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In order to apply for the IHM Bangalore BSc course, students are required to apply for the NCHMCT JEE exam. Listed below are the steps to apply for the exam.

1. Visit the official website of the exam-conducting body and register.

2. Log in to the account made in the previous step.

3. Fill out the application form and upload required documents.

4. Pay the application fees.

5. Submit the form.

17. $P(A/B)=P(B/A)$

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

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

Using (i) and (ii),

$P(A/B)=P(B/A)$

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

$\Rightarrow P(A)=P(B)$

$\therefore$ The correct answer is $(D).P(A)=P(B)$

Yes, the Makhanlal Chaturvedi National University of Journalism and Communication offers a BTech in Printing and Packaging. Additionally, the university also offers Lateral Entry for this programme. The duration of this lateral entry programme is three years. Furthermore, candidates can refer to the following key highlights related to the MCNUJC Bhopal BTech programme:

NOTE: The above-mentioned seat intake is taken from the official website. It is still subject to change and, hence, is indicative.

16. $P(A)=\frac{1}{2}$ $,P(B)=0$

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

$=\frac{P(A\cap B)}{0}$ = which is not defined

The correct answer is $(C)$ not defined.

After completing MBBS, you are eligible for a Postgraduate course in Sports Medicine. Admission is usually through NEET-PG or INI-CET depending on the institute. Top medical colleges and universities in India offer MD/Diploma in Sports Medicine, focusing on injury management, rehabilitation, and athlete care. Selection is merit-based, followed by counselling and seat allotment.

15. The sample space of experiment is

$S=\left\{\begin{array}{l}(1,H),(1,T),(2,H),(2,T),(3,1),\\ (3,2),(3,3),(3,4),(3,5),(3,6),\\ (4,H),(4,T),(5,H),(5,T),\\ (6,1),(6,2),(6,3),(6,4),(6,3),\\ (6,5),(6,6)\end{array}\right\}$

Let, $E$ be the event that ‘coin shows a tail’ and $F$ be the event that ‘atleast one die shows a $3$ ’

$\Rightarrow E=\{1T,2T,4T,5T\}$

$F=\{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\}$

$\Rightarrow E\cap F=\varnothing \Rightarrow P(E\cap F)=0$

Now,

$P(E/F)=\frac{P(E\cap F)}{P(F)}=\frac{0}{P(F)}=0$

$\Rightarrow P(E/F)=0$

Yes, IHM Bangalore offers a single specialisation under its BSc programme. This specialisation is BSc in Hospitality and Hotel Administration. The course runs for a duration of three years. During this duration, students gain advanced knowledge of subjects such as Hotel Accountancy, Food Safety, Hygiene and Nutrition, Facility Planning, Financial Management, Strategic Management, etc.

The Institute of Hotel Management Bangalore BSc fee structure includes various components such as tuition fees, examination fees, training fees, etc. As per the structure, the total tuition fee is INR 3.2 lakh.

Note: The above-mentioned fee is as per the official sources. However, it is indicative and subject to change.

15. When dice is thrown, number of observations in the sample space is $6\times 6=36$

Let, $A:$ event that the sum of the number on the dice is $4$

$B:$ event that the two number appearing on throwing two dice is different

$A=\{(1,3),(2,2),(3,1)\}$

$B=\left\{\begin{array}{l}(1,2),(1,3),(1,4),(1,5),(1,6)\\ (2,1),(2,3),(2,4),(2,5),(2,6)\\ (3,1),(3,2),(3,4),(3,5),(3,6)\\ (4,1),(4,2),(4,3),(4,5),(4,6)\\ (5,1),(5,2),(5,3),(5,4),(5,6)\\ (6,1),(6,2),(6,3),(6,4),(6,5)\end{array}\right\}$

$(A\cap B)=\{(1,3),(3,1)\}$

$P(B)=\frac{30}{36}$ $,P(A\cap B)=\frac{2}{36}$

$P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$36$}\right.}{\raisebox{1ex}{$30$}\!\left/ \!\raisebox{-1ex}{$36$}\right.}=\frac{2}{30}=\frac{1}{15}$

$\therefore$ Required probability is $\frac{1}{15}$

RRB Group D exam qualifying score depends on category and cut-off marks set by Railway Recruitment Board. Generally, candidates need around 40% marks (35% for SC, ST, OBC) to qualify. Final selection, however, depends on merit list, normalization of scores, and PET performance. Cut-offs vary every year based on vacancies, difficulty level, and number of applicants.

NMIMS cutoff 2025 was released for enrollment to the management programmes based on the NMAT entrance exam. In 2024, the cutoff was a 248 score for the General AI category. Hence, according to this score, candidates who attained at least the previously mentioned score become eligible for 2nd round of admission, which involves WAT (Written Ability Test) and PI (Personal Interview). 

For more details, students can go to the official Shiksha's cutoff page for NMIMS by clicking here. 

The difficulty of admission can change from year to year and depends on variables including the quantity of applications and the institute's admission requirements. In summary, selective admissions procedures at Aditya Birla Education Academy are generally based on merit. To improve your chances, it is advised to visit the official website.

13. Here, there are two types of questions, True/False or Multiple-Choice Questions. They are divided into easy and difficult.

True/False: 300 easy, 200 difficult

$MCQ$ : 500 easy, 400 difficult

Let,  $E=$ easy question

$M=$ multiple choice question

Total number of questions= $300+200+500+400=1400$

Total number of multiple-choice questions= $500+400=900$

Therefore, probability of selecting an easy $MCQ$ is

$P(E\cap M)=\frac{500}{1400}=\frac{5}{14}$

The probability of setting a $MCQ$ is

$P(M)=\frac{900}{1400}=\frac{9}{14}$

$\therefore$ $P(E/M)=\frac{P(E\cap M)}{P(M)}=\frac{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$14$}\right.}{\raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$14$}\right.}=\frac{5}{9}$

$\therefore$ Required probability is $\frac{5}{9}$

The St. Clair College is highly renowned for offering the highest placement rate in Canada. The college placement rate attracts international students the most. St. Clair College placement rate stands at 84.4%, and the graduates are employed within 6 months of graduation. According to unofficial sources on the web, the average salary of St. Clair College graduate is CAD 70,000 (INR 43.45 LPA) annually. According to St. Clair College reviews posted by students on Shiksha, the college has an overall rating of 2.9 stars. The students rated the St. Clair College for placement is as follows:

Auro University is one of the best choice for the students. The university is popularly know for its academic excellence and vibrant campus life. The university encourages and promotes learning on a 20:30:50 principle, where lectures constitute 20% of the delivery (Hear); visuals 30% of the learning methods (See); and experience 50% (Do). Auro University has eight schools of study through which it offers UG, PG, and PhD courses. The university has a strong faculty with experienced lecturers and visiting faculty from industry.