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4. Given,

$2P(A)=P(B)=\frac{5}{13}$

$P(A/B)=\frac{2}{5}$

$2P(A)=\frac{5}{13}\Rightarrow P(A)=\frac{5}{13\times 2}=\frac{5}{26}$

$\Rightarrow P(A/B)=\frac{P(A\cap B)}{P(B)}$

$\Rightarrow \frac{2}{5}=\frac{P(A\cap B)}{\frac{5}{13}}$

$\Rightarrow \frac{2}{5}\times \frac{5}{13}=P(A\cap B)\Rightarrow P(A\cap B)=\frac{2}{13}$

$\therefore P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$=\frac{5}{26}+\frac{5}{13}-\frac{2}{13}$

$=\frac{5+10-4}{26}=\frac{11}{26}$

The NMIMS 2024 cutoff for the NMAT was a score of 248 for admission to the MBA/PGDM course. Hence, going by this score, we can say that the NMIMS cutoff 2026 might be somewhere around this score. 

Although it is an estimated guess and the NMAT cutoff is subject to many factors, like difficulty level of the exam, previous year trend, seats available, etc. 

Note - The cutoff score is an estimate and not official.

In order to get admission at Aditya Birla Education Academy candidates must keep certain documents ready. Student can check the list of documents below:

• Scanned Class 10, Class 12 and graduation marksheet
• Leaving Certificate
• Aadhaar Card
• Passport-size photograph
• Signature

Note: The list of documents mentioned above are the general documents. For more details visit the official website.

3. Given,

$P(A)=0.8$

$P(B)=0.5$

$P(B/A)=0.4$

$\mathrm{(i)\; P}(A\cap B)$

$P(B/A)=\frac{P(B\cap A)}{P(A)}$ $[?P(A\cap B)=P(B\cap A)]$

$\Rightarrow 0.4=\frac{P(A\cap B)}{0.8}$

$\Rightarrow P(A\cap B)=0.4\times 0.8$

$=0.32$

$\mathrm{(ii)\; P}(A/B)$

$P(A/B)=\frac{P(A\cap B)}{P(B)}$

$P(A/B)=\frac{0.32}{0.5}$

$=0.64$

$\mathrm{(iii)\; P}(A\cup B)$

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$=0.8+0.5-0.32$

$=0.98$

Candidates seeking admission to courses at Aditya Birla Education Academy must apply online. ABEA offers PG Diploma courses at the postgraduate level. The selection criteria are based on merit. Applicants must complete all details carefully, such as their name, mobile number, and state of residence. Candidates can submit the application form on the institute's official website.

2. Given,

$P(B)=0.5$

$P(A\cap B)=0.32$

$P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{0.32}{0.5}=\frac{32}{50}=\frac{16}{45}$

1. Given,

$P(E)=0.6$

$P(F)=0.3$

$P(E\cap F)=0.2$

$P(E/F)=\frac{P(E\cap F)}{P(F)}=\frac{0.2}{0.3}=\frac{2}{3}$

$P(F/E)=\frac{P(F\cap E)}{P(E)}=\frac{0.2}{0.6}=\frac{2}{6}=\frac{1}{3}$

To get admitted to Aditya Birla Education Academy, candidates must meet the eligibility criteria set by the institute.Students seeking to apply for any of the courses offered at the college must fulfil the admission criteria of the desired programme before applying for it. Candidates looking for course admission must complete graduation in any stream. A good command of English at level C2 (agreed level of competence for English as a second language).

Yes, candidates can gain admission to Aditya Birla Education Academy for a PG Diploma with 60% in Class 12. Aspirants must complete their graduation in any stream. However, the institute has not disclosed the percentage required for the final educational qualification. Nonetheless, admissions at Aditya Birla Education Academy are entirely based on merit.

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• Students should start by logging in to MyUNT using their EUID and password. 
• Select the current financial year from the available dropdown. 
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You can download Gujarat Board Class 10 Maths papers from official GSEB e-service and trusted portals. For recent years (2020–2025).

In order to get admission to Aditya Birla Education Academy, candidates should complete a graduation in any stream. The selection criteria for the course are conducted online. Candidates looking for course admission must complete graduation in any stream. A good command of English at level C2 (agreed level of competence for English as a second language).

36. For the given inequality, x> –3.

The equation of the line is x= –3.

This line divides the xy-plane into planer I and II. We take a point (0,0) to check the correctness of the inequality.

So, 0> –3 which is true.

So, the solution of the region is I which includes the origin.

The dotted line indicates that any point on the line does not satisfy the inequality.

Candidates looking for course admission at Aditya Birla Education Academy must meet the eligibility criteria set by the college. Aspirants must pass graduation in any stream. The selection criteria for the course are merit-based. The application process is conducted online. Candidates must apply at the official website.

35. For the given equation inequality y< 2,  the equation of line is y= 2

This line devides the xy-plane into two planer I and II. We take a point (0,0) to check the correctness of the inequality.

So, 0< 2

0< 2 which is false.

So, the solution of the region is II which does not include the origin.

The dotted line indicates that any point on the line does not satisfy the inequality.

34. For the inequality 3y – 5x<30, the equation of line is 3y – 5x=30. We consider the table below to plot 3y – 5x =30.

$\begin{array}{l}x\\ y\end{array}|\begin{array}{l}0\\ 10\end{array}|\begin{array}{l}-6\\ 0\end{array}|$

This line divides the xy-plane into two planer I and II. We select a point (0,0) and check the correctness the inequality.

3 × 0 – 5 × 0 < 30

0 < 30 which is true.

So, the solution region is I which includes the origin. The dotted line indicates that any point on the line will not satisfy the given inequality.

33.For the inequality –3x+2y≥ –6 the equation of line is – 3x+2y=6.

We consider the table below to plot – 3x+2y= –6.

$\begin{array}{l}x\\ y\end{array}|\begin{array}{l}0\\ -3\end{array}|\begin{array}{l}2\\ 0\end{array}|$

This line divides the xy-plane into two planer I and II. We select a point (0,0) and check the correctness the inequality,

–3 × 0+2 × 0 ≥ –6

0 ≥ –6 which is true.

So, the solution region is I which includes the origin. The continuous line also indicates that any point on the line also satisfy the given inequality.