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Sapienza University of Rome offers various popular majors, including Artificial Intelligence, Arts and Humanities, Biology and Biochemistry, Civil Engineering, Ecology, Computer Science, and more. Some of the popular Sapienza University of Rome majors with the US News subject rankings are listed below:

Graduates of the University of East London receive top employment opportunities with impressive salaries. Below are the details, as per the job roles:

• CEO: GBP 131,000 (INR 1.5 Cr)
• Compliance Manager: GBP 38,750 (INR 44.7 L)
• Accountant: GBP 33,300 (INR 38.4 L)
• Manager: GBP 32,000 (INR 36.9 L)
• Business Intelligence Analyst: GBP 27,770 (INR 32.1 L)

Conversion Rate: 1 GBP = INR 115.61

The Sapienza University of Rome acceptance rate is 39%. The low percentage indicates that the university is quite stringent during admission and follows a strict approach while finding the appropriate candidates. Students must aim for excellent scores in academics, work on their English proficiency, and excel in standardized test scores to increase their chances of selection. Students must also hold a bachelor's degree for graduate programs.

$\begin{array}{l}\overrightarrow{r}=\left(\widehat{i}+2\widehat{j}+3\widehat{k}\right)+\lambda \left(\widehat{i}-3\widehat{j}+2\widehat{k}\right)and-----(1)\\ \overrightarrow{r}=4\widehat{i}+5\widehat{j}+6\widehat{k}+\mu \left(2\widehat{i}+3\widehat{j}+\widehat{k}\right)-----(2)\end{array}$

Here, comparing (1) and (2) with $\overrightarrow{r}={\overrightarrow{a}}_1+\lambda {\overrightarrow{b}}_1$ and $\overrightarrow{r}={\overrightarrow{a}}_2+\mu {\overrightarrow{b}}_2$ , we have

$\begin{array}{l}{a}_1=\widehat{i}+2\widehat{j}+3\widehat{k},b_1=\widehat{i}-3\widehat{j}+2\widehat{k}\\ a_2=4\widehat{i}+5\widehat{j}+6\widehat{k},b_2=2\widehat{i}+3\widehat{j}+\widehat{k}\end{array}$

Therefore,

              $\begin{array}{l}{\overrightarrow{a}}_2-{\overrightarrow{a}}_1=3\widehat{i}+3\widehat{j}+3\widehat{k}\\ {\overrightarrow{b}}_1\times {\overrightarrow{b}}_2=\\ =\widehat{i}\left(-3-6\right)-\widehat{j}\left(1-4\right)+\widehat{k}\left(3+6\right)\\ =-9\widehat{i}+3\widehat{j}+9\widehat{k}\\ \left|{\overrightarrow{b}}_1\times {\overrightarrow{b}}_2\right|==\\ =\\ =3\end{array}$

34. Let f (x) = sin (x2 + 5)

Differentiating w. r t. x we get,

f'¢ (x) = $\frac{d}{dx}$sin (x² + 5)

= cos (x² + 5)  $\frac{d}{dx}$ = cos (x² + 5) 

= cos (x² + 5) [2x].

= 2x cos (x² + 5).

Of course, an online programme in MSc Interior Design is apt for students who wish to get a degree in this field but are not able to opt for a regular on-campus course. It will offer them great flexibility, affordability, and industry recognition.
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Yes, Sapienza University of Rome accepts international students from all over the globe. According to the university statistics for 2025, over 65,000 enrolled in UG, more than 27,000 in PG programs. Out of the total, over 11,000 students are international. Students can check the Sapienza University of Rome enrollment statistics below:

Sapienza University of Rome comprises over 300 undergraduate and graduate programs. Some popular courses are Aerospace Engineering, Law and Legal Studies, Nanotechnology, Physics, Data Science, and more. The Sapienza University of Rome tuition fees for international students range between INR 2 L and INR 3 L. Students can check the tuition fees for popular programs below:

$\begin{array}{l}\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}\\ \frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}\end{array}$

Shortest distance between two lines is given by,

$\begin{array}{l}{x}_1=-1,y_1=-1,z_1=-1\\ a_1=7,b_1=-6,c_1=1\\ x_2=3,y_2=5,z_2=7\\ a_2=1,b_2=-2,c_2=1\end{array}$

Then,

$\begin{array}{l}=4\left(-6+2\right)-6\left(7-1\right)+8\left(-14+6\right)\\ =-16-36-64\\ =-116\end{array}$

Jerry Butler, an American singer & songwriter, known for being the former lead singer of the R&B vocal group: The Impressions, is among the notable individuals to have pursued his studies from the Governors State University.

He earned his UG & PG degrees in Political Science & Music History respectively from GSU, in the years 1993 & 1998.

Jerry also known as the "Iceman" also went on to become the Commissioner of the Cook County.

Butler was inducted into the "National Rhythm & Blues Hall of Fame" in the year 2015.

$\begin{array}{l}\overrightarrow{r}=\left(\widehat{i}+2\widehat{j}+\widehat{k}\right)+\lambda \left(\widehat{i}-\widehat{j}+\widehat{k}\right)and-----(1)\\ \overrightarrow{r}=2\widehat{i}-\widehat{j}-\widehat{k}+\mu \left(2\widehat{i}+\widehat{j}+2\widehat{k}\right)-----(2)\end{array}$

Solution. Comparing (1) and (2) with $\overrightarrow{r}={\overrightarrow{a}}_1+\lambda {\overrightarrow{b}}_1$ and $\overrightarrow{r}={\overrightarrow{a}}_2+\mu {\overrightarrow{b}}_2$ respectively.

We get,

$\begin{array}{l}{a}_1=\widehat{i}+2\widehat{j}+\widehat{k},b_1=\widehat{i}-\widehat{j}+\widehat{k}\\ a_2=2\widehat{i}-\widehat{j}-\widehat{k},b_2=2\widehat{i}+\widehat{j}+2\widehat{k}\end{array}$

Therefore,

$\begin{array}{l}{\overrightarrow{a}}_2-{\overrightarrow{a}}_1=\widehat{i}-3\widehat{j}-2\widehat{k}\\ {\overrightarrow{b}}_1\times {\overrightarrow{b}}_2=\left(\widehat{i}-\widehat{j}+\widehat{k}\right)\times \left(2\widehat{i}+\widehat{j}+2\widehat{k}\right)\end{array}$

$\begin{array}{l}=\left(2-1\right)\widehat{i}-\left(2-2\right)\widehat{j}+\left(1+2\right)\widehat{k}\\ =-3\widehat{i}+3\widehat{k}\\ \left|{\overrightarrow{b}}_1\times {\overrightarrow{b}}_2\right|====3\\ \left({\overrightarrow{b}}_1\times {\overrightarrow{b}}_2\right).\left({\overrightarrow{a}}_2-{\overrightarrow{a}}_1\right)=\left(-3\widehat{i}+3\widehat{k}\right)\left(\widehat{i}-3\widehat{j}-2\widehat{k}\right)\\ =-3-6\\ =-9\end{array}$

Hence, the shortest distance between the given line is given by

$\begin{array}{l}d=\left|\frac{\left({\overrightarrow{b}}_1\times {\overrightarrow{b}}_2\right).\left({\overrightarrow{a}}_2-{\overrightarrow{a}}_1\right)}{\left|{\overrightarrow{b}}_1\times {\overrightarrow{b}}_2\right|}\right|\\ =\left|\frac{-9}{3}\right|\\ =\frac{3}{}=\frac{3}{2}\end{array}$

$\begin{array}{l}\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}\\ \frac{x}{1}=\frac{y}{2}=\frac{z}{3}\end{array}$

Direction ratios of given lines are (7, -5,1) and (1,2,3).

i.e.,  $\begin{array}{l}{a}_1=7,b_1=-5,c_1=1\\ a_2=1,b_2=2,c_2=3\end{array}$

Now,

$\begin{array}{l}=a_1{a}_2+b_1{b}_2+c_1{c}_2\\ =7\times 1+\left(-5\right)\times 2+1\times 3\\ =7-10+3\\ =10-10\\ =0\end{array}$

$\therefore$ These two lines are perpendicular to each other.

The IELTS score required for admission to SFU is overall 6.5 with no part less than 6.0. The same score is required for admission to PG courses as well. Additionally, in place of IELTS scores, students can also submit TOEFL / PTE / Duolingo scores. The minimum test scores required in these English language proficiency test scores are given below:

33. Let g (x) = $x$ is continuous being a modules f x and h (x) = $x$ is also continuous being a modules $\forall x\in ?$

Then, f (x) = g (x) h (x).is also continuous for all x. E. R.

Hence, there is no point of discontinuous for f (x).

$\frac{1-x}{3}=\frac{7y-14}{2\rho }=\frac{z-3}{2}and\frac{7-7x}{3\rho }=\frac{y-5}{1}=\frac{6-z}{5}$

The standard form of a pair of Cartesian lines is;

$\frac{x-x_1}{a_1}=\frac{y-y_1}{b_1}=\frac{z-z_1}{c_1}and\frac{x-x_2}{a_2}=\frac{y-y_2}{b_2}=\frac{z-z_2}{c_2}-----(1)$

So,

$\begin{array}{l}\frac{-\left(x-1\right)}{3}=\frac{7\left(y-5\right)}{2\rho }=\frac{z-3}{2}and\frac{-7\left(x-1\right)}{3\rho }=\frac{y-5}{1}=\frac{-\left(z-6\right)}{5}\\ \frac{x-1}{-3}=\frac{y-2}{2\rho /7}=\frac{z-3}{2}and\frac{x-1}{-3\rho /7}=\frac{y-5}{1}=\frac{z-6}{-5}-----(2)\end{array}$

Comparing (1) and (2) we get

$\begin{array}{l}{a}_1=-3,b_1=\frac{2\rho }{7},c_1=2\\ a_2=\frac{-3\rho }{7},b_2=1,c_2=-5\end{array}$

Now, both the lines are at right angles

So, $a_1{a}_2+b_1{b}_2+c_1{c}_2=0$

$\begin{array}{l}\Rightarrow \left(-3\right)\times \frac{\left(-3\rho \right)}{7}+\frac{2\rho }{7}\times 1+2\times \left(-5\right)=0\\ \Rightarrow \frac{9\rho }{7}+\frac{2\rho }{7}+\left(-10\right)=0\\ \Rightarrow \frac{9\rho +2\rho }{7}=10\\ \Rightarrow 11\rho =70\\ \rho =\frac{70}{11}\end{array}$

$\therefore$ The value of $\rho$ is $\frac{70}{11}$

32. Given, f (x) = sin $x$

Let g (x) = sin x and h (x) = $x$ then as sine f x and modulus f x are continuous in x e R

g and h are continuous.

So, (goh) (x) = g (h (x) = g (|x|) = sin |x| = f (x)

Is a continuous f x being a competitive f x of two continuous f x.

(i) Let  ${\overrightarrow{b}}_1$  and  ${\overrightarrow{b}}_2$  be the vectors parallel to the pair of lines,  $\frac{x-2}{2}=\frac{y-1}{5}=\frac{z+3}{-3}\&\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}$ , respectively.

$\begin{array}{l}{\overrightarrow{b}}_1=2\widehat{i}+5\widehat{j}-3\widehat{k}\&{\overrightarrow{b}}_2=-\widehat{i}+8\widehat{j}+4\widehat{k}\\ \therefore \left|{\overrightarrow{b}}_1\right|==\\ \left|{\overrightarrow{b}}_2\right|===9\\ {\overrightarrow{b}}_1.{\overrightarrow{b}}_2=\left(2\widehat{i}+5\widehat{j}-3\widehat{k}\right).\left(-\widehat{i}+8\widehat{j}+4\widehat{k}\right)\\ =2(-1)+5\times 8+(-3).4\\ =-2+40-12\\ =26\end{array}$

B Tech CSE Placement Package Overview

Tech CSE graduates can range between INR 30-50 LPA (depending on company and skills). The average salary typically falls between INR 6-12 LPA, with variations based on skills, college reputation, and location

Ideal Institute of Engineering Average Package 2024

Department the highest Package (2024) the lowest Package (2024)

Computer Science and Engineering INR 6.40 LPA INR 3.50 LPA

Civil Engineering INR 5.50 LPA INR 2.40 LPA

Electrical Engineering INR 4.80 LPA INR 2.40 LPA

Mechanical Engineering INR 4.80 LPA INR 2.4

0 LPA