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This is a  Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}WehaveP\left(A\right)=\frac{2}{5},P\left(B\right)=\frac{1}{3}andP\left(C\right)=\frac{1}{2}\\ P\left(A\cap C\right)=\frac{1}{5}andP\left(B\cap C\right)=\frac{1}{4}\\ \therefore P\left(C/B\right)=\frac{P\left(B\cap C\right)}{P\left(B\right)}=\frac{1/4}{1/3}=\frac{3}{4}\\ P\left(A\text{'}\cap C\text{'}\right)=1-P\left(A\cup C\right)=1-\left[P\left(A\right)+P\left(C\right)-P\left(A\cap C\right)\right]\\ =1-\left[\frac{2}{5}+\frac{1}{2}-\frac{1}{5}\right]=1-\frac{7}{10}=\frac{3}{10}\\ Hence,therequiredprobabilitiesare\frac{3}{4}and\frac{3}{10}.\end{array}$

Poddar Group of Institutions has an impressive placement record. The placement statistics for 2025 are given in the table below:

Yes, students who are offered admission to the Clusters Academy of Excellence certificate courses might be required to make payment of the fees prescribed by the institute. Those who wish to pay the prescribed fees may be denied admission. Generally, at this stage, students are required to pay a one-time fee. Along with this, students may also be required to make payment of the first installment of tuition fees.

Yes, Pearson, on its own discretion allows you only to reschedule your test to another test date - without any extra charge. This can be availed of only in two circumstances - illness and/or family emergency, either of which doesn't allow you to reach the PTE test centre on the due date. 

Candidates can check the RPSC RAS result 2025 using the process below-

• Visit rpsc.rajasthan.gov.in
• Click on the RAS result link
• Search the desired roll number in the result PDF.
• Download the RAS result pdf.

Poddar Group of Institutions  has released its placement report for 2025. The key highlights of the 2025 placement statistics are given in the table below:

This is a  Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}WehaveP\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3}andP\left(A\cap B\right)=\frac{1}{4}\\ P\left(A\text{'}\right)=1-\frac{1}{2}=\frac{1}{2},P\left(B\text{'}\right)=1-\frac{1}{3}=\frac{2}{3}\\ P\left(A\text{'}\cap B\text{'}\right)=1-P\left(A\cup B\right)=1-\left[P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\right]\\ =1-\left[\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right]=1-\left[\frac{6+4-3}{12}\right]=1-\frac{7}{12}=\frac{5}{12}\\ \left(i\right)P\left(A/B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}=\frac{1/4}{1/3}=\frac{3}{4}\\ \left(ii\right)P\left(B/A\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)}=\frac{1/4}{1/2}=\frac{1}{2}\\ \left(iii\right)P\left(A\text{'}/B\right)=\frac{P\left(A\text{'}\cap B\right)}{P\left(B\right)}=\frac{P\left(B\right)-P\left(A\cap B\right)}{P\left(B\right)}=1-\frac{P\left(A\cap B\right)}{P\left(B\right)}\\ =1-\frac{1/4}{1/3}=1-\frac{3}{4}=\frac{1}{4}\\ \left(iv\right)P\left(A\text{'}/B\text{'}\right)=\frac{P\left(A\text{'}\cap B\text{'}\right)}{P\left(B\text{'}\right)}=\frac{5/12}{2/3}=\frac{5}{12}\times \frac{3}{2}=\frac{5}{8}\end{array}$

The number of students placed during Poddar Group of Institutions placements 2025 was over 159. The table below states the same:

The highest package and the Average package recorded at Poddar Group of Institutions placements 2025 is given in the table below:

This is a  Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}WeknowthatrandomvariableXtakesvalues0,1,2,3,\dots ,nissaidtobebinomialdistribution\\ havingparametersnandp,iftheprobabilityisgivenby\\ P\left(X=r\right)={}_n{C}_r{p}^r{q}^{n-r},whereq=1-pandr=0,1,2,3,\dots \\ Similarly,incaseoftossingacoin3times,\\ n=3andXhasthevalues0,1,2,3,\dots withp=\frac{1}{2},q=\frac{1}{2}.\\ Hence,itissaidtohaveabinomialdistribution.\end{array}$

Yes, while applying for Clusters Academy of Excellence Certificate courses, students are required to upload scanned copies of various documents. Listed below are the documents required to complete the admission process:

• Class 10 marksheet
• Class 12 marksheet
• UG marksheets (if applicable)
• UG degree (if applicable)
• Migration certificate
• School leaving certificate/transfer certificate
• Work experience certificate (if applicable)

Poddar Group of Institutions provides great placements to its students, 10 companies participated in the 2025 placement drive. Refer to the table below to know more:

Key documents for FDDI Counselling includes:

• AIST 2025 Admit Card & Scorecard

• Class 10th & 12th Mark Sheets and Certificates

• Graduation Certificate (for PG programmes)

• Photo ID (Aadhar/PAN/Voter ID)

• Category certificate (if applicable)

• Passport-size photographs

• Counselling call letter

The placement rate for Poddar Group of Institutions has not been disclosed yet. However, the placement highlights recorded during Poddar Group of Institutions placements 2025 is given in the table below:

The UP CPET 2025 answer key allows candidates to estimate their UP CPET scores by calculating the correct and incorrect answers marked in the exam. After that, it helps with counselling and selecting colleges based on expected UP CPET cut-offs.

The highest package offered during Poddar Group of Institutions placements 2025 stood at INR 15 LPA. The table below presents the same: