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IIT M FOUNDATION DIPLOMA FN EXAM QDF2 28 Apr 2024 - 28 Apr 2024
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Comprehension passage - the questions below it refer to this
A person went to the market to buy hens. Old hens can be bought for ₹ 200.00 each but young hens can be bought for ₹ 500.00 each. The old hens lay 3 eggs per week and the young hens lay 5 eggs per week. Each egg costs Rs. 11. A hen costs ₹ 50.00 per week to feed. If the financial constraint is ₹ 8000 per week to buy hens and the capacity constraint is that the total number of hens bought cannot exceed 20 per week. The objective is to earn more profit. Let x represent the number of old hens and y represent the number of young hens. Use the above information to answer the given subquestionsChoose the correct Primal optimization problem from the following.
If (x*, y*) is the optimal solution of the primal, u1 and u2 are Lagrange multipliers then which of the following options is/are true?
Which of the following options is/are true?
- The Given LPP is infeasible.
- The Given LPP is feasible.
- The optimum value is x = 0 and y = 16
- The optimum value is x = 20 and y = 0
Comprehension passage - the questions below it refer to this
Based on the above data, answer the given subquestions.
Find the number of discontinuous points.
Find the number of points where the function is not differentiable.
Let A be a real symmetric positive definite matrix. Which of the following options is/are true?
- The eigenvectors of A may or may not be orthogonal.
- If A is similar to a diagonal matrix B, then B is also positive definite.
- AT A is not positive definite.
- AT A is not similar to a diagonal matrix.
In a large town, it is estimated that 20% of students own a laptop. A random sample of 400 students is selected from the town. What is the variance of the number of students with the laptops in a given sample?
A quality control manager at a factory measures the thickness of glass sheets produced. Five randomly selected sheets have the thicknesses(in mm) 10, 8, 11, 9, 12 respectively. Assuming the thickness follows a normal distribution and the variance is known, what is the maximum likelihood estimator (MLE) of the mean thickness, (μ), in mm of the glass sheets?