BITSAT Math: Algebra Marathon

JEE Mains & Advanced Course

• Foundation Sessions for beginners
• Complete PYQs (Past Year Questions 2015-2023)
• NTA + Cengage Chapterwise Questions
• Handwritten Notes available

Free Resources

• Join Telegram for free and focused JEE material: t.me/mathematicallyinclined
• URL for course details: tinyurl.com/jeewithnehamam
• Note: No courses are sold

Algebra Chapters Weightage

• Sequence & Series: 8% (2 questions in 2022, 3 in 2021, 4 in 2020)
• Matrices & Determinants: 8% (3 questions each year)
• Binomial Theorem: 7% (2 questions in 2022, 2 in 2021, 4 in 2020)
• Probability: 4% (1 question in 2022, 3 in 2021, 2 in 2020)
• Quadratic Equations: 4% (2 questions in 2022, 1 in 2021, 2 in 2020)
• Permutation & Combination (P & C): 4% (2 questions in 2022 and 2021, 1 in 2020)
• Complex Numbers: 3% (2 questions in 2022, 1 in 2021 and 2020)
• Statistics: 3% (2 questions in 2022, 1 in 2021 and 2020)
• Linear Programming Problem: 2% (2 questions in 2022, 1 in 2021)
• Mathematical Reasoning: 1% (1 question in 2022)

Sample Questions and Solutions

Example Questions

1. Roots of the equation:

   • Equation: ( x^2 + bx - c = 0 ) (where ( b, c > 0 ))
   • Options: Both positive, Both negative, Of opposite sign, None of these

2. Arithmetic Progression (AP) Error:

   • Misread common difference of an AP as -2 instead of 2 and got sum of first 5 terms as -5. Find the actual sum.
   • Options: 25, -25, -35, 35

3. Probability with Dice:

   • Number of possible outcomes when at least one dice shows an odd number
   • Options provided

4. Binomial Distribution:

   • Mean: 4, Variance: 2, Find P(X=1)
   • Options: ( \frac{1}{4}, \frac{1}{32}, \frac{1}{16}, \frac{1}{8} )

5. Geometric Series:

   • Infinite series with sum 4 and second term ( \frac{3}{4} )
   • Options provided

6. Probability of Electronic Component:

   • Initial failure probability is 0.10, lasting one year if successful initially is 0.99. Find probability it lasts a year.
   • Options: 0.99, 0.871, 0.891, 0.762

7. Linear Programming Problem Changes:

   • Impact of changing constraints
   • Options: Re-evaluate, Solution undefined, Objective function modified, Constraints change ignored

8. Prime and Less than Four (Probability Question):

   • Probability ( P(EF) ) for events E: {X is a prime number} and F: {X < 4}
   • Options provided

Example Solutions

• Solutions are provided for each question, often with multiple-choice format (A, B, C, D).

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These notes emphasize the importance of algebra in BITSAT and other competitive exams, focusing on key areas and providing sample questions to aid in preparation. The discussion includes weightage by topic and sample problems to illustrate typical question formats.