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Questions and Answers
What is the derivative of the function f(x) = (x^2 - 5x + 6)/x with respect to x?
What is the derivative of the function f(x) = (x^2 - 5x + 6)/x with respect to x?
In a class of 15 students with 6 girls, what is the probability of selecting a committee of 4 students with exactly 2 girls?
In a class of 15 students with 6 girls, what is the probability of selecting a committee of 4 students with exactly 2 girls?
If vector A = 3i - 4j and vector B = 2i + j, what is the vector product A x B?
If vector A = 3i - 4j and vector B = 2i + j, what is the vector product A x B?
For the matrices A = | 1 3 | and B = | 2 4 |, what is the inverse of the matrix (AB)^-1?
For the matrices A = | 1 3 | and B = | 2 4 |, what is the inverse of the matrix (AB)^-1?
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Study Notes
12th Public Examination Important Questions for Mathematics: Focus on Calculus, Probability, Vectors, Matrices, and Differential Equations
As we approach the 12th public examination, we're going to dive into some important questions from the realm of mathematics, covering calculus, probability, vectors, matrices, and differential equations. These subtopics are crucial for students who want to strengthen their mathematical foundations and prepare for the exams.
Calculus
- Limits: Evaluate the limit of the sequence: lim_(n→∞) (n^2 - 5n + 6)/n^2.
- Derivatives: Find the derivative of the function f(x) = (x^2 - 5x + 6)/x with respect to x.
Probability
- Discrete Probability: In a class of 10 students, 4 are girls. A committee of 3 students is to be selected. Calculate the probability that 2 of them are girls.
- Continuous Probability: A car's speedometer shows speeds uniformly from 0 to 120 mph. If a car's speed is 60 mph, find the probability that its speed is less than 80 mph.
Vectors
- Vector Addition: Given the vectors A = 2i - 3j and B = 4i + j, find the vector C = A + B.
- Scalar Multiplication: Find the vector D = 2A - 3B, where A and B are the vectors from question 5.
Matrices
- Matrix Multiplication: Calculate the product AB, given the matrices A = | 1 2 | and B = | 3 2 |.
- Matrix Transpose: Find the transpose of the matrix A from question 7.
Differential Equations
- First-Order DE: Solve the first-order differential equation dy/dx + 2x*y = 3x^2, given that y(1) = 1.
- Second-Order DE: Solve the homogeneous second-order differential equation y'' + y = 0 with initial conditions y(0) = 1, y'(0) = -2.
As a mathematically rich and educational resource, these questions are designed to strengthen your understanding of the subtopics and foster problem-solving skills. By working through these questions, you'll not only deepen your mathematical knowledge but also hone your ability to use mathematical concepts to solve real-world problems. With diligent practice and a solid foundation in these subtopics, you'll be well-prepared for the 12th public examination.
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Description
Prepare for your 12th public examination with important questions focusing on calculus, probability, vectors, matrices, and differential equations. Strengthen your mathematical foundations by solving problems related to limits, derivatives, discrete and continuous probability, vector operations, matrix calculations, and differential equations.
