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.

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.

box bet horse racingl

Introduction to Box Betting

Box betting in horse racing is a popular wagering strategy that allows bettors to cover multiple combinations of horses in a single race. This type of bet enhances the chances of winning by ensuring that the bettor’s selected horses can finish in any order. Box bets are commonly used in various types of wagers, including Exacta, Trifecta, and Superfecta.

Types of Box Bets

1. Exacta Box

• Definition: An Exacta Box involves selecting two or more horses to finish first and second in any order.
• Example: If you box horses A, B, and C, you win if the horses finish in any of the following combinations: AB, BA, AC, CA, BC, or CB.
• Cost: The cost of an Exacta Box increases with the number of horses. For example, a 3-horse Exacta Box costs 6 times the base bet (3 x 2 = 6 combinations).

2. Trifecta Box

• Definition: A Trifecta Box involves selecting three or more horses to finish first, second, and third in any order.
• Example: If you box horses A, B, and C, you win if the horses finish in any of the following combinations: ABC, ACB, BAC, BCA, CAB, or CBA.
• Cost: The cost of a Trifecta Box increases significantly with the number of horses. For example, a 3-horse Trifecta Box costs 6 times the base bet (3 x 2 x 1 = 6 combinations).

3. Superfecta Box

• Definition: A Superfecta Box involves selecting four or more horses to finish first, second, third, and fourth in any order.
• Example: If you box horses A, B, C, and D, you win if the horses finish in any of the following combinations: ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA, CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB, DBAC, DBCA, DCAB, or DCBA.
• Cost: The cost of a Superfecta Box increases exponentially with the number of horses. For example, a 4-horse Superfecta Box costs 24 times the base bet (4 x 3 x 2 x 1 = 24 combinations).

Advantages of Box Betting

• Increased Chances of Winning: By covering multiple combinations, box betting significantly increases the likelihood of winning a bet.
• Flexibility: Box bets allow bettors to select multiple horses without worrying about the exact order of finish.
• Strategic Wagering: Box betting can be a strategic move for bettors who have a strong opinion on certain horses but are unsure of their exact finishing positions.

Disadvantages of Box Betting

• Higher Cost: The cost of box bets increases with the number of horses, making them more expensive than straight bets.
• Lower Payouts: While box bets increase the chances of winning, they often result in lower payouts compared to straight bets.
• Complexity: Box bets can be complex and require a good understanding of the potential combinations and costs.

Tips for Effective Box Betting

1. Research: Conduct thorough research on the horses, jockeys, and track conditions to make informed selections.
2. Budget Management: Set a budget for your bets and avoid overspending on box bets.
3. Combination Selection: Choose horses that have a good chance of finishing in the top positions but also consider their odds to maximize potential payouts.
4. Use Software: Utilize betting software or calculators to determine the cost and potential payouts of box bets.

Box betting in horse racing is a versatile and strategic wagering option that can enhance your chances of winning. By understanding the types of box bets, their advantages and disadvantages, and implementing effective betting strategies, you can make informed decisions and potentially increase your returns.

7 horse bet

Horse racing is a thrilling sport that offers various betting options for enthusiasts. One such intriguing bet is the 7 Horse Bet, which can be both exciting and potentially lucrative. This article delves into what the 7 Horse Bet entails, how it works, and some strategies to consider when placing this type of wager.

What is a 7 Horse Bet?

A 7 Horse Bet, also known as a Super Heinz, is a type of wager that involves selecting 7 horses in a single race or across multiple races. This bet is a combination of different types of bets, including:

• 21 Doubles
• 35 Trebles
• 35 Four-Folds
• 21 Five-Folds
• 7 Six-Folds
• 1 Seven-Fold Accumulator

In total, a 7 Horse Bet consists of 120 separate bets. This type of bet is particularly popular among seasoned bettors who are looking for a high-risk, high-reward option.

How Does a 7 Horse Bet Work?

To place a 7 Horse Bet, you need to select 7 horses and decide on the amount you wish to stake per bet. Since there are 120 individual bets, the total stake will be 120 times the amount you choose. For example, if you stake \(1 per bet, your total outlay would be \)120.

Example Scenario

Let’s say you select the following horses:

1. Horse A
2. Horse B
3. Horse C
4. Horse D
5. Horse E
6. Horse F
7. Horse G

Your 7 Horse Bet would include:

• 21 Doubles: AB, AC, AD, AE, AF, AG, BC, BD, BE, BF, BG, CD, CE, CF, CG, DE, DF, DG, EF, EG, FG
• 35 Trebles: ABC, ABD, ABE, ABF, ABG, ACD, ACE, ACF, ACG, ADE, ADF, ADG, AEF, AEG, AFG, BCD, BCE, BCF, BCG, BDE, BDF, BDG, BEF, BEG, BFG, CDE, CDF, CDG, CEF, CEG, CFG, DEF, DEG, DFG
• 35 Four-Folds: ABCD, ABCE, ABCF, ABCG, ABDE, ABDF, ABDG, ABEF, ABEG, ABFG, ACDE, ACDF, ACDG, ACEF, ACEG, ACFG, ADEF, ADEG, ADFG, AEFG, BCDE, BCDF, BCDG, BCEF, BCEG, BCFG, BDEF, BDEG, BDFG, BEFG, CDEF, CDEG, CDFG, CEFG, DEFG
• 21 Five-Folds: ABCDE, ABCDF, ABCDG, ABCEF, ABCEG, ABCFG, ABDEF, ABDEG, ABDFG, ABEFG, ACDEF, ACDEG, ACDFG, ACEFG, ADEFG, BCDEF, BCDEG, BCDFG, BCEFG, BDEFG, CDEFG
• 7 Six-Folds: ABCDEF, ABCDEG, ABCDFG, ABCEFG, ABDEFG, ACDEFG, BCDEFG
• 1 Seven-Fold Accumulator: ABCDEFG

If any combination of these bets wins, you will receive a payout based on the odds of the winning horses.

Strategies for Placing a 7 Horse Bet

1. Research and Analysis

• Form Guide: Study the form guide to understand the recent performance of each horse.
• Jockey and Trainer: Consider the experience and track record of the jockey and trainer.
• Track Conditions: Assess the track conditions and how they might affect each horse’s performance.

2. Diversify Your Selections

• Favorites and Outsiders: Include a mix of favorites and outsiders to balance risk and potential reward.
• Different Classes: Select horses from different classes to increase the likelihood of winning combinations.

3. Manage Your Bankroll

• Set a Budget: Determine your total budget for the bet and stick to it.
• Stake Wisely: Allocate your stake per bet based on your risk tolerance and the potential returns.

4. Stay Informed

• Live Updates: Keep track of live updates and adjust your strategy if necessary.
• Expert Opinions: Follow expert opinions and tips to refine your selections.

The 7 Horse Bet is a complex yet exciting wager that offers the potential for significant returns. By understanding how it works and employing effective strategies, you can enhance your chances of success in horse racing betting. Remember to always bet responsibly and within your means.

Frequently Questions