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20. $\underset{x\to 0}{lim}\frac{sinax+bx}{ax+sinbx}=\frac{\underset{x\to 0}{lim}\frac{sinax}{ax}\times ax+bx}{\underset{x\to 0}{lim}ax+\frac{sinbx}{bx}\times bx}.$

$\frac{\underset{x\to 0}{lim}\frac{sinax}{ax}\times \underset{x\to 0}{lim}ax+\underset{x\to 0}{lim}bx}{\underset{x\to 0}{lim}ax+\underset{x\to 0}{lim}\frac{sinbx}{bx}\times \underset{x\to 0}{lim}bx}$

$=\frac{\underset{x\to 0}{lim}ax+\underset{x\to 0}{lim}bx}{\underset{x\to 0}{lim}ax+\underset{x\to 0}{lim}bx}$

$=\underset{x\to 0}{lim}\frac{ax+bx}{ax+bx}$

$=\underset{x\to 0}{lim}1$

= 1.

The Bharathiar University Distance Education's admission portal for MBA admissions 2025 is expected to commence soon. According to the sources collated from the web, the application portal for various MBA courses is expected to open around the month of June. Those who wish to know more are advised to get in touch with the admissions committee.

19. $\underset{x\to 0}{lim}xsecx=\underset{x\to 0}{lim}\frac{x}{cosx}$

$=\frac{0}{cos0}$

$=\frac{0}{1}$

= 0.

The BSc nursing course at the Gokul Global University is offering the BSc Nursing course for four years. The students need to attain an aggregate of 45% in their Class 12 exam with Physics, Chemistry and Biology as compulsory subjects from a recognised board.

At SRK Institute of Technology students can offers several BTech courses. These programmes are offered in full-time mode and the admission criteria is same across all of the offered BTech courses. Find below the list of SRKIT Vijayawada BTech courses:

• Civil Engineering
• Electrical & Electronics Engineering
• Mechanical Engineering
• Electronics & Communication Engineering
• Computer Science & Engineering
• CSE (Data Science)
• CSE (AI & ML)
• Information Technology

SBI PO Mains result 2025 was announced on May 21, 2025. The result was announced on the official website. Candidates who appeared in the Mains exam can download their results by logging with the required credentials. SBI PO Mains exam 2025 was conducted on May 5, 2025.

After completion of the Bharathiar University Distance Education MBA selection process, selected students must pay the tuition fees to secure their admission. As per official sources, the total tuition fee to pursue MBA courses ranges from INR 21,100.

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

18. $\underset{}{}$$\underset{x?0}{lim}\frac{ax+xcosx}{bsinx}=\underset{x?0}{lim}\frac{x(a+cosx)}{bsinx}$

$=\frac{1}{b}*\frac{(a+cos0)}{1}$

$=\frac{a+1}{b}$

There are various career opportunities for JRSU BBA Aviation Management degree holders. Graduates can find opportunities in both government and private sectors. Mentioned below are a few top job profiles along with the salary package:

Read more: BBA in Aviation 

Bharathiar University Distance Education offers an MBA programme in the distance mode. To be able to enroll into this course, students must have obtained a UG degree in any stream from a recognised university or board in India. Those who are eligible can visit the official website of the institute to apply for the course.

36. In an English word there are 5 vowels and 21 consonants.

The number of ways of selecting 2 vowel out of 5 = ⁵C₂

= $\frac{5!}{2!\left(5?2\right)!}$

= 5 * 2 = 10

The number of ways of selecting 2 consonants out of 21 = ²¹C₂

= $\frac{21!}{2!\left(21?2\right)!}$

= 21 * 10

= 210

Therefore, the number of combinations of 2 vowels and 2 consonants is 10 * 210 = 2100

Each of these 2100 combinations has 4 letters which can be rearranged among themselves in 4! Ways.

Therefore, the required number of ways

= 4! * 2100

= 4 * 3 * 2 * 1 * 2100

= 50400

35. Since the 6-digit numbers to be formed from the digits 0, 1, 3, 5, 7 and 9 has to be divisible by 10 we have to fix the unit place as 0. Now, the remaining 5 places can be filled only by the digits 1, 3, 5, 7 and 9.

Therefore, the required number of ways

= 5!

= 5 * 4 * 3 * 2 * 1

= 120

Yes, Jharkhand Raksha Shakti University offers a three-year BBA programme in Aviation Management. Admission to the programme is merit-based. Additionally, the scores of CUET may also be considered for selection. Before applying, the aspirants must check out the course-specific eligibility criteria.

16. $\underset{x\to 0}{lim}\frac{cosx}{\pi -x}=\frac{cos0}{\pi -0}=\frac{1}{\pi }$

Admission to IHM Panipat's courses is possible even if a candidate does not appear for NCHMCT JEE. Admission to the BSc programme is mostly determined on the rank and grades obtained in the NCHMCT JEE. To be eligible for courses, candidates must have completed Class 12. Candidates can get direct admission solely through their eligibility and merit in the UG Diploma courses.

Yes, students can pursue MBA from Bharathiar University Distance Education. It is a postgraduate course offered in distance mode. The duration for each course is two years. Moreover, the tuition fee for a duration of two years amounts to INR 21,100. The aforementioned fee is as per official sources. However, it is subject to change.

The GGU provides variety of specialisation to choose from. The required eligibility is slightly different in all the offered specialisations. For the BSc Microbiology course, students need to pass Class 12 exams from Science stream with Physics, Chemistry, Biology and/or Mathematics as compulsory subjects from a recognised board.

15. $\underset{x\to \pi }{lim}\frac{sin(\pi -x)}{\pi (\pi -x)}=\frac{1}{\pi }\times \underset{x\to \pi }{lim}\frac{sin(\pi -x)}{\pi -x}$

$=\frac{1}{\pi }.$

SRK Institute of Technology BTech selection criteria is primarily entrance-based. The college admits students based on their performance in the accepted exam and the past academic performance. Students need to appear for the Andhra Pradesh EAMCET exam to get selected for the course. The basic eligibility required to apply for the course is to complete Class 12 or equivalent from a recognised board.  

14. $\underset{x\to 0}{lim}\frac{sinax}{sinbx}=\underset{x\to 0}{lim}\frac{\frac{sinax}{ax}\times ax}{\frac{sinbx}{bx}\times bx}$

$=\frac{a}{b}$