{1}{2}\frac{{\in }_{0}A}{d}\times k{v}^2$

$U_i=\frac{1}{2}\frac{{\in }_{0}A}{d}\times 10v^2$

$U_f=\frac{1}{2}\frac{{\in }_{0}A}{d}\times 15v^2$

$\frac{U_f}{U_i}=\frac{3}{2}$

$\frac{U_f-U_i}{U_i}\times 100=\left(\frac{3}{4}-1\right)\times 100$

$\frac{1}{2}\times 100$

Yes, the application form for RGUKT: Rajiv Gandhi University of Knowledge Technologies Andhra Pradesh admission can get rejected if the details filled by the candidate are incorrect. It can also be rejected if the candidate has not uploaded the correct documents required like marksheets, certificates, ID proofs, etc. Another possible reason is when the candidate does not fulfil the eligiblity criteria for their preferred course. 

Yes, TSSM Narhe has collaborated with many institutes, colleges, and universities. The below-mentioned are the TSSM College of Engineering Pune collaborations:

Note: Visit the official website of TSSM College of Engineering Pune for other collaboration details.

 $\Delta =\left|\begin{array}{ccc}\hfill 8\hfill & \hfill 1\hfill & \hfill 4\hfill \\ \hfill 1\hfill & \hfill 1\hfill \\ \hfill \lambda \hfill & \hfill -3\hfill & \hfill 0\hfill \end{array}\right|=12-3\lambda$

So for $\lambda$ = 4, it is having infinitely many solutions. ${\Delta }_x=\left|\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 4\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \\ \hfill \mu \hfill & \hfill -3\hfill & \hfill 0\hfill \end{array}\right|$ = 6 $3\mu =0\Rightarrow -6-3\mu =0$

For $\mu =-2$ distance of $\left(4,-2,-\frac{1}{2}\right)$ from 8x + y + 4z + 2= 0 $\left|\frac{32-2-2+2}{\sqrt[]{64+1+16}}\right|=\frac{10}{3}$ units

The tuition fee is charged yearly or semester-wise. IIM Trichy PGPM tuition fees is INR 19.5 lakh. Candidates can pay this fee amount in frequency as suggested by the institute. It must be noted that the given fee information is as per the official website/ sanctioning body. It is still subject to changes and hence, is indicative.

 $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt[]{1-x^2}},$ $I.F.e^{{\displaystyle \int \frac{xdx}{x^2-1}}}=\sqrt[]{\left|x^2-1\right|}=\sqrt[]{1-x^2}$ $\left(?x\in \left(-1,1\right)\right)$

Solution of differential equation is $y\sqrt[]{1-x^2}={\displaystyle \int \left(x^4+2x\right)dx=\frac{x^5}{5}+x^2+c}$

Curve is passing through origin, c = 0 $y=\frac{x^5+5x^2}{5\sqrt[]{1-x^2}}$

$\therefore {\displaystyle \underset{-\frac{\sqrt[]{3}}{2}}{\overset{\frac{\sqrt[]{3}}{2}}{\int }}\frac{x^5+5x^2}{5\sqrt[]{1-x^2}}dx=\frac{\pi }{3}-\frac{\sqrt[]{3}}{4}}$

 $\frac{z_2-0}{\left(1+2i\right)-0}=\left|\frac{OB}{OA}\right|e^{\frac{i\pi }{4}}\Rightarrow z_2=\left(1+2i\right)\left(1+i\right)=-1+3i\therefore arg{z}_2=\pi -ta{n}^{-1}3and\left|z_2\right|=\sqrt[]{10}$

$z_1-2z_2=3-4i\therefore arg\left(z_1-2z_2\right)=-ta{n}^{-1}\frac{4}{3}\Rightarrow \left|z_1-2z_2\right|=\left|2+4i+1-3i\right|=\sqrt[]{10}$

Yes, candidates can enrol for admission at the School of Law, Pandit Deendayal Energy University with Class 12 scores. The eligibility criteria are to complete Class 12. Students are selected based on the entrance exam. The institute offers BA LLB and LLB courses. The application process at the School of Law, Pandit Deendayal Energy University is conducted online. 

IIIT Ranchi is neither a fully government owned or private owned institute. IIIT Ranchi is under a PPP or Priate Public Partnership model. This means that it is run by an administration comprised of both the goverment and the private owners of IIIT Ranchi.

              x = 10   $2?\left(nt?\frac{x}{?}\right)cm$

              V (wave velocity) =   $\frac{??}{2?}$

              v_max = 10 * 2p n

              10 * 2pn = 4 *   $\frac{??}{2?}$

              10 * 2pn =   $4\frac{2?\text{?}n?}{2?}$

               x = 5?

TSSM College of Engineering Pune placements 2025 will be updated here once out. TSSM College of Engineering Pune is visited by top companies for placements such as Capgemini, TCS, TATA Motors, Tech Mahindra, and others. TSSM Bhivarabai College of Engineering has concluded its placement drive for 2023. The placement offered by the college are good.