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Cu is the only element of 3d – series whose M²⁺ / M value is positive because of fact that low hydration enthalpy and high sublimation & ionization enthalpies.

With the help of conservation of volume, we can write

$27\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3\Rightarrow R=3r.......\left(1\right)$

With the help of conservation of charge, we can write

Q = 27 q.(2)

Potential energy of single drop = U1 = $\frac{q^2}{8\pi {\epsilon }_{0}r}$ $\frac{{}^{}}{{}_{}}$

Potential energy of bigger drop = $U_2=\frac{Q^2}{8\pi {\epsilon }_{0}R}=\frac{27\times 27\times q^2}{8\pi {\epsilon }_0\left(3r\right)}=243\left(\frac{q^2}{8\pi {\epsilon }_{0}r}\right)=243U_1$ ${}_{}\frac{{}^{}}{{}_{}}\frac{{}^{}}{{}_{}}\frac{{}^{}}{{}_{}}{}_{}$

$\Rightarrow \frac{U_2}{U_1}=243$

$l=\frac{90-30}{4000}=15mA$

$I_1=\frac{30}{5000}=6mA\&l_2=9mA$

$v=\omega \sqrt[]{A^2-s^2}\Rightarrow \frac{A\omega }{2}=\omega \sqrt[]{A^2-s^2}\Rightarrow s=\frac{\sqrt[]{3}A}{2}\Rightarrow x=3$

$\Delta Q=\Delta U+\Delta W$

^{$\Rightarrow Q=\Delta U+\frac{Q}{5}\Rightarrow \Delta U=\frac{4Q}{5}=n{C}_v\Delta T\Rightarrow \frac{4Q}{5}=\frac{5R}{2}\Delta T\Rightarrow \Delta T=\frac{8Q}{25R}$}

^{$Q=nc\Delta T=1\times C\times \frac{80}{25R}\Rightarrow C=\frac{25R}{8}\Rightarrow x=25$}

By properties,

OA.AB = PA.AQ, OA=1, AB = 12

12 = a²

$a=2\sqrt[]{3}$

$\therefore AreaofPQB=\frac{1}{2}\times 12\times 2.2\sqrt[]{3}=24\sqrt[]{3}$ sq. units

Band Width = 2 × n × the highest modulation frequency

$\Rightarrow n=\frac{90k{H}_z}{2\times 5kHz}=9$

Maximum Distance = 3 (x + x) = 6x = 3 × 2x = 3 × 50 = 150 cm

Post Brexit, the UK remains hand in hand with the European Higher Education Area (EHEA). Also because having co-founded the EHEA along with three other countries back in 1998: Germany, France and Italy the United Kingdom continues its partnership. Apart from UK, there are other countries like Ukraine, Russia, Vatican City, and Turkey are not a part of EHEA. 

 $l={\displaystyle \underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{co{s}^{2}x}{1+3^x}dx..........\left(i\right)}$

Using properties, ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(x\right)dx={\displaystyle \underset{a}{\overset{b}{\int }}f\left(a+b-x\right)dx}}$

$l={\displaystyle \underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{co{s}^{2}x}{1+3^{-x}}dx}={\displaystyle \underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{3^{x}co{s}^{2}x}{1+3^x}dx.......\left(ii\right)}$

Adding (i) and (ii), we get

$2l={\displaystyle \underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{\left(1+3^x\right)co{s}^{2}x}{1+3^x}}dx={\displaystyle \underset{-\pi /2}{\overset{\pi /2}{\int }}co{s}^{2}xdx=2}{\displaystyle \underset{0}{\overset{\pi /2}{\int }}co{s}^{2}xdx}$

$\therefore l=\frac{\pi }{4}$

The following universities in Europe are best for pursuing Economics courses for international students:

• London School of Economics and Political Sciences (LSE) 
• University of Oxford 
• University of Cambridge 
• University College London (UCL) 
• Bocconi University 
• University of Warwick 
• Tilburg University

The Staff Selection Commission released the SSC CGL cutoff with the result PDF. The Commission released the category-wise SSC CGL cutoff for all the post-groups with the result. The Commission released the Tier 1 cutoffs separately for all the post groups and categories.

The SSC CGL Tier 1 exam 2025 was conducted till October 14.

Case I :- $2?-?=\frac{1}{2}m{v}_1^2........\left(i\right)$ $\frac{}{}{}_{}^{}$

Case II :- $10?-?=\frac{1}{2}m{v}_2^2........\left(ii\right)$ $\frac{}{}{}_{}^{}$

$\Rightarrow \frac{1}{9}=\frac{v_1^2}{v_2^2}$

$\Rightarrow v_1:v_2=1:3$

x = 1

Yes, in countries like Germany, Norway and Italy international students can study for free in Europe. The tuition-free universities are mostly public universities which offer free education to students. There is also another option, to study for free in Italy. Thus, international students must look out for such European universities where there is a good scholarship amount offered or where tuition fee waivers are offered specifically for international students.

Quantum University is very good college for B.Tech. it has been providing me with all the things necessary to boost my career and develop my skills required to work in the industry. The faculty members are also very supportive and help focus on individual development of each student. The quality of placements are pretty decent. 90% students are placed.

The cheapest countries to study in Europe are Italy, Norway, Germany, Austria, Hungary, Greece, Belgium, etc. These country universities would still require students to pay for their living and personal expenses. Each country has a specific set of private and public universities. Usually public universities in Europe are cheaper and more affordable for international students. Thus, if possible international students shoukd opt for public universities only to avoid unnecessary expenditures.