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71. 

Candidates should keep the following things ready beforehand while submitting the UTET application form.

• Valid Email ID.
• Mobile number.
• Details about identity proof- Passport/Aadhaar card/voter ID/ration card.
• Scanned images of the candidates photograph and signature as per the specified format.
• Educational qualification certificates.
• Debit or credit card/net banking details, etc.

Yes, the CAT accepting MBA colleges conduct either GD/PI or WAT/PI. Since MBA is a professional course about business and team management, personality assessment round is essential to ensure that the aspirant has the flair for management which can be polished during the programme. Communication skills, problem solving ability, management and leadership are essential qualities for MBA thus, every B-School conducts GD/PI or WAT/PI.

Karnavati University conducts the Karnavati University Admission Test (KUAT) to shortlist applicants to BCom (Hons) admissions. It also grants admission to the BCom (Hons) course based on the CUET UG scores secured by the applicants. The exact dates for these exams may vary yearly.

CAT cut offs for non-IIMs is usually lower than IIMs.

CAT admission process for non-IIMs includes Written Ability Test (WAT) or Group Discussion (GD) and Personal Interview (PI). For admission the institutes also take into consideration candidate's academic record and work experience. Overall, the admission process of all CAT accepting colleges is same where selection is based on candidate's overall personality, communication ability and consistency in academics.

36. Given, A={9,10,11,12,13}.

f(x)=the highest prime factor of n.

and f: A → N.

Then, f(9)=3 [? prime factor of 9=3]

f (10)=5 [? prime factor of 10=2,5]

f(11)=11 [? prime factor of 11 = 11]

f(12)=3 [? prime factor of 12 = 2, 3]

f(13)=13 [? prime factor of 13 = 13]

?Range of f=set of all image of f(x) = {3,5,11,13}.

35. Given, f={(ab, a+b): a, b $\in$ z}

Let a=1 and b=1;                   a, b $\in$ z.

So, ab=1 × 1=1

a+b=1+1=2.

So, we have the order pair (1,2).

Now, let a= –1 and b= –1; a, b $\in$ z

So, ab=(–1) × (–1)=1

a+b=(–1)+(–1)= –2

So, the ordered pair is (1, –2).

?The element 1 has two image i.e., 2 and –2.

Hence, f is not a function.

Yes,  Karnavati University BCom (Hons) admission 2025 is currently open. As of now, the university is accepting online registrations through its official website. After registering their candidature, aspirants must fill out the application form and submit it along with the prescribed application fee. Before applying, candidates must ensure that they fulfil the eligibility criteria specified by the university. Further, candidates seeking admission based on CUET UG scores must separately apply for the entrance exam.

34. Given,

A={1,2,3,4}

B={1,5,9,11,15,16}

f={(1,5),(2,9),(3,1),(4,5),(2,11)}.

(i) As every element of f is an element of A × B

We can clearly say that f $\subset$ A × B.

?f is a relation from A to B.

(ii) As the element 2 of the domain has two image i.e., 9 and 11. f is not a function.

When exploring the BA programme at NIPS Hotel Management Bhubaneswar, it's important to look beyond just the course name. Consider the specialisations available, how well the curriculum aligns with current industry trends, faculty experience, internship and hands-on training opportunities, and whether the fees justify the career outcomes. These factors help ensure the programme supports your long-term goals.

69. 

The given eqⁿ of the lines are.

4x + 7y + 5 = 0______ (1)

2x - y = 0 ______ (2)

Solving (1) and (2) we get,

4 x + 7 (2 x)+5 = 0

4x +14 x + 5= 0

x = $\frac{-5}{18}$

and y = 2x = $2\left(\frac{-5}{18}\right)=\frac{-5}{9}$

The UTET 2025 application form was released on July 10 on the official website at ukutet.com. The last date to apply was August 5, 2025. The UTET registration was carried out online. Candidates need to pay the UTET application fee 2025 for successful submission of the online form.

33. Given, R= { (a, b): a, b $\in$ N and a = b²}

(i) Let a = 2 $\in$ N

Then b = 2² = 4 $\in$ N

but a ≠ b.

Hence the given statement is not true.

(ii) For a=b² the inverse b=a² may not hold true

Example (4,2) $\in$ R, a=4, b=2 and a=b²

but (2,4) $\notin$ R.

Hence, the given statement is not true.

(iii) If (a, b) $\in$ R

a=b²…… (1)

and (b, c) $\in$ R

b=c²……. (2)

so for (1) and (2),

a= (c²)²=c⁴.

is, a ≠c²,

Hence, (a, c) $\notin$ R.

? The given statement is false.

NIPS Bhubaneswar has seen top hospitality recruiters like Taj Hotels, Oberoi Group, and Trident Group regularly participate in placement drives. These companies offer roles across departments such as operations, food and beverage, front office, and housekeeping, providing students with a strong launchpad for a career in the hospitality industry post-graduation.

32. Given, f(x) = (ax + b)

= {(1,1),(2,3),(0, – 1),(–1, –3)} .

As (1,1) $\in$ f.

Then, f(1)=1   [? f(x) = y for (x, y)]

a × 1+b=1

a+b=1…… (1)

and (0, – 1) $\in$ f .

Then, f(0)= –1

a× 0+b= –1

b= –1…….(2)

Putting value of (2) in (1) we gets

a – 1=1

a=1+1

a=2

So, (a, b)=(2, –1)