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54. Given, P (A) = P (B) where P is power set

Let x$\cancel{\in }$A.

Then, {x} $\subset$P (A)$\subset$ P (B)

i.e., x$\cancel{\in }$ B

A$\subset$ B

Similarly, B $\subset$A

A = B

With 49 percentage it's hard to get admission in MCOE as the first round closing score would be 97% and final round closing score would be 95.89%

Maybe you can try any other private colleges.

If you have further queries feel free to connect:)

53. Given, A $\subset$B.

Let x$\cancel{\in }$ C - B then x $\cancel{\in }$C but X$B$ .

However, A $\subset$B, elements of B should have elements of A

i.e., X$B$ 

So, x $\cancel{\in }$C A i.e., x$\cancel{\in }$ C but X$A$

C - B $\subset$C-  A

52. (i) Let A-  B≠$?$ , our assumption.

i.e., x$\in$ A But x≠ B where x is an element.

But as A B, the above condition of assumption is wrong if A $\subset$B then A -  B =$?$

(ii) Let x$\in$ A.

As A - B =$?$ we can say that x$\in$ B because if $x\cancel{\in }B,$ A - B ≠$?$

if A - B =$?$ then A $\subset$B.

(iii) We know that,

B $\subset$A$\cup$ B always true

Let x$\in$A$\cup$B i.e., x$\in$ A or x$\in$ B.

As A $\subset$B,

If x $\in$A then x$\in$ B, all elements of A are among the elements of B

So, (A$\cup$B) = B

(iv) We know that,

(A$\cap$ B) $\subset$A as A$\subset$ B.

Let x $\in$A then x $\in$B

So, x $\in$(A$\cap$ B)

i.e., A$\subset$ (A$\cap$ B)

So, A = (A $\cap$B)

Hence, A$\subset$ B

A - B = $?$.

A$\cup$ B = B

A $\cap$B = A.

i.e., the 4 conditions are equivalent.

NIILM University offers a variety of BTech specialisations to match students' interests and career goals. These include Computer Science and Engineering (CSE), Artificial Intelligence & Machine Learning (AI & ML), Data Science, Computer Engineering, Civil Engineering, Mechanical Engineering, Electrical Engineering, Electronic Engineering, and Electronics & Communication Engineering.

The annual tuition fee for the BTech programme at NIILM University is INR 80,000. Over the four-year course, the total tuition fee amounts to INR 3.2 Lakh. However, students are advised to confirm the latest fee details with the university, as the structure may change over time. 

51. Let x$\in$b

As B$\subset$ A$\cup$ B we can write

Let x $\in$A $\cup$B.

as A $\cup$B = A $\cup$C.

x$\in$ A$\cup$ C.

i.e., x$\in$ A or x $\in$C

when x$\in$ A, and x$\in$ B,

x$\in$ A$\cap$ B

But A$\cap$ B = A $\cap$C

So, x$\in$ A $\cap$C

i.e., x$\in$ A and x$\in$ C

x $\in$C

when, x$\in$ C

as x $\in$B and x $\in$C

So, B $\subset$C

Similarly, C $\subset$B

So, B = C

To apply for the BTech programme at NIILM University, students must have completed their Class 12 with Physics, Chemistry, and Mathematics (PCM) from a recognised board. For lateral entry, candidates need a Diploma in engineering. Meeting the eligibility criteria is essential to move forward in the admission process.

For distribution of BBA seats offered by Bharathiar University Distance Education, the institute considers marks obtained in the qualifying examination. Candidates who aspire to get a seat are required to apply for the course by visiting the institute's official website. If shortlisted, students are required to complete the admission confirmation process. Lastly, students must pay admission to secure their seats.

50. (i) False Let A = {a}, a $\in$A then B = {a}, b} I e,  $a\cancel{\in B.}$

(ii) False. Let A. = {a}, if A $\subset$B, B = {a, b} and B $\in$C I e, C = {a, b}, c} I e, A = {a}. 

(iii) True. Let x$\in$A, if A$\subset$ B then x$\in$B and if B$\subset$ C, x$\in$ C I e, elements of A are also elements of C. A$\subset$ C.

(iv) False. Let A = {a} and B = {b} then A$\not\subset$$B$ . Let C = {a, c} then B$\not\subset$$\subset$ but a $\in$A and a c, i.e., A$\subset$ C.

(v) False. Let A = {a} and B = {b} so, A$\not\subset$$B$ i.e., A$B$ .

(vi) True. Let A$\subset$ B such that y$\in$ B i.e., y A But x$\in$$B$ and suppose x$\in$A.

Then by above definition,  A $\subset$B i.e., x$\in$ B and x$\in$ A which is not the case

Karnavati University offers a full-time BSc (Hons) in Psychology. The programm is offered through the university's Unitedworld School of Liberal Arts and Mass Communication (USLM). There are 60 seats available at the university for the BSc (Hons) programme. These seats are offered to eligible applicants based on their eligibility and performance in CUET UG/ KUAT & PI. It must be noted that the mentioned information is sourced from the official website of the university/ sanctioning body. It is still subject to change and hence indicative.

Bharathiar University Distance Education has only 40 seats available for admission to the BBA course. Thus, a total of 40 students can take admission into the course in a single academic year. Moreover, it is important to note that the seat intake state above is sourced from official sources. However, it is subject to change at the discretion of concerned authorities.

49. A = {x: xR and x satisfy x² - 8x + 12 = 0}

So, x² - 8x + 12 = 0

x² - 6x 2x + 12 = 0

x (x- 6) 2 (x -6) = 0

(x -6) (x- 2) = 0

x = 6, 2.

So, A = {2, 6) B = {2, 4, 6} C = {2, 4, 6, 8, ….}

D = {6}

D⊂ A ⊂B ⊂C

i e, D ⊂A, D⊂ B, D⊂ C, A⊂ B, A ⊂C and B⊂ C.

Yes, candidates can get admission to K J Somaiya School of Engineering for its BTech programme without appearing for the JEE Mains exam. The school accepts various entrance exams, such as JEE Main, MHT CET, CUET, SAT India, and PERA CET to shortlist the BTech candidates. Those who are selected must present the relevant documents to prove their eligibility.

48. Let A and B be set of people who speaks Frenchand Spanish respectively. Then,

n (A) = 50, people speak French

n (B) = 20, people speak Spanish.

n (A $\cap$B) = 10, speaks both French& Spanish.

So, number of people who speaks at least one of these two languages

= n (A $\cup$B)

= n (A) + n (B) n (A $\cap$B)

= 50 + 20 10

= 60

With an 136 integrated rank in AP ECET you would be their top priority in admissions and you have a great opportunity to enroll in top colleges such as

1.Indian institute of technology , Tirupati as closing rank is 200

2.Andhra University college of engineering,Vishakapatnam as closing rank goes upto 1000

3.Konneru lakshmaiah education foundation as closing rank is 500

4.JNTU Kakinada as closing rank is 1000 and have many placement opportunities 

If you have further questions feel free to connect :)

Karnavati University provides entrance-based admissions to its BSc programme. The university considers the entrance exam scores of the applicants to shortlist them for the subsequent selection round, which is a personal interview. The university conducts the Karnavati University Admission Test (KUAT). Candidates seeking BSc admission at the university must apply and appear for the KUAT. Alternatively, they can submit their CUET UG scores to get shortlisted for the interview round.

The institute offers Fellowship, Certificate, Short Term and PG Management courses. The selection criteria are merit-based. The institute offers more than 10 courses in various streams such as Healthcare Management, Medicine, etc. Students can check the table below to know detailed course-wise eligibility and selection criteria: