Ask & Answer: India's Largest Education Community

$\begin{array}{l}LetthenumberofstudentspassedinMathematicsM,EbeinEnglishandSbeinScience.\\ Thenn\left(U\right)=100,n\left(M\right)=12,n\left(E\right)=15,n\left(S\right)=8\\ n\left(E\cap M\right)=6,n\left(M\cap S\right)=7,n\left(E\cap S\right)=4andn\left(E\cap M\cap S\right)=4\\ Letusdrawavenndiagram.Accordingtothevenndiagram,weget\\ a+b+d+e=15\dots \left(i\right)\\ b+c+e+f=12\dots \left(ii\right)\\ d+e+f+g=8\dots \left(iii\right)\\ n\left(E\cap M\right)=6\therefore b+e=6\dots \left(iv\right)\\ n\left(M\cap S\right)=7\therefore e+f=7\dots \left(v\right)\\ n\left(E\cap S\right)=4\therefore d+e=4\dots \left(vi\right)\\ n\left(E\cap M\cap S\right)=4\therefore e=4\dots \left(vii\right)\\ Fromeqn.\left(iv\right)and\left(vii\right)wegetb+4=6\therefore b=2\\ Fromeqn.\left(v\right)and\left(vii\right)weget4+f=7\therefore f=3\\ Fromeqn.\left(vi\right)and\left(vii\right)wegetd+4=4\therefore d=0\\ Fromeqn.\left(i\right)wegeta+b+d+e=15\\ \Rightarrow a+2+0+4=15\Rightarrow a=9\\ Fromeqn.\left(ii\right)wegetb+c+e+f=12\\ \Rightarrow 2+c+4+3=12\Rightarrow c=3\\ Fromeqn.\left(iii\right)wegetd+e+f+g=8\\ \Rightarrow 0+4+3+g=8\Rightarrow g=1\\ \therefore \left(i\right)NumberofstudentswhopassedinEnglishandMathematicsbutnotinScience,b=2\\ \left(ii\right)NumberofstudentswhopassedinMathematicsandSciencebutnotinEnglish,f=3\\ \left(iii\right)NumberofstudentswhopassedinMathematicsonly,c=3.\end{array}$

The GB Shah College for Technology and Management BCA programme is known to provide a well-rounded education in Computer Applications, preparing various students for careers in Software Development, Web Development, IT Management, Data Analytics,  and several other emerging technologies. The curriculum designed is comprehensive in nature. The BBA programme is known to provide industry exposure, quality education, and skill development among students. 

Yes. NTA has already released qualifying cut off score for AIAPGET 2025. The cut off differs for each category. Check the qualifying cutt off for AIAPGET 2025 in the table given below:

$\begin{array}{l}Letx\in A\cap \left(B\cup C\right)\\ \Rightarrow x\in Aand\left(x\in Borx\in C\right)\\ \Rightarrow \left(x\in Aandx\in B\right)or\left(x\in Aandx\in C\right)\\ \Rightarrow \left(x\in A\cap B\right)or\left(x\in A\cap C\right)\\ \Rightarrow \left(x\in A\cap B\right)\cup \left(x\in A\cap C\right)\dots \left(i\right)\\ Lety\in \left(x\in A\cap B\right)\cup \left(x\in A\cap C\right)\\ \Rightarrow y\in \left(x\in A\cap B\right)or\left(x\in A\cap C\right)\\ \Rightarrow \left(y\in Aandy\in B\right)or\left(y\in Aandy\in C\right)\\ \Rightarrow y\in Aand\left(y\in Bory\in C\right)\\ \Rightarrow y\in Aandy\subset \left(B\cup C\right)\\ \Rightarrow y\in A\cap \left(B\cup C\right)\dots \left(ii\right)\\ Fromeq\left(i\right)and\left(ii\right)weget\\ A\cap \left(B\cup C\right)=\left(A\cap B\right)\cup \left(A\cap C\right)\\ L.H.S.=R.H.S.Henceproved.\end{array}$

GB Shah College for Technology and Management offers undergraduate programmes to students. At the undergraduate level, there are courses such as BCA and BBA. The admission to these courses is conducted through the Gujarat Common Admission System (GCAS) as per the various guidelines set by AICTE and Gujarat Technological University (GTU). The eligibility criteria include, 12th pass (any stream) from a recognised board. 

Yes, you can learn a basic data analyst course in 1 month and get a certificate. Datamites has simple beginner courses that you can finish in a short time. Your BCom background and good communication skills will help you understand the topics quickly. You may not become an expert in one month, but you can build a strong starting point. Keep learning and practicing to improve your skills further.

$\begin{array}{l}Giventhat:T=\left\{x|\frac{x+5}{x-7}-5=\frac{4x-40}{13-x}\right\}\\ \Rightarrow \frac{x+5}{x-7}-5=\frac{4x-40}{13-x}\\ \Rightarrow \frac{x+5}{x-7}-\frac{4x-40}{13-x}=5\\ \Rightarrow \frac{\left(x+5\right)\left(13-x\right)-\left(x-7\right)\left(4x-40\right)}{\left(x-7\right)\left(13-x\right)}=5\\ \Rightarrow \frac{13x-x^2+65-5x-4x^2+40x+28x-280}{13x-x^2-91+7x}=5\\ \Rightarrow -5x^2+76x-215=5\left(13x-x^2+7x-91\right)\\ \Rightarrow -5x^2+76x-215=65x-5x^2+35x-455\\ \Rightarrow 76x-100x=-455+215\\ \Rightarrow -24x=-240\Rightarrow x=\frac{240}{24}=10\\ \therefore T=10\\ Hence,Tisnotanemptyset.\end{array}$

$\begin{array}{l}L.H.S.=\left(A\cup B\right)-B=\left(A\cup B\right)\cap B\text{'}\left[?A-B=A\cap B\text{'}\right]\\ =\left(A\cap B\text{'}\right)\cup \left(B\cap B\text{'}\right)\left[?A\cap A\text{'}=?\right]\\ =\left(A-B\right)\cup ?\\ =A-B=R.H.S.Henceproved.\end{array}$

$\begin{array}{l}L.H.S.=A-\left(A\cap B\right)=A\cap \left(A\cap B\right)\text{'}\\ =A\cap \left(A\text{'}\cup B\text{'}\right)=\left(A\cap A\text{'}\right)\cup \left(A\cap B\text{'}\right)\\ =?\cup \left(A-B\right)\left[?A-B=A\cap B\text{'}\right]\\ =A-B=R.H.S.\\ Hence,thegivenstatementisproved.\end{array}$

Yes, students can join GB Shah College for Technology and Management without 60% in PCM as the eligibility criteria is pass in Class 12 (any stream) from a recognised board. The mode of GB Shah College for Technology and Management course admissions is online. Admission to various courses is based on merit and other criteria decided by the college. Candidates willing to get admission must first register online on the GCAS portal. Then, do the choice filling and college selection. Then, students must prepare the merit list and seat allotment. Then, pay the admission fee and wait for the seat allotment.

$\begin{array}{l}L.H.S.=A-\left(A-B\right)=A-\left(A\cap B\text{'}\right)\left[?A-B=A\cap B\text{'}\right]\\ =A\cap \left(A\cap B\text{'}\right)=A\cap \left[A\text{'}\cup \left(B\text{'}\right)\text{'}\right]\left[?\left(A\cap B\right)\text{'}=A\text{'}\cup B\text{'}\right]\\ =A\cap \left[A\text{'}\cup B\right]\left[?\left(A\text{'}\right)\text{'}=A\right]\\ =\left(A\cap A\text{'}\right)\cup \left(A\cap B\right)=?\cup \left(A\cap B\right)\\ =A\cap B=R.H.S.\\ Hence,thegivenstatementisproved.\end{array}$

$\begin{array}{l}L.H.S.=A\cup \left(B-A\right)=A\cup \left(B\cap A\text{'}\right)\left[?A-B=A\cap B\text{'}\right]\\ =\left(A\cup B\right)\cap \left(A\cup A\text{'}\right)\\ =A\cup B\cap U\left[?A\cup A\text{'}=U\right]\\ =A\cup B=R.H.S.\left[?A\cup U=A\right]\\ Hence,thegivenstatementisproved.\end{array}$