Podcast
Questions and Answers
The maximum value of (x + 2y) under the constraints 2x+3y≤6, x + 4y ≤ 4, x, y ≥0 is
The maximum value of (x + 2y) under the constraints 2x+3y≤6, x + 4y ≤ 4, x, y ≥0 is
- 3.2 (correct)
- 3
- 2
- 4
The incidence of occupational disease in an industry is such that the workmen have a 10% chance of suffering from it. The probability that out of 5 workmen, 3 or more will contract the disease is
The incidence of occupational disease in an industry is such that the workmen have a 10% chance of suffering from it. The probability that out of 5 workmen, 3 or more will contract the disease is
- 0.0856 (correct)
- 0.0000856
- 0.00856
- 0.000856
In binomial distribution if n = 25 E (X) = 10, then var (X) =
In binomial distribution if n = 25 E (X) = 10, then var (X) =
2.5
If a fair coin is tossed 8 times, then the probability that it shows heads at least once is
If a fair coin is tossed 8 times, then the probability that it shows heads at least once is
The probability that a person who undergoes a kidney operation will recover is 0.7. If the six patients who undergoes similar operations, then the probability that half of them will recover is
The probability that a person who undergoes a kidney operation will recover is 0.7. If the six patients who undergoes similar operations, then the probability that half of them will recover is
In a test of Mathematics, there are two types of questions to be answered-short answered and long answered. The relevant data is given below. Time taken to solve: Short answered questions 5 minute; Long answered questions 10 minute. Marks: Short answered questions 3; Long answered questions 5. Number of questions: Short answered questions 10; Long answered questions 14. The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, the linear constraints are x≥ 0, y ≥ 0, x ≤10 , y ≤14 and 5x+10y≤180. Then the vertices of a feasible region are
In a test of Mathematics, there are two types of questions to be answered-short answered and long answered. The relevant data is given below. Time taken to solve: Short answered questions 5 minute; Long answered questions 10 minute. Marks: Short answered questions 3; Long answered questions 5. Number of questions: Short answered questions 10; Long answered questions 14. The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, the linear constraints are x≥ 0, y ≥ 0, x ≤10 , y ≤14 and 5x+10y≤180. Then the vertices of a feasible region are
The position of points O (0, 0) and P (2, - 2) in the region of graph of inequation 2x – 3y <5, will be
The position of points O (0, 0) and P (2, - 2) in the region of graph of inequation 2x – 3y <5, will be
Find out maximum value of z=5x+7y subject to x + y ≤ 4, 3x + 8y ≤ 24, 10x + 7y ≤ 35, x, y ≥ 0.
Find out maximum value of z=5x+7y subject to x + y ≤ 4, 3x + 8y ≤ 24, 10x + 7y ≤ 35, x, y ≥ 0.
A vertex of the linear inequalities 2x+3y≤6, x+4y≤4 and x, y ≥ 0, is
A vertex of the linear inequalities 2x+3y≤6, x+4y≤4 and x, y ≥ 0, is
In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none are rotten, if the sampling is with replacement, is
In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none are rotten, if the sampling is with replacement, is
In binomial probability distribution, mean is 3 and standard deviation is 3/2. Then the probability distribution is
In binomial probability distribution, mean is 3 and standard deviation is 3/2. Then the probability distribution is
The corner points of the feasible region determined by the system of linear constraints are (0,10), (5,5) (15,15), (0,20). Let z = px + qy, where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is
The corner points of the feasible region determined by the system of linear constraints are (0,10), (5,5) (15,15), (0,20). Let z = px + qy, where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is
If a fair coin is tossed 8 times, then the probability that it shows heads exactly 5 times is
If a fair coin is tossed 8 times, then the probability that it shows heads exactly 5 times is
If for a binomial distribution X~B (7, p) P (X = 1) = P ( X = 2), then p is
If for a binomial distribution X~B (7, p) P (X = 1) = P ( X = 2), then p is
An urn contains 4 white and 3 red balls. If 3 balls ar are drawn one by one with replacement and probability of getting exactly two red ball is a(3/b)³, then a+b is
An urn contains 4 white and 3 red balls. If 3 balls ar are drawn one by one with replacement and probability of getting exactly two red ball is a(3/b)³, then a+b is
The points which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x+y≤7,x+2y≤8 is
The points which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x+y≤7,x+2y≤8 is
Two different kinds of food A and B are being considered to form a weekly diet. The minimum weekly requirement for fats, carbohydrates and proteins are 18, 24 and 16 units respectively. One kg of food A has 4, 16 and 8 units respectively of these ingredients and one kg of food B has 12, 4 and 6 units respectively. The price of food A is Rs.4 per kg and that of food B is Rs.3 per kg. Find out minimum cost.
Two different kinds of food A and B are being considered to form a weekly diet. The minimum weekly requirement for fats, carbohydrates and proteins are 18, 24 and 16 units respectively. One kg of food A has 4, 16 and 8 units respectively of these ingredients and one kg of food B has 12, 4 and 6 units respectively. The price of food A is Rs.4 per kg and that of food B is Rs.3 per kg. Find out minimum cost.
If p.m.f. of r.v. X is P(X)=4(4-x)/10 , x = 0,1,2,3,4, then Var(X)=
If p.m.f. of r.v. X is P(X)=4(4-x)/10 , x = 0,1,2,3,4, then Var(X)=
Inequations 3x-y≥3 and 4x-y> 4
Inequations 3x-y≥3 and 4x-y> 4
The values of x and y for which the objection function z = 3x + 4y under the constraints y ≤x+2,4x ≤ x + 2, 4x +3 + 3y ≤ 12, x > 0 , y ≥ 0 is maximum are
The values of x and y for which the objection function z = 3x + 4y under the constraints y ≤x+2,4x ≤ x + 2, 4x +3 + 3y ≤ 12, x > 0 , y ≥ 0 is maximum are
Shaded region is represented by
Shaded region is represented by
An insurance agent insures lives of 5 men, all having same age and good health. The probability that a man of this age will survive the next 30 years is known to be 2/3. What is the probability that in the next 30 years almost 3 men will survive?
An insurance agent insures lives of 5 men, all having same age and good health. The probability that a man of this age will survive the next 30 years is known to be 2/3. What is the probability that in the next 30 years almost 3 men will survive?
One coin is thrown 100 times, then the probability of getting head in odd number is
One coin is thrown 100 times, then the probability of getting head in odd number is
An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success.
An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success.
For an L.P.P. the feasible region is shown shaded in the figure. Find the maximum value of the objective function z = 5x +7y
For an L.P.P. the feasible region is shown shaded in the figure. Find the maximum value of the objective function z = 5x +7y
The point at which, the maximum value of (3x + 2y) subject to the constraints x+y≤2, x≥0, y ≥0 obtained, is
The point at which, the maximum value of (3x + 2y) subject to the constraints x+y≤2, x≥0, y ≥0 obtained, is
For a bionomial distribution X~B (n, p) if n=5 and P(X = 1) = 8P (X = 3), then mean of the distribution is
For a bionomial distribution X~B (n, p) if n=5 and P(X = 1) = 8P (X = 3), then mean of the distribution is
The minimum value of objective function c = 2x + 2y in the given feasible region, is
The minimum value of objective function c = 2x + 2y in the given feasible region, is
A die is thrown 6 times. If "getting an odd number" is a success, then the probability of getting 5 successes is....
A die is thrown 6 times. If "getting an odd number" is a success, then the probability of getting 5 successes is....
Flashcards
Linear Inequalities
Linear Inequalities
Equations involving inequalities instead of equality, defining a region on a graph.
Feasible Region
Feasible Region
Set of all possible points that satisfy the given constraints.
Maximize Objective Function
Maximize Objective Function
Finding the highest value of a function under given constraints.
Vertices of Feasible Region
Vertices of Feasible Region
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Probability of Event
Probability of Event
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Binomial Distribution
Binomial Distribution
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Expected Value (E(X))
Expected Value (E(X))
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Variance
Variance
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Standard Deviation
Standard Deviation
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Combinations
Combinations
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Constraints
Constraints
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P(more than 3 successes)
P(more than 3 successes)
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Inequation
Inequation
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Sampling with Replacement
Sampling with Replacement
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Sampling without Replacement
Sampling without Replacement
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Binomial Probability Formula
Binomial Probability Formula
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Objective Function in LPP
Objective Function in LPP
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Probability Mass Function (PMF)
Probability Mass Function (PMF)
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Conditional Probability
Conditional Probability
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Multiple Events Probability
Multiple Events Probability
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Shaded Region
Shaded Region
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Linear Programming Problem (LPP)
Linear Programming Problem (LPP)
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Random Variable
Random Variable
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Probabilistic Events
Probabilistic Events
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Critical Values
Critical Values
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Study Notes
Questions and Answers
- Question 1: Find the maximum value of (x + 2y) given constraints 2x + 3y ≤ 6, x + 4y ≤ 4, x, y ≥ 0
- Question 2: Find the probability that 3 or more out of 5 workmen in an industry will contract an occupational disease given a 10% chance of contracting it.
- Question 3: If n = 25 and E(X) = 10 in a binomial distribution, find Var(X).
- Question 4: Find the probability of getting at least one head in 8 coin tosses.
- Question 5: A kidney operation recovery rate is 0.7. What is the probability that half of 6 patients recover?
- Question 6: A math test has short-answer and long-answer questions with respective time and mark allocations. What is the optimal strategy to maximize marks?
- Question 7: Given points O(0, 0) and P(2, -2), determine if they are inside or outside the region of the inequality 2x - 3y < 5.
- Question 8: Find the maximum value of z = 5x + 7y subject to x + y ≤ 4, 3x + 8y ≤ 24, 10x + 7y ≤ 35, x, y ≥ 0.
- Question 9: Find a vertex of the following inequalities: 2x + 3y ≤ 6, x + 4y ≤ 4, x, y ≥ 0.
- Question 10: 100 eggs in a box, 10 rotten. Probability that a sample of 5 eggs contains none rotten - with replacement sampling.
- Question 11: Binomial probability distribution, mean = 3, standard deviation = 3/2. Find the probability distribution.
- Question 12: Find the minimum cost for acquiring units of food A, priced at Rs.4 per kg, and units of food B, priced at Rs.3 per kg.
- Question 13: An event has heads occurring exactly 5 times in 8 coin tosses. Find the probability.
- Question 14: Solve for p in a binomial distribution given the conditions X ~ B(7, p), P(X = 1) = P(X = 2).
- Question 15: A container has 4 white and 3 red balls. Find the probability that, with replacement, drawing 3 balls yields exactly 2 red balls.
- Question 16: Find the solution points for a linear programming problem with given constraints.
- Question 17: A diet problem involving two types of food A and B, considering weekly minimum requirements of fats, carbohydrates, and proteins. Find weekly diet
- Question 18: A random variable X with given probability mass function (PMF): P(X) = (4-x)/5 with x = 0, 1, 2, 3, 4. Find Var(X).
- Question 19: Determine if the system of inequalities 3x-y ≥ 3 and 4x - y > 4 have solutions for all x, y, or for specific positive values.
- Question 20: Find the values of x and y for which an objective function z = 3x + 4y is maximized under specific constraints.
- Question 21: Identify the shaded region represented in the graph.
- Question 22: Find the probability that exactly 3 men out of 5 will survive 30 years.
- Question 23: Throwing a coin 100 times, find the probability of getting heads in an odd number of times.
- Question 24: In an experiment, success occurs twice as often as failure. Find the probability of at least 3 successes in 4 trials.
- Question 25: A question on finding the maximum value of an objective function (z = 5x + 7y) in a linear programming problem with given constraints.
- Question 26: Find the point that maximizes (3x + 2y) under given constraints in a linear programming problem.
- Question 27: A binomial distribution question with n = 5 trials. Find the mean of binomial distribution with given P(X = 1) and P(X = 3)
- Question 28: Find the minimum value of objective function c = 2x + 2y in a given feasible region.
- Question 29: A die is thrown 6 times. Find P(getting an odd number 5 times)
- Question 30: Find the common solution for constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0.
Additional Topics (from other pages)
- Linear programming: Maximizing objective functions under constraints, feasible regions, corner points.
- Binomial distribution: Mean, variance, probabilities, conditions.
- Probability: Calculations involving probabilities of events.
- Statistics: Concepts and applications of basic statistical measures
- Inequalities: Solving systems of inequalities.
Additional Notes (from other pages)
- Problem Solving Strategies: Understanding how to approach various problems with given constraints, objective functions, and probabilities
- Mathematical Models: Linear programming application to real-world scenarios, involving resources, costs, profits.
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