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

Sol:

$\begin{array}{l}GiventhatbagI=\left\{3B,2W\right\}\\ andbagII=\left\{2B,4W\right\}\\ Let{E}_1=TheeventthatbagIisselected\\ E_2=TheeventthatbagIIisselected\\ andE=Theeventthatablackballisselected\\ \therefore P\left(E_1\right)=\frac{1}{2},P\left(E_2\right)=\frac{1}{2},P\left(E/E_1\right)=\frac{3}{5}andP\left(E/E_2\right)=\frac{1}{3}\\ \therefore P\left(E\right)=P\left(E_1\right).P\left(E/E_1\right)+P\left(E_2\right).P\left(E/E_2\right)\\ =\frac{1}{2}\times \frac{3}{5}+\frac{1}{2}\times \frac{1}{3}=\frac{3}{10}+\frac{1}{6}=\frac{9+5}{30}=\frac{14}{30}=\frac{7}{15}\\ Hence,therequiredprobabilityis\frac{7}{15}.\end{array}$

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

Sol:

$\begin{array}{l}Let{W}_{1}and{W}_{2}betwobagscontaining\left(4W,5B\right)and\left(9W,7B\right)ballsrespectively.\\ Let{E}_{1}betheeventthatthetransferredballfromthebag{W}_{1}to{W}_{2}iswhiteand\\ E_{2}betheeventthatthetransferredballisblack.\\ andEbetheeventthattheballdrawnfromthesecondbagiswhite.\\ \therefore P\left(E_1\right)=\frac{4}{9},P\left(E_2\right)=\frac{5}{9},P\left(E/E_1\right)=\frac{10}{17}andP\left(E/E_2\right)=\frac{9}{17}\\ \therefore P\left(E\right)=P\left(E_1\right).P\left(E/E_1\right)+P\left(E_2\right).P\left(E/E_2\right)\\ =\frac{4}{9}\times \frac{10}{17}+\frac{5}{9}\times \frac{9}{17}=\frac{40}{153}+\frac{45}{153}=\frac{85}{153}=\frac{5}{9}\\ Hence,therequiredprobabilityis\frac{5}{9}.\end{array}$

Its a four year undergraduate engineering program.

This programme focuses on the principle of applications of Artificial intelligence and DataScience. Sanjivini university designed to equip students with the skills and knowledge for their career with various fields like AI and DataScience.

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

Sol:

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

Sol:

$\begin{array}{l}Thediceisthrownthreetimes\\ \therefore Samplespacen\left(S\right)={\left(6\right)}^3=216\\ Let{E}_{1}betheeventwhenthesumofnumbersonthedicewassixand{E}_{2}betheeventwhen\\ threetwo\text{'}soccur.\\ \Rightarrow E_1=\left\{\left(1,1,4\right),\left(1,2,3\right),\left(1,3,2\right),\left(1,4,1\right),\left(2,1,3\right),\left(2,2,2\right),\left(2,3,1\right),\left(3,1,2\right),\left(3,2,1\right),\left(4,1,1\right)\right\}\\ \Rightarrow n\left(E_1\right)=10andn\left(E_2\right)=1\left[?E_2=\left\{2,2,2\right\}\right]\\ \therefore P\left(E_2/E_1\right)=\frac{P\left(E_1\cap E_2\right)}{P\left(E_1\right)}=\frac{1/216}{10/216}=\frac{1}{10}.\end{array}$

The salary for RAS (Rajasthan Administrative Service) in the RPSC falls under the INR 9,300 to INR 39,100 pay scale in the grade pay if INR 3,600 to 5,400. The in-hand salary of the candidates recruited in the RPSC RAS usually ranges from INR 33,500 to INR 66,000.

Yes. Seat allotment is done based on your merit rank, course preference, and campus availability at the time of FDDI counselling.

The highest offered during Poddar Group of Institutions placements was INR 15 LPA. The company that provided the highest package is not known yet. Once out it will be updated on this page.

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

Sol:

During the Poddar Group of Institutions placement drive students were placed in various sectors. Refer to the table below to know more:

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

Yes, selected candidates are required to pay a non-refundable seat confirmation fee during FDDI counselling, which is later adjusted in tuition. The Counselling fees will be notified at the time of counselling.

Candidates who hold a bachelor's degree or are graduate from any recognised university recognised by the Government in consultation with the RPSC are eligible to appear for the RPSC RAS examination. Moreover, the age of the candidates should be between 21 to 40 years. There is RPSC RAS upper age relaxation for reserved categories such as SC, ST, OBC, EWS and others.

Course wise placements for Poddar Group of Institutions have not been released yet. However, students can refer to the overall number of students placed and the highest salary given in the table below:

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

Sol:

$\begin{array}{l}\left(i\right)Toprove:P\left(A\right)=P\left(A\cap B\right)+P\left(A\cap \overline{B}\right)\\ R.H.S.=P\left(A\cap B\right)+P\left(A\cap \overline{B}\right)\\ =P\left(A\right).P\left(B\right)+P\left(A\right).P\left(\overline{B}\right)=P\left(A\right)\left[P\left(B\right)+P\left(\overline{B}\right)\right]\\ =P\left(A\right).1=P\left(A\right)=L.H.S\\ Henceproved.\\ \left(ii\right)Toprove:P\left(A\cup B\right)=P\left(A\cap B\right)+P\left(A\cap \overline{B}\right)+P\left(\overline{A}\cap B\right)\\ R.H.S.=P\left(A\cap B\right)+P\left(A\cap \overline{B}\right)+P\left(\overline{A}\cap B\right)\\ =P\left(A\right).P\left(B\right)+P\left(A\right).P\left(\overline{B}\right)+P\left(\overline{A}\right).P\left(B\right)\\ =P\left(A\right).P\left(B\right)+P\left(A\right)\left[1-P\left(B\right)\right]+\left[1-P\left(A\right)\right].P\left(B\right)\\ =P\left(A\right).P\left(B\right)+P\left(A\right)-P\left(A\right).P\left(B\right)+P\left(B\right)-P\left(A\right).P\left(B\right)\\ =P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)=P\left(A\cup B\right)=L.H.S.\\ Henceproved.\end{array}$

National Institute of Technology Kurukshetra accepts the JEE Main entrance exam for admitting students to its BTech course. The NIT Kurukshetra cutoff 2025 has been released for Round 1, wherein the closing ranks varied between 281 and 46438 for female candidates. For NIT Kurukshetra, the cutoff ranks were released under both AI and HS quotas. For the Home State quota, the closing ranks were between 1201 and 52806 for female category candidates. Detailed branch-wise cutoff ranks are tabulated below:

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

Sol:

$\begin{array}{l}Foraprobabilitydistribution,weknowthatif{P}_i\ge 0\\ \left(i\right){\displaystyle \sum _{i=1}^n{P}_i=1\Rightarrow k+k^2+}2k^2+k=1\\ \Rightarrow 3k^2+2k-1=0\Rightarrow 3k^2+3k-k-1=0\\ \Rightarrow 3k\left(k+1\right)-1\left(k+1\right)=0\Rightarrow \left(3k-1\right)\left(k+1\right)=0\\ \therefore k=\frac{1}{3}andk=-1\\ Butk\ge 0\therefore k=\frac{1}{3}\\ \left(ii\right)Meanofthedistribution\\ E\left(X\right)={\displaystyle \sum _{i=1}^n{X}_i{P}_i}=0.5k+1.5k^2+1.5\left(2k^2\right)+2k\\ =\frac{k}{2}+k^2+3k^2+2k=4k^2+\frac{5}{2}k\\ =4{\left(\frac{1}{3}\right)}^2+\frac{5}{2}\left(\frac{1}{3}\right)=\frac{4}{9}+\frac{5}{6}=\frac{23}{18}\end{array}$

The RPSC RAS marks of the candidates who take the exam are released after the announcement of results. The Rajasthan Public Service Commission (RPSC) releases the marks of all the candidates who appear for the exam on its official website. To check the RAS marks and download the scorecard, candidates need to click the official link and login to their registered accountd using the roll number and date of birth.