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Exercise 13.1

1. 1. $\underset{x\to 3}{lim}$x + 3 = 3 + 3 = 6.

29. We are given 17 players of which 5 players can bowl and 17 – 5 = 12 can bat. But we need to select a team of 11 in which there are exactly 4 bowlers.

Hence, the required number of ways

=⁵C₄ (bowl) x ¹²C _(11-4) (bat)

= $\frac{5!}{4!\left(5-4\right)!}$ × $\frac{12!}{7!\left(12-7\right)!}$

= 5 × 11 × 9 × 8

= 3960

For admission in BBA at Jharkhand Raksha Shakti University, aspirants must meet the prescribed eligibility criteria. The eligible students can visit the official website to apply. For selection, the aspirants performance in the last qualifying exam is considered. Additionally, the CUET scores may also be considered. After selection, a merit list may get released and candidates are called for counselling. Following seat allotment, students can pay the admission fee amount to confirm their seats. 

The University of Illinois is among an exclusive group of US based universities to be classifed as a Tier-1 research institution (R1). As per an official media release by UIC, the institute retained its status of being a R1 university since 1987.

The R1 universities are known for conducting an high volume of research & an minimium expenditure of USD 50 million in research related activities over the course of an academic year.

The R1 status is awarded by the Carnegie Classification of Institutions of Higher Education.

The eligible students can either go to the official website or reach out to admission office for application submission. For application submission, a fee may also have to be paid. Candidates shall ensure that the details provided in JRSU BBA application are updated and correct. Mentioned below are steps to be followed for the online form filling:

1. Visit the official website.
2. Click on the "Apply Now or Application" link.
3. Fill out details and upload documents.
4. Pay application fees and submit the form.

NOTE: The above-mentioned is a generic process. Hence, is indicative.

Pursuing a BA degree from Bharathiar University Distance Education helps students gain knowledge of various domains such as Psychology, Sociology, History, English, and others. However, in today's competitive times, having only theoretical knowledge might not be enough to be successful in the corporate landscape. In today's time, employers are looking for candidates who possess both theoretical and practical knowledge. Listed below are some of the skills demanded in today's corporate world:

• Foreign Language
• Digital Marketing
• HR Analytics
• Public Administration
• Graphic Designing
• Public Relations Management

28. In a deck of 52 cards there are 4 ace cards. The required number of ways of selecting one ace card from the four = ⁴C₁ = $\frac{4!}{1!\left(4-1\right)!}$ = $\frac{4!}{3!}$ = $\frac{4\times 3!}{3!}$ = 4

After selecting one ace we need to select the remaining 4 card from the remaining 48 card to have a combination of 5 cards. The required number of ways

= ⁴⁸C₄

= $\frac{48!}{4!\left(48-4\right)!}$

= 1,94,580

Therefore, the total number of ways for selecting 5 card combination out of a deck of 52 cards if there is exactly one ace in each combination

= ⁴C₁×⁴⁸C₄

= 4 × 1,94,580

= 7,78,320

No, Bharathiar University Distance Education does not provide a refund of fees if a student wishes to cancel or withdraw his/her admission. The official website states that if a student wishes to leave the programme before completion, such candidates is not entitled to a refund of paid service fees. In case a refund is approved at the discretion of the Management, then the amount is sent via the debit/credit card used for the original transaction. 

While the MBA programme isn't ranked separately, NIPER Ahmedabad consistent performance in national rankings highlights the institute's credibility and academic strength, making its MBA programme a valuable choice.

No, NIPER Ahmedabad does not have a separate ranking for its MBA programme. However, the institute's overall NIRF rank (#15 in Pharmacy, 2024) reflects its strong academic foundation, which also supports the quality of its management education.

27. Since we are to select 3 balls from each colour in order to select 9 balls from the collections of 6, 5 and 5 balls of red, white and blue colours respectively, we can have the combination

⁶C₃ (red) ×⁵C₃ (white) ×⁵C₃ (blue)

= $\frac{6!}{3!\left(6-3\right)!}$ × $\frac{5!}{3!\left(5-3\right)!}$ × $\frac{5!}{3!\left(5-3\right)!}$

= 20 × 10 × 10

= 2000

The university may publish important admission dates on its official website. Students must know the schedule to apply on or before the prescribed deadline. As the CUET scores may also be accepted, aspirants must know its dates. CUET exam is scheduled from May 13 to Jun 3.

26.The number of ways of selecting a team consisting of 3 boys from 5 boys and 3 girls from 4 girls is

⁵C₃×⁴C₃

= $\frac{5!}{3!\left(5-3\right)!}$ × $\frac{4!}{3!\left(4-3\right)!}$

= $\frac{20}{2}$ × $\frac{4}{1}$

= 40

Jharkhand Raksha Shakti University admit candidates on a merit-basis. Hence, the applicants performance in Class 12 or equivalent exam is evaluated for selection. Additionally, the scores in CUET may also be considered during the selection. Apart from this, it is crucial that the aspirants fulfil the course-specific eligibility criteria. To be eligible, candidates should have passed Class 12 with a minimum of 50% aggregate.

A minimum of 50% in English as a required subject in Class 12 is required for admission to the three-year BBA program, which is merit-based. Due to competition, the cutoff for admission is typically much higher in practice. Recent patterns indicate that, depending on the volume of applications and available seats, the final admission cutoff frequently falls between 80% and 85%.

25. A chord is drawn by connecting 2 points on a circle.

As we are given with 21 points on the circle, we have the following combination to find the number of chords.