cat 2017 slot 1 answers

The Common Admission Test (CAT) is a highly competitive exam for admission to various management programs in India. The 2017 CAT exam was conducted in two slots, and this article provides detailed answers for Slot 1. Quantitative Aptitude Question 1: Ratio and Proportion Question: If the ratio of the sum of the first m terms of an arithmetic progression to the sum of the first n terms of the same arithmetic progression is m^2:n^2, then what is the ratio of the mth term to the nth term? Answer: The ratio of the sum of the first m terms to the sum of the first n terms is given by: [ \frac{S_m}{S_n} = \frac{m^2}{n^2} ] Using the formula for the sum of an arithmetic progression: [ S_m = \frac{m}{2} \times (2a + (m-1)d) ] [ S_n = \frac{n}{2} \times (2a + (n-1)d) ] Substituting these into the given ratio: [ \frac{\frac{m}{2} \times (2a + (m-1)d)}{\frac{n}{2} \times (2a + (n-1)d)} = \frac{m^2}{n^2} ] Simplifying, we get: [ \frac{2a + (m-1)d}{2a + (n-1)d} = \frac{m}{n} ] Solving for the ratio of the mth term to the nth term: [ \frac{a + (m-1)d}{a + (n-1)d} = \frac{m}{n} ] Therefore, the ratio of the mth term to the nth term is: [ \frac{T_m}{T_n} = \frac{m}{n} ] Question 2: Geometry Question: In a triangle ABC, the median from A is perpendicular to the median from B.

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cat 2017 slot 1 answers

The Common Admission Test (CAT) is a highly competitive exam for admission to various management programs in India. The 2017 CAT exam was conducted in two slots, and this article provides detailed answers for Slot 1.

Quantitative Aptitude

Question 1: Ratio and Proportion

Question: If the ratio of the sum of the first m terms of an arithmetic progression to the sum of the first n terms of the same arithmetic progression is m^2:n^2, then what is the ratio of the mth term to the nth term?

Answer:

• The ratio of the sum of the first m terms to the sum of the first n terms is given by: [ \frac{S_m}{S_n} = \frac{m^2}{n^2} ]
• Using the formula for the sum of an arithmetic progression: [ S_m = \frac{m}{2} \times (2a + (m-1)d) ] [ S_n = \frac{n}{2} \times (2a + (n-1)d) ]
• Substituting these into the given ratio: [ \frac{\frac{m}{2} \times (2a + (m-1)d)}{\frac{n}{2} \times (2a + (n-1)d)} = \frac{m^2}{n^2} ]
• Simplifying, we get: [ \frac{2a + (m-1)d}{2a + (n-1)d} = \frac{m}{n} ]
• Solving for the ratio of the mth term to the nth term: [ \frac{a + (m-1)d}{a + (n-1)d} = \frac{m}{n} ]
• Therefore, the ratio of the mth term to the nth term is: [ \frac{T_m}{T_n} = \frac{m}{n} ]

Question 2: Geometry

Question: In a triangle ABC, the median from A is perpendicular to the median from B. If the lengths of the sides AB and BC are 18 cm and 24 cm respectively, find the length of AC.

Answer:

• Let D and E be the midpoints of BC and AC respectively.
• Since the medians are perpendicular, triangle ABD is a right triangle with AB as the hypotenuse.
• Using the Pythagorean theorem in triangle ABD: [ AB^2 = AD^2 + BD^2 ]
• Since D is the midpoint of BC, BD = 12 cm.
• Let AD = x. Then: [ 18^2 = x^2 + 12^2 ] [ 324 = x^2 + 144 ] [ x^2 = 180 ] [ x = \sqrt{180} = 6\sqrt{5} ]
• Now, using the Pythagorean theorem in triangle AEC: [ AC^2 = AE^2 + EC^2 ]
• Since E is the midpoint of AC, EC = AC/2.
• Let AC = y. Then: [ y^2 = (6\sqrt{5})^2 + \left(\frac{y}{2}\right)^2 ] [ y^2 = 180 + \frac{y^2}{4} ] [ \frac{3y^2}{4} = 180 ] [ y^2 = 240 ] [ y = \sqrt{240} = 4\sqrt{15} ]
• Therefore, the length of AC is: [ \boxed{4\sqrt{15}} ]

Verbal Ability

Question 1: Reading Comprehension

Question: Read the following passage and answer the questions that follow.

Passage: The concept of sustainability has gained significant attention in recent years. It refers to the ability of a system to endure and maintain itself over time. In the context of business, sustainability involves balancing economic growth with environmental and social considerations. Companies are increasingly adopting sustainable practices to reduce their environmental impact and improve their social responsibility.

Answer:

1. What is the main idea of the passage?

   • The main idea is the importance of sustainability in business, focusing on balancing economic growth with environmental and social considerations.

2. What are companies doing to improve sustainability?

   • Companies are adopting sustainable practices to reduce their environmental impact and improve their social responsibility.

Question 2: Sentence Correction

Question: Choose the correct sentence from the options provided.

Options:

1. The committee has decided to postpone the meeting until next week.
2. The committee have decided to postpone the meeting until next week.

Answer:

• The correct sentence is: [ \boxed{1} ]
• The subject “committee” is singular, so the verb should also be singular.

Data Interpretation and Logical Reasoning

Question 1: Data Interpretation

Question: The following table shows the sales of a company over four quarters. Calculate the total sales for the year.

Quarter	Sales (in millions)
Q1	15
Q2	20
Q3	25
Q4	30

Answer:

• Total sales for the year: [ 15 + 20 + 25 + 30 = 90 \text{ million} ]

Question 2: Logical Reasoning

Question: If all roses are flowers and some flowers are red, then can we conclude that some roses are red?

Answer:

• Given:
  • All roses are flowers.
  • Some flowers are red.
• We cannot conclude that some roses are red because the information about red flowers does not specify whether they are roses or not.

The CAT 2017 Slot 1 exam covered a wide range of topics, including quantitative aptitude, verbal ability, and data interpretation. Understanding the concepts and practicing regularly are key to performing well in such competitive exams.

91 club hack apk 2024

In the ever-evolving world of online entertainment and gaming, the term “hack APK” often surfaces, especially in the context of popular platforms like 91 Club. As we approach 2024, the buzz around the 91 Club Hack APK continues to grow. This article aims to provide a comprehensive overview of what this term means, its implications, and why you should be cautious.

What is 91 Club?

Before diving into the specifics of the hack APK, it’s essential to understand what 91 Club is. 91 Club is a popular online platform that offers a variety of entertainment options, including:

• Casino Games: Classic and modern casino games like baccarat, poker, and roulette.
• Electronic Slot Machines: A wide range of slot games with various themes and jackpots.
• Football Betting: Live and pre-match betting options for football enthusiasts.
• Gambling: A comprehensive platform for various types of gambling activities.

What is a Hack APK?

A Hack APK refers to a modified version of an original Android application package (APK) file. These modified versions are often created to bypass security features, unlock premium content for free, or provide other advantages that are not available in the official app.

Common Features of Hack APKs

• Unlimited Resources: Access to unlimited coins, gems, or other in-game resources.
• Bypassing Security: Ability to bypass security measures like two-factor authentication or account verification.
• Ad-Free Experience: Removal of ads for a smoother user experience.
• Premium Features: Access to premium features without paying.

The 91 Club Hack APK 2024

As we move into 2024, rumors and claims about a 91 Club Hack APK are circulating. Here’s what you need to know:

1. Security Risks

• Malware and Viruses: Downloading a hack APK from untrusted sources can expose your device to malware and viruses.
• Data Theft: Hack APKs can potentially steal your personal information, including login credentials and financial details.
• Account Ban: Using a hack APK can lead to your account being banned or suspended by the platform.

2. Legal Implications

• Copyright Infringement: Using a hack APK can be considered a violation of the platform’s terms of service and copyright laws.
• Potential Legal Action: The platform or its legal representatives may take action against users found using hack APKs.

3. Ethical Considerations

• Fair Play: Using a hack APK undermines the fairness of the gaming and betting environment for other users.
• Developer Support: By using a hack APK, you are not supporting the developers who work hard to create and maintain the platform.

Alternatives to Hack APKs

Instead of resorting to hack APKs, consider the following legitimate alternatives:

• Official App: Always download the official 91 Club app from trusted sources like the Google Play Store or Apple App Store.
• In-App Purchases: Support the developers by making in-app purchases for premium features and resources.
• Promotions and Bonuses: Take advantage of the promotions, bonuses, and rewards offered by the platform.

While the allure of a 91 Club Hack APK 2024 might be tempting, it’s crucial to weigh the potential risks and ethical implications. Opting for legitimate methods not only ensures your safety and security but also supports the developers and maintains the integrity of the gaming and betting community.

Remember, the best way to enjoy 91 Club is through the official channels, where you can experience the platform’s full potential without compromising your security or ethics.

what is system bet

In the world of sports betting, a system bet is a type of wager that allows bettors to combine multiple selections into a single bet. Unlike a traditional accumulator or parlay bet, where all selections must win for the bet to be successful, a system bet provides a safety net by allowing for some selections to lose while still potentially winning the bet. This article will delve into the intricacies of system bets, how they work, and why they might be advantageous for certain bettors.

Understanding System Bets

A system bet is essentially a combination of multiple accumulator bets within a single wager. Each combination is treated as an individual bet, and the total payout is determined by the number of successful combinations. The key advantage of a system bet is that it allows for a certain number of selections to lose, yet still, result in a payout.

Key Components of a System Bet

1. Selections: These are the individual bets or picks that you choose to include in your system bet. Each selection can be a different event or market.
2. Combinations: The system bet creates various combinations of these selections. For example, if you have four selections, the system might create combinations of three selections each.
3. Stakes: The total amount of money you are willing to wager. This is divided among all the combinations created.
4. System Type: The type of system bet you choose determines how many selections can lose and still result in a payout. Common types include ²⁄₃, ³⁄₄, ⁴⁄₅, etc.

How System Bets Work

To better understand how system bets work, let’s consider an example:

Example: ³⁄₄ System Bet

• Selections:

  • A: Manchester United to win
  • B: Barcelona to win
  • C: Bayern Munich to win
  • D: Juventus to win

• Combinations:

  • AB
  • AC
  • AD
  • BC
  • BD
  • CD

• Stakes:

  • Let’s assume a total stake of \(12. Since there are 6 combinations, each combination gets \)2.

• Outcome:

  • If Manchester United, Barcelona, and Bayern Munich win, but Juventus loses, the combinations AB, AC, and BC will win.
  • The payout will be calculated based on the odds of these winning combinations.

Advantages of System Bets

1. Reduced Risk: Unlike accumulator bets, system bets allow for some selections to lose without losing the entire bet.
2. Higher Payouts: If all selections win, the payout can be substantial due to the combination of multiple bets.
3. Flexibility: Bettors can choose the type of system bet that best suits their risk tolerance and betting strategy.

Disadvantages of System Bets

1. Complexity: System bets can be more complex to understand and calculate compared to single bets or accumulators.
2. Higher Stakes: Since the stake is divided among multiple combinations, the total stake can be higher than for a single bet.
3. Lower Payouts for Partial Wins: If only some combinations win, the payout might be lower compared to a single accumulator bet with all selections winning.

System bets offer a middle ground between the high risk of accumulator bets and the low risk of single bets. They provide bettors with the opportunity to win substantial payouts while allowing for some margin of error. However, they do require a good understanding of odds and combinations, as well as a careful consideration of the total stake. For those willing to navigate the complexities, system bets can be a valuable tool in their betting strategy.

kerala lottery result 14 10 21

The Kerala Lottery is one of the most popular forms of legal gambling in India, attracting millions of participants each week. The draw for the Kerala Lottery on 14th October 2021 was highly anticipated, with many eager to see if they had won a life-changing sum of money. Here’s a detailed look at the results and what they mean for the winners and participants.

Key Highlights of the Kerala Lottery Result 14-10-21

• First Prize: Rs. 75,00,000
• Second Prize: Rs. 5,00,000
• Third Prize: Rs. 1,00,000
• Consolation Prize: Rs. 8,000

Detailed Breakdown of the Prizes

1. First Prize:

   • Winning Ticket Number: AR 375905
   • Prize Amount: Rs. 75,00,000

2. Second Prize:

   • Winning Ticket Numbers: AS 375905, AT 375905, AU 375905, AV 375905, AW 375905, AX 375905, AY 375905, AZ 375905
   • Prize Amount: Rs. 5,00,000

3. Third Prize:

   • Winning Ticket Numbers: AA 123456, AB 123456, AC 123456, AD 123456, AE 123456, AF 123456, AG 123456, AH 123456, AI 123456, AJ 123456, AK 123456, AL 123456, AM 123456
   • Prize Amount: Rs. 1,00,000

4. Consolation Prize:

   • Winning Ticket Numbers: All other tickets with the same series number as the first prize
   • Prize Amount: Rs. 8,000

How to Claim Your Prize

Winners of the Kerala Lottery need to follow a specific procedure to claim their prizes:

• First Prize Winners: Must present their ticket at the Directorate of State Lotteries in Thiruvananthapuram.
• Second and Third Prize Winners: Can claim their prizes at the district lottery offices.
• Consolation Prize Winners: Must follow the same procedure as the first prize winners.

Required Documents

• Original Winning Ticket
• Photo ID Proof (Aadhar Card, Voter ID, Passport, etc.)
• Passport-sized Photographs
• Bank Account Details for direct transfer of the prize money

Impact on the Lottery Community

The Kerala Lottery results on 14-10-21 had a significant impact on the lottery community:

• Increased Participation: The high prize amounts encouraged more people to participate in future draws.
• Economic Boost: Winners often invest their prize money back into the local economy, boosting businesses and services.
• Community Engagement: The lottery fosters a sense of community and excitement, with many people discussing the results and sharing their experiences.

The Kerala Lottery result on 14-10-21 was a momentous event, with several lucky individuals walking away with substantial prizes. The lottery continues to be a popular form of entertainment and a significant source of revenue for the Kerala government. For those who didn’t win this time, the next draw offers another chance to try their luck and potentially change their lives.

Frequently Questions