MCQ- System of Equations in Real World Problems (Class- 9, Experience- 5)

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Multiple Choice Quiz: Test Your Knowledge about Polynomial Expression!

Question 1: Linear equations with two variables is solved by which method?

A. Substitution Method
B. Elimination Method
C. Cross Multiplication Method
D. All are correct

Question 2: When two straight lines are parallel, what are the solutions of the equations?

A. single solution
B. infinite solutions
C. There is no solution
D. Two solutions

Question 3: How many points are required in the Graphical method to solve the linear equations?

A. a
B. two
C. Three
D. Four

Question 4: When two lines intersect at a point, what are the solutions of the equations?

A. single solution
B. infinite solutions
C. There is no solution
D. Two solutions

Question 5: What is the discriminant of the equation ax² + bx + c = 0?

A. b² - 4ac
B. b² + 4ac
C. b² ✕ 4ac
D. b² ÷ 4ac

Question 6: If the discriminant is b² - 4ac = 0, what are the nature of the roots?

A. real and equal
B. real and unequal
C. imaginary and equal
D. Fictitious and uneven

Question 7: What is the general procedure for determining the roots of a quadratic equation?

A. Graphical Method
B. Substitution Method
C. discriminant method
D. Write the equation

Question 8: How is a quadric equation ax² + bx + c = 0 solved by graphing?

A. Marking the displacement on the x axis
B. Constructing graphs based on the assertion of equations
C. Plotting the two intersections of the equation on the x-axis
D. Solving the equation

Question 9: What is done in the substitution method?

A. Substituting the value obtained in the first equation into the second equation
B. Adding the two equations
C. Substituting the value obtained in the first equation into the first equation
D. Multiplying two equations

Question 10: What will be the value of y if we solve the equation x + 2y = 7 and 3x - y = 5 in Substitution Method?

A. 1
B. 2
C. 3
D. 4

Question 11: What is elimination method?

A. Substituting the value of a variable
B. Eliminating a variable from the equation
C. Adding the two equations
D. Multiplying two equations

Question 12: If two systems of equations are assigned the same solution, are they consistent?

A. Yes, they are generally consistent.
B. No, they are usually inconsistent.
C. Yes, but there is no fixed solution
D. No, they are not approved solutions

Question 13: What will be the value of x if the equations 3x + 2y = 12 and 2x - 2y = 4 are solved by elimination method?

A. 1
B. 2
C. 3
D. 4

Question 14: What type of equation does the equation 3x - y = 7 and 6x - 2y = 14 represent?

A. Consistency and a simple solution
B. Consistency and no solution
C. Consistency and infinite solutions
D. Consistency and two different solutions

Question 15: If two linear equations are graphed at the same point, what will be their solution?

A. There will be a solution
B. There will be two solutions
C. There will be at least one solution
D. There will be no solution

Question 16: What if b² - 4ac ＞ 0 is the product of an integer?

A. The equation will have no real solution
B. The equation will have two real and unequal solutions
C. The equation will have two real and equal solutions
D. The equation has no real solution

Question 17: If the discriminant is b² - 4ac＜0, what are the nature of the roots?

A. real and equal
B. real and unequal
C. There is no real origin
D. Two real roots

Question 18: What is the solution of the quadratic equation x² + x - 6 = 0?

A. 2, - 3
B. - 2, 3
C. 1, - 6
D. - 1, 6

Question 19: What if b² - 4ac ＞ 0?

A. The equation has no real solution
B. The equation will have two real and unequal solutions
C. The equation will have two real and equal solutions
D. The equation will have a real solution

Question 20: If the discriminant is b² - 4ac＞0 and is an integer, what are the nature of the roots?

A. Real, unequivocal and rational
B. Real, equal and rational
C. imaginary and equal
D. Fictitious and uneven

Question 21: What is a linear equation with two variables?

A. Equation with two unknown values
B. Equation with an unknown value
C. A quadratic equation in an unknown value
D. Quadratic equation of an unknown value

Question 22: What is the relationship between the lines y = 2x + 3 and y = 2x - 1?

A. They intersect at a point
B. They are parallel
C. They match together
D. They are vertical

Question 23: If the solutions of two simple systems of equations are inconsistent, do they represent the same point?

A. yes
B. no
C. sometimes
D. maybe

Question 24: What type of line does the graph of the equation 3x + 4y = 12 represent?

A. curve
B. straight line
C. vertical line
D. horizontal line

Question 25: What type of solution does an equation have if two lines never intersect graphically?

A. infinite solutions
B. There is no solution
C. Only one solution
D. Two solutions

Question 26: If two linear equations are represented at the same point, what is of them characteristics?

A. compatible
B. Consistency
C. unauthorized
D. which is not

Question 27: What is the substitution method (Substitution Method)?

A. Substituting one unknown value for another unknown value
B. Adding the equations
C. Multiplying equations
D. Dividing the equations

Question 28: What is the first step to solve the equation x + y = 7 and 2x - y = 3 by Substitution Method?

A. Determining the value of y from x + y = 7
B. 2x - y = 3 to determine the value of y -
C. Adding the two equations
D. Determining the value of x from x + y = 7

Question 29: How many solutions can be obtained if a linear equations with two variables is solved with the help of a straight line?

A. zero, one or infinity
B. one or two
C. just one
D. Only two

Question 30: Which method is not for solving a linear equations in two variables?

A. Substitution Method
B. Elimination Method
C. Cross Multiplication Method
D. Differential Equation Method

Question 31: What if b² - 4ac ＜ 0?

A. The equation will have a real solution
B. The equation has no real solution
C. The equation will have two real and unequal solutions
D. The equation will have two real and equal solutions

Question 32: If two simple systems of equations are inconsistent, what is of them characteristics?

A. One will be solved
B. Both will have solutions
C. None of them will have a solution
D. One will have a solution

Question 33: What kind of equation are the equations 2x + 3y = 5 and 4x + 6y = 10?

A. Consistency and a simple solution
B. Consistency and no solution
C. Consistency and infinite solutions
D. Consistency and two different solutions

Question 34: How are two linear equations compatible?

A. If the equation has a solution
B. If the equation has no solution
C. If the solution to the equation is arbitrary
D. If the solution of the equation is determined

Question 35: What is the solution to the equation of two straight lines when they meet?

A. Only one solution
B. infinite solutions
C. There is no solution
D. Two solutions

Question 36: Which observation is true about solving linear equations in two variables with the help of straight lines?

A. If two straight lines intersect at a point, then there is a general solution.
B. If two straight lines coincide, then there is no solution.
C. If two straight lines are parallel, then there are infinite solutions.
D. None of the above

Question 37: What is the solution of the equations x + y = 5 and x - y = 1?

A. x = 2, y = 3
B. x = 3, y = 2
C. x = 1, y = 4
D. x = 4, y = 1

Question 38: If two linear equations are solvable, which of them has a common solution?

A. yes
B. no
C. sometimes
D. always

Question 39: What if b² - 4ac = 0?

A. The equation has no real solution
B. The equation will have two real and unequal solutions
C. The equation will have two real and equal solutions
D. The equation will have a real solution

Question 40: Which of the following is not a method of solving linear equations with two variables?

A. Graphical Method
B. Algebraic Method
C. Geometric Method
D. Linear Method

Question 41: In solving linear equations in two variables, which method first extracts the value of one variable from one equation and then substitutes it into the other equation?

A. Elimination Method
B. Substitution Method
C. Cross Multiplication Method
D. Geometric Method

Question 42: Which of the following methods is not used to solve linear equations in two variables?

A. Cross Multiplication Method
B. Graphical Method
C. Algebraic Method
D. Differentiation Method

Question 43: What is used in the geometric method?

A. the number
B. diagram
C. table
D. Statistics

Question 44: What do we have to do to solve linear equations with two variables in geometric method?

A. To be solved numerically
B. Equations must be squared
C. Draw a straight line
D. to be solved with the help of clauses

Question 45: What does it mean if two straight lines intersect at a point?

A. There are infinite solutions
B. There is only one solution
C. There is no solution
D. There are two solutions

Question 46: If two straight lines never intersect each other, what is the solution of their equation?

A. Only one solution
B. infinite solutions
C. There is no solution
D. Two solutions

Question 47: What if b² - 4ac ＞ 0 and is not a product of integers?

A. The equation will have no real solution
B. The equation will have two real and unequal solutions
C. The equation has no real solution
D. The equation will have two real and equal solutions

Question 48: To solve the equation y = 4 - x and 2x + y = 10 by substitution method, in which equation should the value of y be substituted?

A. y = 4 - x
B. 2x + y = 10
C. x + y = 4
D. x - y = 2

Question 49: What must be done first to solve the equation y = 2x + 1 and x - y = 3 by Substitution Method?

A. y = 2x + 1 to determine the value of x -
B. x - y = 3 to determine the value of x -
C. Determining the value of y - from y = 2x + 1
D. x - y = 3 to determine the value of y -

Question 50: What will be the value of x if we solve x = 2y + 3 and 3x + y = 12 by substitution method?

A. 3
B. 6
C. 9
D. 12

Question 51: If x + y = 6 and 2x - y = 4 are solved by elimination method, what will be the value of x?

A. 1
B. 2
C. 3
D. 4

Question 52: What should be multiplied in the equations 3x + 4y = 10 and 2x - y = 3 to equalize the products of x in the elimination method?

A. 2 in the first equation and 3 in the second equation
B. 3 in the first equation and 4 in the second equation
C. 1 in the first equation and 2 in the second equation
D. 4 in the first equation and 3 in the second equation

Question 53: If the equations 2x + y = 5 and 4x - y = 7 are solved by elimination method, what will be the value of y?

A. 1
B. 2
C. 3
D. 4

Question 54: What should be done to solve the equations 5x + 2y = 18 and 3x - 2y = 6 in Elimination Method?

A. Add the two equations
B. The two equations must be subtracted
C. One equation must be subtracted from another equation
D. One equation must be multiplied by another equation

Question 55: 3x + 2y = 14 and 6x - 4y = 8 If the two equations are solved by elimination method, what will be the value of x?

A. 1
B. 2
C. 3
D. 4

Question 56: Why is the cross multiplication method used?

A. To solve the equation
B. To find the equation
C. To write the equation
D. To determine the sum between the equations

Question 57: Cross Multiplication Method ac = bd To solve the equation How does it work?

A. a⋅d = b⋅c
B. a⋅b = c⋅d
C. a⋅d = b⋅c
D. a⋅c = b⋅d

Question 58: What to do to determine the solution graphically?

A. Draw straight lines
B. Multiplication of equations
C. determine the clause
D. Using logarithms

Question 59: Which of the following is the characteristic of geometric method?

A. Equations of straight lines are expressed numerically
B. Properties of equations are described
C. Equations are projected onto the diagram
D. Angles of straight lines are determined

Question 60: Cross Multiplication Method x2 = 35 To solve the equation How does it work?

A. x⋅5 = 3⋅2
B. x⋅2 = 3⋅5
C. x⋅5 = 3⋅2
D. x⋅3 = 2⋅5

Question 61: After solving by Cross Multiplication Method, what will be the value of x?

A. x = 34
B. x = 43
C. x = 52
D. x = 25

Question 62: How does the Cross Multiplication Method work?

A. Equating the product of the equation
B. Equating the products of equations and determining a variable from them
C. Equating the sum of the equations
D. Determining sums between equations

Question 63: Cross Multiplication Method 2x 3 = 45 To solve the equation How does it work?

A. 2x⋅5 = 4⋅3
B. 2x⋅5 = 4⋅3
C. 2x⋅4 = 3⋅5
D. 2x⋅4 = 5⋅3

Question 64: Cross Multiplication Method 34 = x6 to solve the equation How does it work?

A. 3⋅6 = 4⋅x
B. 3⋅6 = 4⋅x
C. 3⋅4 = x⋅6
D. 3⋅6 = 4⋅x

Question 65: What does the value of b² - 4ac mean?

A. Discriminant of Equation
B. The product of Equation
C. The response to Equation
D. The product of Equation

Question 66: What is the role of certainty in solving a quadratic equation?

A. Determining the nature of the equation
B. Solving the equation
C. Determining the product of the equation
D. Determining the product of the equation

Question 67: What is determined by b² - 4ac?

A. Discriminant of Equation
B. Solving the equation
C. The nature of the equation
D. The product of Equation

Question 68: What is determined based on the certainty of a quadric equation?

A. The nature of the equation
B. Solving the equation
C. The locus of equations
D. The product of Eq

Question 69: What are the nature of value of the quadratic equation x² - 4x + 4 = 0?

A. 2, - 2
B. 2, 2
C. 4, - 4
D. None of them