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This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Herem=\frac{{\displaystyle \sum _{}^{}{x}_i}}{N},S=\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{5}-{\left(\frac{{\displaystyle \sum _{}^{}{x}_i}}{5}\right)}^2}\\ \therefore SD=\sqrt[]{\frac{K^2{\displaystyle \sum _{}^{}{x}_i^2}}{5}-{\left(\frac{K{\displaystyle \sum _{}^{}{x}_i}}{5}\right)}^2}=\sqrt[]{\frac{K^2{\displaystyle \sum _{}^{}{x}_i^2}}{5}-K^2{\left(\frac{{\displaystyle \sum _{}^{}{x}_i}}{5}\right)}^2}\\ =K\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{5}-{\left(\frac{{\displaystyle \sum _{}^{}{x}_i}}{5}\right)}^2}=K.S\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

Xavier Institute of Management and Entrepreneurship has an impressive placement record. The placement statistics for recent years are given in the table below:

$A^2=\left(\begin{array}{ll}\mathrm{c}\mathrm{o}\mathrm{s}?2\theta & i\mathrm{s}\mathrm{i}\mathrm{n}?2\theta \\ i\mathrm{s}\mathrm{i}\mathrm{n}?2\theta & \mathrm{c}\mathrm{o}\mathrm{s}?2\theta \end{array}\right)$

Similarly, $A^5=\left(\begin{array}{cc}\mathrm{c}\mathrm{o}\mathrm{s}?5\theta & i\mathrm{s}\mathrm{i}\mathrm{n}?5\theta \\ i\mathrm{s}\mathrm{i}\mathrm{n}?5\theta & \mathrm{c}\mathrm{o}\mathrm{s}?5\theta \end{array}\right)=\left(\begin{array}{ll}a& b\\ c& d\end{array}\right)$

(1) $a^2+b^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta -{\mathrm{s}\mathrm{i}\mathrm{n}}^2?5\theta =\mathrm{c}\mathrm{o}\mathrm{s}?10\theta =\mathrm{c}\mathrm{o}\mathrm{s}?{75}^{?}$

(2) $a^2-d^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta -{\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta =0$

(3) $a^2-b^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta +{\mathrm{s}\mathrm{i}\mathrm{n}}^2?5\theta =1$

(4) $a^2-c^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta +{\mathrm{s}\mathrm{i}\mathrm{n}}^2?5\theta =1$

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Givenobservationarea,b,c,dande\\ \therefore Mean=m=\frac{a+b+c+d+e}{5}\\ \therefore {\displaystyle \sum _{}^{}{x}_i}=5m\\ Nowmeanofa+K,b+K,c+K,d+Kande+Kis\\ =\frac{a+K+b+K+c+K+d+K+e+K}{5}\\ =\frac{\left(a+b+c+d+e\right)+5K}{5}=\frac{5m+5K}{5}=m+K\\ \therefore S.D.=\sqrt[]{\frac{{\displaystyle \sum _{}^{}{\left(x_i+K\right)}^2}}{N}-{\left(\frac{{\displaystyle \sum _{}^{}{x}_i+K}}{N}\right)}^2}\\ =\sqrt[]{\frac{{\displaystyle \sum _{}^{}\left(x_i^2+K^2+2x_{i}K\right)}}{N}-{\left(m+K\right)}^2}\\ =\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{N}+\frac{{\displaystyle \sum _{}^{}{K}^2}}{N}+\frac{2K{\displaystyle \sum _{}^{}{x}_i}}{N}-m^2-K^2-2mK}\\ =\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{N}+K^2+2Km-m^2-K^2-2mK}=\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{N}-m^2}\left[?\frac{{\displaystyle \sum _{}^{}{x}_i}}{N}=m\right]\\ =S\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

Yes all including international students are allowed to work part time at UofT but some work may require work permit and or study permit. Students should be advised to check all requirements before applying on official uni website

According to the ICFAI University Mizoram placement report 2023, the the highest domestic package bagged by the students stood at INR 6.75 LPA. Moreover, the highest international package for 2023 stood at INR 9.32 LPA. Top recruiters who participated in the drive include Axis Bank, Genpact, SBI, and more.

Note: The abovementioned data is not course specific.

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Here\overline{x}=\frac{{\displaystyle \sum _{}^{}{x}_i}}{n}\\ 50=\frac{{\displaystyle \sum _{}^{}{x}_i}}{100}\Rightarrow {\displaystyle \sum _{}^{}{x}_i}=5000\\ \therefore S.D.=\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{n}-{\left(\frac{{\displaystyle \sum _{}^{}{x}_i}}{n}\right)}^2}\\ 5=\sqrt[]{\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{100}-{\left(\frac{5000}{100}\right)}^2}\Rightarrow 25=\frac{{\displaystyle \sum _{}^{}{x}_i^2}}{100}-2500\\ \Rightarrow \frac{{\displaystyle \sum _{}^{}{x}_i^2}}{100}=2500+25\Rightarrow \frac{{\displaystyle \sum _{}^{}{x}_i^2}}{100}=2525\\ \therefore {\displaystyle \sum _{}^{}{x}_i^2}=2525\times 100=252500\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

 $\int {\left(\frac{x}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)}^{2}dx=\int \left(\frac{x}{\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)\cdot \frac{x\mathrm{c}\mathrm{o}\mathrm{s}?xdx}{(x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x{)}^2}$

$\begin{array}{rr}& =\frac{x}{\mathrm{c}\mathrm{o}\mathrm{s}?x}\left(-\frac{1}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)+\int \left(\frac{\mathrm{c}\mathrm{o}\mathrm{s}?x+x\mathrm{s}\mathrm{i}\mathrm{n}?x}{{\mathrm{c}\mathrm{o}\mathrm{s}}^2?x}\right)\left(\frac{1}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)dx\\ & =-\frac{x\mathrm{s}\mathrm{e}\mathrm{c}?x}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}+\int {\mathrm{s}\mathrm{e}\mathrm{c}}^2?xdx\\ & =-\frac{x\mathrm{s}\mathrm{e}\mathrm{c}?x}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}+\mathrm{t}\mathrm{a}\mathrm{n}?x+C\end{array}$

The placement package recorded at XIME Chennai placements 2022 to 2024 is given in the table below:

ICFAI University Mizoram is expected to release the highest package bagged by the BCom students soon. In the meantime, students can check out the overall placement data released by the university for 2023. As per that, the the highest domestic package offered stood at INR 6.75 LPA.

Note: The above-mentioned data is not course-specific. It represents the overall placement stats of the college.

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}TheformulaforS.D.=\sigma =\sqrt[]{\frac{{\displaystyle \sum _{}^{}{\left(x_i-\overline{x}\right)}^2}}{n}}\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

Xavier Institute of Management and Entrepreneurship provides great placements to its students. Check out the table for the XIME Chennai placements 2022 to 2024 given below: 

Since $\left(\mathrm{3,3}\right)$ lies on $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

$\frac{9}{a^2}-\frac{9}{b^2}=1$

Now, normal at $\left(\mathrm{3,3}\right)$ is $y-3=-\frac{a^2}{b^2}(x-3)$ ,

which passes through $\left(\mathrm{9,0}\right)\Rightarrow b^2=2a^2$

So,  ${\mathrm{e}}^2=1+\frac{{\mathrm{b}}^2}{{\mathrm{a}}^2}=3$

Also,  ${\mathrm{a}}^2=\frac{9}{2}$

(From (i) and (ii)

Thus,  $\left({\mathrm{a}}^2,{\mathrm{e}}^2\right)=\left(\frac{9}{2},3\right)$

Yes, students with top ranks in VSAT are eligible for merit-based scholarships. As per the scholarships students can avail upto 100% fee waivers. However, the eligibility criteira, requirements vary for which candidates will have to reach out to the exam body officials. The university publishes the scholarship structure along with the results.

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Thestandarddeviationsisgreaterthanorequaltothemeandeviationtakenfromthe\\ arithmeticmean.\\ Hence,thevalueofthefillerisgreaterthanorequal.\end{array}$

If two candidates score same marks, the exam body will follow tie-in method and check their marks in PCM subjects. If that is also same, they will select the student based on seniority through DOB.

The highest package offered during XIME Chennai placements 2024 stood at INR 14.10 LPA. Check out the table for the highest package trends recorded during the past Xavier Institute of Management and Entrepreneurship Chennai placements:

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Themeandeviationofthedataisleastwhenmeasuredfromthemedian.\\ Hence,thevalueofthefillerisleast.\end{array}$