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Applying Leibniz theorem,  

$\sqrt[]{1-{\left(f\text{'}\left(x\right)\right)}^2}=f\left(x\right)\Rightarrow \frac{f\text{'}\left(x\right)}{\sqrt[]{1-{\left(f\left(x\right)\right)}^2}}=1$ on integrating both sides, we get

$f\left(x\right)=sinx+C$ put x = 0 and f (0) = 0 we get C = 0

$Now\underset{x\to 0}{lim}\frac{{\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}}{x^2},\left(\frac{0}{0}\right)$ by L’ Hospital rule $\underset{x\to 0}{lim}\frac{f\left(x\right)}{2x}=\underset{x\to 0}{lim}\frac{sinx}{2x}=\frac{1}{2}$

Object is moving in upward direction with constant velocity so in upward motion (+2N) and for downward motion (-2N) So option (1) is correct representation.

Chitkara University Institute of Engineering and Technology offers the flagship Bachelor of Technology (BTech) programme in a variety of specializations. The course is a popular programme for students seeking to build a career in Engineering. The total tuition fees for CIET Chandigarh BTech is INR 8.4 L - 18.9 L. Students can also check out the various scholarship schemes offered by CIET Chandigarh.

Amity University Online MBA application is done fully online. You just need to visit their official site (amityonline.com), register with basic details. After that, start filling the form. Make sure you upload your Class 10, Class 12, and graduation documents. Lastly, pay the application fee of INR 1,100 and you're registered. Keep your documents handy so that the process becomes smoother.

Following is the structure of the stops on this route:

Case I:

The NIFT Bangalore cutoff 2025 has been released up to multiple rounds, wherein the closing rank for B.F.Tech. in Apparel Production during Round 3 admission was 190 for the students belonging to the General AI quota. For other categories, check out the table provided below:

Adiabatic equation : $P_1{V}^{\gamma }=P_2{V}^{\gamma }\Rightarrow \left(200\right){\left(1200\right)}^{\gamma }=P{\left(300\right)}^{\gamma }$

$\Rightarrow P=\left(200\right){\left(4\right)}^{\frac{3}{2}}=1600KPa$

$W=\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}=\frac{240-480}{1.5-1}=-480J$  

Following is the structure of the stops on this route:

Case I:

$\frac{dy}{dx}=\frac{2^{x+y}-2^x}{2^y}\Rightarrow {\displaystyle \int \frac{2^{y}dy}{2^y-1}={\displaystyle \int 2^{x}dx\Rightarrow put{2}^y-1=t\Rightarrow 2^{y}ln2dy=dt}}$

$\frac{1}{ln2}{\displaystyle \int \frac{dt}{t}={\displaystyle \int 2^{x}dx\Rightarrow \frac{1}{ln2}lnt=\frac{2^x}{ln2}+\frac{C}{ln2}}}$    put x = 0 and y = 1 we get C = -1

$\therefore ln\left(2^y-1\right)=2^x-1$    put x = 1 and we get y = log₂ (1 + e)

Battery is connected while dielectric is inserted so potential difference will be  remains same.

$U_i=\frac{1}{2}c{V}^2$

$U_f=\frac{1}{2}Kc{V}^2$

$\Rightarrow \Delta U=\frac{1}{2}\left(K-1\right)c{V}^2=\frac{1}{2}\times 1\times 200\times 10^{-9}\times 200^2=4$

Yes, students can get admission to the BSc programme from Symbiosis Institute of Health Sciences with 85% score in 10+2. The minimum requirement for the General category is typically 50%, while for Scheduled Caste/Scheduled Tribes, it's 45%. While your score is well above the minimum, it's important to note that the selection process may also consider other factors like the SNAP score. 

The number of students placed has not been out yet. However, the placement rate recorded was 100%. The table below presents the same:

University of Washington offers various amenities such as high-speed Wi-Fi, ethernet, common kitchens, community lounges, makerspaces (such as Area 01 and The MILL). Also, study rooms, on-campus fitness centers, and music/video laboratories are all available in residence halls.  Along with more than 35 other campus restaurants and cafes, dining options include Local Point, Center Table, and Cultivate.

The key highlights recorded during the Adani Institute of Digital Technology Management MBA placements are provided in the table below:

from given information : I = A = 60°, r = $\frac{A}{2}=30°$ =>  $\mu =\sqrt[]{3}=\frac{c}{v}$

$\Rightarrow v=\frac{c}{\sqrt[]{3}}\Rightarrow time=\frac{\left(\frac{5\sqrt[]{3}}{100}\right)}{\left(\frac{3\times 10^8}{\sqrt[]{3}}\right)}=5\times 10^{-10}s$

Yes, The University of Washington offers on-campus housing facilities for its Indian students. UW offers Greek life housing, apartments, contemporary amenities, and traditional residence halls. In order to accommodate various demands and price ranges, each choice offers features including furnished rooms, communal kitchens, study spaces, and a variety of floor patterns. There is a strong sense of community because first-year students frequently live on campus. Specialized living learning communities with an emphasis on academic or cultural subjects are also available.

The overall average package recorded during Adani Institute of Digital Technology Management MBA placements was INR 8 LPA. Refer to the table below to know more:

Symbiosis Centre for Media and Communication BA seat intake is 120. This is the annual seat intake of the institute. Students must note that this information is taken from the official website and is subject to change. To know more about the SCMC Pune BA Mass Communication course and its intake, students can visit the official website of the institute.