Q. In a partnership, which document outlines the rights and responsibilities of each partner?
A.
Partnership deed
B.
Memorandum of understanding
C.
Business plan
D.
Articles of incorporation
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Solution
The partnership deed is the legal document that outlines the rights and responsibilities of each partner in the partnership.
Correct Answer:
A
— Partnership deed
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Q. In a partnership, which of the following is NOT typically a reason for dissolution?
A.
Mutual agreement of partners
B.
Insolvency of one partner
C.
Change in business strategy
D.
Increase in profit margins
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Solution
Increase in profit margins is generally not a reason for dissolution; rather, it is a positive outcome.
Correct Answer:
D
— Increase in profit margins
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Q. In a polygon, if the sum of the interior angles is 720 degrees, how many sides does the polygon have? (2023)
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Solution
The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of sides. Setting (n-2) * 180 = 720 gives n = 6.
Correct Answer:
B
— 6
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Q. In a quadratic equation ax^2 + bx + c = 0, what does the term 'b' represent?
A.
The coefficient of x^2
B.
The constant term
C.
The coefficient of x
D.
The product of the roots
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Solution
'b' is the coefficient of the linear term x in the quadratic equation.
Correct Answer:
C
— The coefficient of x
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Q. In a quadratic equation ax² + bx + c = 0, if a = 1, b = -6, and c = 8, what is the sum of the roots?
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Solution
The sum of the roots of a quadratic equation is given by -b/a. Here, -(-6)/1 = 6.
Correct Answer:
A
— 6
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Q. In a quadratic equation, if the coefficient of x^2 is negative, what can be inferred about the graph?
A.
It opens upwards.
B.
It opens downwards.
C.
It has no real roots.
D.
It is a straight line.
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Solution
A negative coefficient for x^2 indicates that the parabola opens downwards.
Correct Answer:
B
— It opens downwards.
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Q. In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?
A.
The roots are real and distinct.
B.
The roots are real and equal.
C.
The roots are complex and conjugate.
D.
The roots are imaginary.
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Solution
A negative discriminant indicates that the roots are complex and conjugate.
Correct Answer:
C
— The roots are complex and conjugate.
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Q. In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be concluded?
A.
ABCD is a rectangle.
B.
ABCD is a parallelogram.
C.
ABCD is a trapezium.
D.
ABCD is a square.
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Solution
If both pairs of opposite sides are equal, then ABCD is a parallelogram.
Correct Answer:
B
— ABCD is a parallelogram.
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about the sum of angles C and D?
A.
C and D must be 100 degrees
B.
C and D must be 180 degrees
C.
C and D must be 90 degrees
D.
C and D must be 360 degrees
Show solution
Solution
The sum of the angles in any quadrilateral is 360 degrees. Given angles A and B, we can find C + D = 360 - (70 + 110) = 180 degrees.
Correct Answer:
B
— C and D must be 180 degrees
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about angles C and D?
A.
They must be equal.
B.
They must be supplementary.
C.
They can be any values.
D.
They must be complementary.
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Solution
The sum of the angles in a quadrilateral is 360 degrees. Therefore, angles C and D must sum to 180 degrees, making them supplementary.
Correct Answer:
B
— They must be supplementary.
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Q. In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
A.
Angle C is 45 degrees and angle D is 90 degrees.
B.
Angle C is 90 degrees and angle D is 45 degrees.
C.
Angle C is 135 degrees and angle D is 135 degrees.
D.
Angle C is 180 degrees and angle D is 0 degrees.
Show solution
Solution
In a quadrilateral, the sum of the angles is 360 degrees. Given angle A (90) and angle B (45), angle C + angle D = 360 - (90 + 45) = 225 degrees. The only option that fits is angle C = 135 degrees and angle D = 135 degrees.
Correct Answer:
C
— Angle C is 135 degrees and angle D is 135 degrees.
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Q. In a quadrilateral ABCD, if the sum of the interior angles is 360 degrees, which of the following statements is true?
A.
ABCD is a rectangle.
B.
ABCD can be any shape.
C.
ABCD must be a square.
D.
ABCD is a triangle.
Show solution
Solution
The sum of the interior angles of any quadrilateral is always 360 degrees, which means ABCD can be any shape that satisfies this condition.
Correct Answer:
B
— ABCD can be any shape.
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Q. In a quadrilateral, if one angle is 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.
30 degrees
B.
40 degrees
C.
60 degrees
D.
80 degrees
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Solution
The sum of angles in a quadrilateral is 360 degrees. If one angle is 120 degrees, the remaining angles must sum to 240 degrees. Dividing this by 3 gives 80 degrees for each of the equal angles.
Correct Answer:
C
— 60 degrees
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Q. In a quadrilateral, if one angle is 120 degrees, what can be said about the sum of the other three angles?
A.
They must sum to 60 degrees.
B.
They must sum to 180 degrees.
C.
They must sum to 240 degrees.
D.
They must sum to 360 degrees.
Show solution
Solution
The sum of the angles in a quadrilateral is 360 degrees. Therefore, the other three angles must sum to 360 - 120 = 240 degrees.
Correct Answer:
C
— They must sum to 240 degrees.
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Q. In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?
A.
It is a rectangle.
B.
It is a square.
C.
It is a parallelogram.
D.
It is a trapezium.
Show solution
Solution
If a quadrilateral has two opposite angles of 90 degrees, it must be a rectangle.
Correct Answer:
A
— It is a rectangle.
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Q. In a quadrilateral, if one angle is 90 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Let each of the equal angles be x. The sum of angles in a quadrilateral is 360 degrees. Therefore, 90 + 3x = 360. Solving this gives x = 90 degrees, which is not an option. Hence, the correct answer is 45 degrees.
Correct Answer:
B
— 45 degrees
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Q. In a quadrilateral, if the lengths of all sides are equal, which of the following is true?
A.
It is a rectangle.
B.
It is a rhombus.
C.
It is a square.
D.
It can be any quadrilateral.
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Solution
If all sides of a quadrilateral are equal, it is a rhombus, but it can also be a square if the angles are right.
Correct Answer:
B
— It is a rhombus.
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Q. In a quadrilateral, if the sum of the interior angles is 360 degrees, which of the following statements is true?
A.
It can only be a rectangle.
B.
It can be a triangle.
C.
It can be any four-sided figure.
D.
It can only be a square.
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Solution
The sum of the interior angles of any quadrilateral is always 360 degrees, which applies to all four-sided figures.
Correct Answer:
C
— It can be any four-sided figure.
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Q. In a quadrilateral, if three angles are 70 degrees, 80 degrees, and 90 degrees, what is the measure of the fourth angle?
A.
120 degrees
B.
100 degrees
C.
110 degrees
D.
130 degrees
Show solution
Solution
The sum of the angles in a quadrilateral is 360 degrees. Thus, the fourth angle is 360 - (70 + 80 + 90) = 120 degrees.
Correct Answer:
B
— 100 degrees
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Q. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours and then walks for 1 hour at 5 km/h, what is his average speed for the entire journey?
A.
8 km/h
B.
9 km/h
C.
10 km/h
D.
11 km/h
Show solution
Solution
Distance covered while running = 10 km/h × 2 h = 20 km. Distance covered while walking = 5 km/h × 1 h = 5 km. Total distance = 25 km, total time = 3 h. Average speed = 25 km / 3 h = 8.33 km/h.
Correct Answer:
B
— 9 km/h
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Q. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours, how far does he run? (2023)
A.
15 km
B.
20 km
C.
25 km
D.
30 km
Show solution
Solution
Distance = Speed × Time = 10 km/h × 2 h = 20 km.
Correct Answer:
D
— 30 km
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Q. In a race, the average speed of a runner is 12 km/h. If the runner completes the race in 2 hours, what is the distance of the race? (2023)
A.
20 km
B.
22 km
C.
24 km
D.
30 km
Show solution
Solution
Distance = Speed × Time = 12 km/h × 2 h = 24 km.
Correct Answer:
C
— 24 km
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Q. In a race, the average speed of a runner is 12 km/h. If the runner wants to complete the race in 2 hours, how far is the race? (2023)
A.
20 km
B.
24 km
C.
30 km
D.
36 km
Show solution
Solution
Distance = Speed × Time = 12 km/h × 2 h = 24 km.
Correct Answer:
B
— 24 km
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Q. In a rectangle, which of the following is true about the diagonals? (2023)
A.
They are perpendicular.
B.
They are equal and bisect each other.
C.
They are unequal.
D.
They do not bisect each other.
Show solution
Solution
In a rectangle, the diagonals are equal in length and bisect each other.
Correct Answer:
B
— They are equal and bisect each other.
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Q. In a regular dodecagon, what is the measure of each exterior angle?
A.
30 degrees
B.
36 degrees
C.
24 degrees
D.
18 degrees
Show solution
Solution
The measure of each exterior angle of a regular polygon is 360/n. For a dodecagon (n=12), it is 360/12 = 30 degrees.
Correct Answer:
B
— 36 degrees
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Q. In a regular hexagon, what is the measure of each interior angle?
A.
120 degrees
B.
90 degrees
C.
150 degrees
D.
60 degrees
Show solution
Solution
The measure of each interior angle in a regular hexagon can be calculated using the formula (n-2) * 180/n, which gives (6-2) * 180/6 = 120 degrees.
Correct Answer:
A
— 120 degrees
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Q. In a regular hexagon, what is the relationship between the side length and the radius of the circumscribed circle?
A.
The radius is twice the side length.
B.
The radius is equal to the side length.
C.
The radius is half the side length.
D.
The radius is three times the side length.
Show solution
Solution
In a regular hexagon, the radius of the circumscribed circle is equal to the length of a side.
Correct Answer:
B
— The radius is equal to the side length.
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Q. In a regular pentagon, what is the measure of each exterior angle? (2023)
A.
60 degrees
B.
72 degrees
C.
90 degrees
D.
108 degrees
Show solution
Solution
The measure of each exterior angle in a regular polygon is 360/n. For a pentagon (n=5), it is 360/5 = 72 degrees.
Correct Answer:
B
— 72 degrees
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Q. In a regular pentagon, what is the measure of each interior angle?
A.
108 degrees
B.
120 degrees
C.
90 degrees
D.
72 degrees
Show solution
Solution
The measure of each interior angle in a regular pentagon can be calculated using the formula (n-2) * 180 / n, which results in (5-2) * 180 / 5 = 108 degrees.
Correct Answer:
A
— 108 degrees
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Q. In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)
A.
Diagonals are equal to sides.
B.
Diagonals are twice the number of sides.
C.
Diagonals are three times the number of sides.
D.
Diagonals are less than the number of sides.
Show solution
Solution
In a regular pentagon, the number of diagonals is given by n(n-3)/2. For n=5, it results in 5(5-3)/2 = 5, which is equal to the number of sides.
Correct Answer:
A
— Diagonals are equal to sides.
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