WorksheetsUntitled Quiz
Total questions: 87
Worksheet time: 2hrs 31mins
Which of the following is true about the ellipse whose equation is given by?
Which of the following statement is a true on ℝ?
If is true, then which of the following is necessarily true?
Suppose the proposition is false (F), which of the following is true?
Suppose is even; is prime; is divisible by. Which one of the following has the truth value F on the set of natural numbers?
If and are non-negative integers, which of the following is NOT true?
If the truth values of is T and is F, then which one of the following compound proposition has truth value F?
Consider the following argument: „„If there is no rain, then there is starvation. There is rain. Therefore there is no starvation.‟‟ Letting and,
Suppose that p represents the statement „„He missed the tournament.‟‟, q represents the statement „„He got the gold medal.‟‟ And r represents the statement „„He took a trip abroad.‟‟. Then which of the following symbolic expression represents the st
You are given a data on the age of students, in a primary school. Age Number of students Which of the following is NOT true about the data?
If 25% of the item are less than 20 and 25% are more than 40, then find the quartile deviation.
The sum of the squares of deviation for 10 observations taken from their mean 30 is 90. Find the coefficient of variation.
A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter require 3 hours each and in the manufacturing of product B, the machine and carpenter require 5 hours and 3 hours respectively. The machine and carpenter work at most 80 hours and 50 hours per week respectively. The profit on A and B is Birr 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then find the constraints for the function 68xy+.
A shopkeeper wants to purchase two articles A and B of cost price Birr 4 and 3 respectively. He thought that he may earn 30 praise by selling article A and 10 praise by selling article B. He has not to purchase total article worth more than Birr 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are:
Which one of the following is the vertex of a feasible region by the linear constraints 3418, 233 and ,0xyxyx y+ ≤+ ≥?
A toy manufacturer produces two types of dolls; a basic version doll A and a deluxe version doll B. Each doll of type B takes twice as long to produce as one doll of type A. The company has time to make a maximum of 2000 dolls of type A per day, the supply of plastic is sufficient to produce 1500 dolls per day and each type requires an equal amount of it. The deluxe version, i.e. type B requires a fancy dress of which there are only 600 per day available. If the company makes a profit of Birr 3 and Birr 5 per doll, respectively, on doll A and B, then the number of each should be produced per day in order to maximize profit, is equal to:
The corner point of the feasible region determined by the system of linear constraints are . The objective function is Z 43xy=+ . Compare the quantity in column A and column B
In Mathematics test there are multiple choice and workout part questions to be answered. The relevant data is given in the following table: Type of questions Time taken to solve Marks Number of questions Multiple choice 5 minute 3 10 Workout 10 minute 5 14 The total mark is 100. Students can solve all questions. To secure maximum marks, a student solves x multiple choice and y workout questions in three hours, then linear constraints except,0xy are:
What is the minimum value of Z in the given linear programming model?
What type of curve does the graph of the equation represent, for any constant k less than?
a circle
a hyperbola
a parabola
an ellipse
The equation of the circle tangent to the at whose center is on the line is:
C.
D.
Which one of the following represents an equation of hyperbola whose foci are and and whose transverse axis has length?
C.
D.
The equation of the ellipse with vertices at and , and passing through the origin is:
A.
C.
B.
D.
The length of the major axis of the ellipse is:
A.
B.
C.
D.
The orbit of Mercury around the sun forms an ellipse with eccentricity, length of major axis and the sun at one focus. Which of the following is the best approximation of the maximum distance from Mercury to the sun?
C.
D.
Consider a circle whose center is on the. If a line given by is tangent to the circle at point , what is the equation of the circle?
C.
D.
Which one of the following compound propositions is a tautology?
C.
D.
The equation of an ellipse with center , vertices at and is:
C.
D.
For what value of does the parabola pass through the points and?
A.
B.
C.
D.
If the truth value of a proportion p is False, then which one of the following compound proposition has a truth value Truth?
B.
C.
D.
Which of the following statements violates the rules for truth value assignments of the propositions p and q connected by the logical connectives?
A.
B.
C.
D.
You are given a data on the age of students, in a primary school. Age Number of students Which of the following is NOT true about the data?
A. The median is
B. The mode is
C. The mean is
D. The range is
Suppose and are perpendicular lines intersecting at. If the angle of inclination of is, what is the equation of?
A.
B.
C.
D.
Suppose p, q and r are statements such that and have truth values of T and F respectively. Which of the following compound statements has a truth value T?
A.
B.
C.
D.
What is the equation of the line passing through the mid-point of the line segment with end points and and perpendicular to the line whose angle of inclination is double the angle of inclination of the line?
C.
D.
If each of the compound propositions is true, then which one of the following is true?
A.
B.
C.
D.
What is the equation of the tangent line to the circle with equation at?
B.
C.
D.
Which one of the following is equivalent to?
A.
B.
C.
D.
The planet Mercury‟s orbit around the sun is an ellipse with eccentricity, length of major axis km and the sun at one focus. What is the maximum distance from Mercury to the sun?
km
km
If p and q are propositions such that p and are true, which of the following compound proposition can possibly have a false truth- value?
A.
B.
C.
D.
Which one of the following is equation of a circle whose center is on axis and radius is?
C.
D.
Which of the following equations represents the circle passing through and?
C.
D.
Which one of the following quantifiers has truth value T?
A.
B.
C.
D.
Then which of the following symbolic expression represents the statement: „„If he takes a trip abroad and he does not miss the tournament, then he will get the gold medal.‟‟?
C.
D.
If each of the compounds propositions and is True, then which one of the following is True?
A.
B.
C.
D.
Below are the marks of grade 12 students in Mathematics out of 100. What is the variance of the frequency distribution given below? Marks Number of students
A.
B.
C.
D.
If the graphs of the equations and are perpendicular, then which of the following is necessarily true?
B.
C.
D.
Consider the following argument form. Production is high if rain continues. Rain does not continue. Therefore, either production is low or rain continues. Let production is low rain continues Which of the following is necessarily true?
The argument form is valid due to row.
The argument form is valid due to rowsand.
The argument form is invalid due to row.
The argument form is invalid due to rowsand.
Let p, q and r be propositions such that is false. Then which one of the following propositions is true?
A.
B.
C.
D.
Let be the circle whose equation is. Let be the line whose equation is . Which one of the following is true?
A. is tangent to .
C. is below.
B. intersects at two points.
D. is above.
Consider the following argument: „„If there is no rain, then there is starvation. There is rain. Therefore there is no starvation.‟‟ Letting and, which of the following is the correct symbolic form of the argument and its validity?
A. ⊦, valid argument.
B. ⊦, invalid argument.
C. ⊦, valid argument.
D. ⊦, invalid argument.
One of the following is an asymptote of the hyperbola.
A.
C.
B.
D.
If the following lines cut the circle at exactly two points?
C.
D.
What is the distance from the origin to the line that passes through and?
A.
B.
C.
D.
The following is the table of simple frequency distribution of a data with variable. x Frequency The standard deviation of the data is equal to:
A.
B.
C.
D.
If is equation of a circle with radius, then what is the value of?
A.
B.
C.
D.
Which of the following is a true statement on the set of real numbers?
A.
B.
C.
D.
What is the contra positive of „„If, then is an integer and?‟‟
A.
B.
C.
D.
Suppose the following statements are the premises of an argument. „„He was lazy or he did not like the classroom. If he was lazy, he could not pass the exam. He passed the exam.‟‟ Which one of the following can be a conclusion that makes the argument valid?
A. He did like the classroom.
B. He did not like the classroom.
C. If he was not lazy, he did like the classroom.
D. He was not lazy and he did like the classroom.
The following table shows the frequency distribution of a group data in which the frequency of the class interval,, is missed. Class interval Frequency If the mean of the data is, what is the frequency of the first class interval?
A.
B.
C.
D.
If the end points of a diameter of a circle are and, then which one of the following equations represent the circle?
C.
D.
The graph of a hyperbola and the lines of its asymptotes are as shown in the following figure. Which one of the following is an equation of the hyperbola?
A.
B.
C.
D.
The mark that students scored in an examination is grouped in class intervals as shown in the following table. Class Interval (Mark) Number of Students What is the median of the mark?
A.
B.
C.
D.
If is true, then which one of the following is necessarily true?
A.
B.
C.
D.
The equation of the line that passes through and perpendicular to is:
C.
D.
Maximize Z 510xy, subject to 424 321 9 ,0 xy xy xy xy .
A. 20 at 1, 0
B. 30 at 0, 6
C. 37 at 4, 5
D. 33 at 6, 3
A mirror has an elliptic edge. If the shortest and the longest distances between any two points on the edge of the mirror through the geometric center of the mirror are respectively and, which of the following is a possible equation of the edge of the mirror?
C.
D.
Two perpendicular lines and are intersecting at. If the angle of inclination of is, then what is the equation of?
B.
C.
D.
A feasible solution to linear programming:
A. Must be a corner point of feasible region.
B. Must optimize the value of the objective function.
C. Need not satisfy all of the constraints, only some of them.
D. Must satisfy all of the problem‟s constraints simultaneously.
A satellite moves along a hyperbolic curve whose horizontal transverse axis is and an asymptote. Then, what is the eccentricity of the hyperbola?
A.
B.
C.
D.
Which of the following represent the shaded region?
A.
C.
B.
D.
Find the solution of the set of constraints.
A.
B.
C.
D.
Suppose and are perpendicular lines intersecting at. If the angle of inclination of is, what is the equation of?
A.
B.
C.
D.
The maximum value of the object function Z 510xy, subject to the constraints 2120 60 20 0 0 xy xy xy x y is equal to:
A. 800
B. 300
C. 600
D. 400
Which of the following is true about the constraint of a linear optimizing function Z=x given by 1, 3, and,0x x x x x x x?
A. There are two feasible regions.
C. There is no feasible region.
B. There are infinite feasible regions.
D. There are three feasible regions.
Compare the quantity in column A and column B. Maximum of Z
A. The quantity in column A is greater
B. The two quantities are equal
C. The quantity in column B is greater
D. The relationship cannot be determined based on the given information.
A circle of radius 1 unit is internally tangent to the circle at. Then, the equation of the smaller circle is:
A.
C.
B.
D.
The sum of two positive numbers is at most 5. The difference between two times a second number and the first number is at most 4. If the first number is x and second number is y, then which of the following is the mathematical formulation for maximizing the product of these two numbers?
A.
C.
B.
D.
For arbitrary propositions p and q, which one of the following is a valid equivalence?
C.
D.
What is the minimum value of Z in the given linear programming model?
5
3
It has no minimum value
0
The region represented by 235 0xy and 432 0xy is:
A. Not in first quadrant
B. Unbounded in first quadrant
C. Bounded in first quadrant
D. It is in second quadrant
What are the linear constraints for the given linear programming model?
510180,10,14xyxy
10180,10,14xyxy
510180,10,14xyxy
510180,10,14xyxy
If the truth value of the compound proposition is F, then which of the following triplets does NOT represent the correct values of p, q and r respectively?
F, F, F
F, F, T
T, F, F
T, T, T
Consider a line with equation y=mx+b. Which of the following is true?
The line intersects the x-axis, if 0m= and 0b>.
The line intersects the y-axis, if 0m≠ and 0b>.
The line passes through the origin.
The line has no slope.
Let p, q and r be propositions such that is false and is true. Which of the following is FALSE?
A.
B.
C.
D.
A problem to be solved using linear programming method is given as follows: “A coffee packer blends coffee from Harar and from Sidama to prepare two kinds products, viz., “Super” and “Deluxe” brands. Each kilogram of Super coffee contains 0.5kg of Harar coffee and 0.5kg of Sidama coffee, whereas each kilogram of Deluxe coffee contains 0.25kg of Harar coffee and 0.75kg of Sidama coffee. The packer has 120kg of Harar coffee and 160kg of Sidama coffee in store. Moreover, the plan is to get 20 Birr profit on each kilogram of Super coffee and a profit of 30 Birr on each kilogram of Deluxe coffee. In order to maximize profit the packer needs to know the amount (in kg) of each brand of coffee that should be blended.” If x= the amount of Super coffee in kilograms and y= the amount of Deluxe coffee in kilograms, then which one of the following standard forms of linear programming models should be used to solve the above problem?
Maximize P 3020xy subject to: 0.50.75120 0.50.25160 0,0 xy xy xy
Maximize P 2030xy subject to: 0.750.25120 0.50.5160 0,0 xy xy xy
Maximize P 2030xy subject to: 0.50.25120 0.50.75160 0,0 xy xy xy
Maximize P 3020xy subject to: 0.50.5120 0.250.75160 0,0 xy xy xy
The maximum and minimum values of the objective function Z=2xy subject to constraints occur respectively at:
A. one point and three points.
C. one point and infinitely points.
B. two points and one point.
D. one point and one point.
