Q. In a team setting, what is the significance of setting common goals?
A.
It creates a competitive environment.
B.
It aligns team members towards a unified direction.
C.
It reduces the need for communication.
D.
It allows for individual achievements to be highlighted.
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Solution
Common goals unify team members, ensuring that everyone is working towards the same objectives.
Correct Answer:
B
— It aligns team members towards a unified direction.
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Q. In a team setting, which of the following behaviors is most likely to enhance team cohesion?
A.
Withholding personal opinions
B.
Engaging in team-building activities
C.
Focusing solely on individual tasks
D.
Avoiding social interactions
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Solution
Engaging in team-building activities is likely to enhance team cohesion by fostering relationships and trust among team members.
Correct Answer:
B
— Engaging in team-building activities
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Q. In a team setting, which of the following best describes the term 'synergy'? (2023)
A.
The sum of individual efforts
B.
The combined effect that is greater than the sum of individual efforts
C.
A method of conflict resolution
D.
A strategy for time management
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Solution
Synergy refers to the combined effect that is greater than the sum of individual efforts, highlighting the power of teamwork.
Correct Answer:
B
— The combined effect that is greater than the sum of individual efforts
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Q. In a tennis tournament, if a player wins 75% of their matches and has played 20 matches, how many matches did they win?
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Solution
Winning 75% of 20 matches means the player won 0.75 * 20 = 15 matches.
Correct Answer:
A
— 15
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Q. In a tennis tournament, if player X has a 75% win rate and plays 12 matches, how many matches is player X expected to win?
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Solution
With a 75% win rate, player X is expected to win 0.75 * 12 = 9 matches.
Correct Answer:
C
— 9
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Q. In a tennis tournament, if the top seed is defeated in the first round, what is the likely impact on the tournament's structure?
A.
The tournament will be canceled.
B.
The top seed's absence will not affect the tournament.
C.
The tournament will have a different winner than expected.
D.
The tournament will be easier for all other players.
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Solution
The defeat of the top seed often leads to unexpected outcomes and can change the dynamics of the tournament.
Correct Answer:
C
— The tournament will have a different winner than expected.
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Q. In a tennis tournament, if the top seed is eliminated in the first round, what does this imply about the tournament's unpredictability?
A.
The tournament is predictable.
B.
The tournament is highly competitive.
C.
The top seed was not prepared.
D.
All players are of equal skill.
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Solution
The elimination of the top seed suggests that upsets can occur, indicating a competitive environment.
Correct Answer:
B
— The tournament is highly competitive.
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Q. In a tennis tournament, if the top seed is eliminated in the first round, what is the impact on the tournament structure?
A.
The tournament will proceed as planned.
B.
The tournament will be canceled.
C.
Other players will have an easier path to the finals.
D.
The top seed will be replaced by a lower seed.
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Solution
The elimination of the top seed opens up opportunities for other players, making their path to the finals potentially easier.
Correct Answer:
C
— Other players will have an easier path to the finals.
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Q. In a tournament, if a player wins 3 matches and loses 1, what is their win-loss ratio?
A.
3:1
B.
1:3
C.
2:1
D.
1:2
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Solution
The win-loss ratio is calculated as Wins:Losses = 3:1.
Correct Answer:
A
— 3:1
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Q. In a tournament, if a player wins 75% of their matches and plays 20 matches, how many matches did they win?
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Solution
If a player wins 75% of 20 matches, then they win 0.75 * 20 = 15 matches.
Correct Answer:
A
— 15
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Q. In a tournament, if the top 4 teams are awarded points as follows: 1st place - 10 points, 2nd place - 7 points, 3rd place - 5 points, 4th place - 3 points, what is the total number of points awarded?
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Solution
Total points = 10 + 7 + 5 + 3 = 25 points awarded.
Correct Answer:
A
— 25
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Q. In a trapezium, which of the following statements is true?
A.
All sides are equal.
B.
Only one pair of opposite sides is parallel.
C.
Both pairs of opposite sides are parallel.
D.
It has four right angles.
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Solution
In a trapezium, only one pair of opposite sides is parallel.
Correct Answer:
B
— Only one pair of opposite sides is parallel.
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Q. In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?
A.
AB is parallel to AC
B.
AB is perpendicular to AC
C.
AC is longer than AB
D.
All sides are equal
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Solution
The slope of AB is (6-2)/(4-1) = 4/3, and the slope of AC is (6-2)/(1-1) which is undefined. Since one slope is undefined, AB is perpendicular to AC.
Correct Answer:
B
— AB is perpendicular to AC
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Q. In a triangle, if one angle is 90 degrees, what can be inferred about the other two angles?
A.
They are both acute angles.
B.
One is obtuse and the other is acute.
C.
They are both obtuse angles.
D.
They are equal.
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Solution
In a right triangle, the sum of the other two angles must be 90 degrees, making them both acute.
Correct Answer:
A
— They are both acute angles.
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Q. In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the largest angle, what is the measure of the smallest angle?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Let the smallest angle be x. Then the second angle is 2x and the largest angle is 2x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (2x - 30) = 180. Solving this gives x = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the first angle, what is the measure of the smallest angle?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Let the smallest angle be x. Then the second angle is 2x and the third angle is x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (x - 30) = 180. Solving this gives x = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a triangle, if one angle is twice the size of another angle, what is the measure of the smallest angle? (2023)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Let the smallest angle be x. Then the second angle is 2x, and the third angle is 180 - 3x. Solving gives x = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a triangle, if one angle measures 45 degrees and the other measures 45 degrees, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the maximum length of the third side?
A.
16 cm
B.
17 cm
C.
18 cm
D.
19 cm
Show solution
Solution
According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, the maximum length of the third side can be 16 cm (7 + 10 - 1). Hence, the answer is 17 cm.
Correct Answer:
B
— 17 cm
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Q. In a triangle, if the lengths of two sides are 7 cm and 10 cm, what is the range of possible lengths for the third side?
A.
3 cm to 17 cm
B.
3 cm to 10 cm
C.
10 cm to 17 cm
D.
7 cm to 10 cm
Show solution
Solution
According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides and greater than the difference of the two sides. Therefore, the range is 3 cm to 17 cm.
Correct Answer:
A
— 3 cm to 17 cm
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Q. In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
A.
3 cm
B.
15 cm
C.
5 cm
D.
17 cm
Show solution
Solution
According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.
Correct Answer:
A
— 3 cm
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Q. In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?
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Solution
Let the common difference be d. From the equations 4 + 5d = 24, solving gives d = 4.
Correct Answer:
C
— 6
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Q. In an arithmetic progression, if the 1st term is x and the common difference is 2, what is the expression for the 6th term?
A.
x + 10
B.
x + 12
C.
x + 8
D.
x + 14
Show solution
Solution
The 6th term is given by a + 5d. Here, it is x + 5*2 = x + 10.
Correct Answer:
A
— x + 10
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Q. In an arithmetic progression, if the 2nd term is 10 and the 4th term is 14, what is the first term? (2023)
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Solution
Let the first term be a and the common difference be d. From the equations a + d = 10 and a + 3d = 14, we can solve for a and find it to be 8.
Correct Answer:
B
— 8
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Q. In an arithmetic progression, if the 2nd term is 8 and the 4th term is 14, what is the 1st term?
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Solution
Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 3d = 14, solving gives a = 6.
Correct Answer:
A
— 6
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Q. In an arithmetic progression, if the 3rd term is 12 and the 7th term is 24, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 2d = 12 and a + 6d = 24, we can find d = 3.
Correct Answer:
C
— 4
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Q. In an arithmetic progression, if the 3rd term is 15 and the 6th term is 24, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 5d = 24, we can solve for d, which gives d = 3.
Correct Answer:
B
— 4
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Q. In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what is the first term?
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Solution
Let the first term be a and the common difference be d. From the equations a + 3d = 20 and a + 6d = 26, we can solve for a and find it to be 12.
Correct Answer:
B
— 12
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Q. In an arithmetic progression, if the 5th term is 20 and the 10th term is 35, what is the first term?
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Solution
Let the first term be a and the common difference be d. From the given terms, we have a + 4d = 20 and a + 9d = 35. Solving these gives a = 10.
Correct Answer:
B
— 10
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Q. In an arithmetic progression, if the first term is 10 and the common difference is 5, what is the sum of the first 8 terms?
A.
120
B.
130
C.
140
D.
150
Show solution
Solution
The sum of the first n terms is given by S_n = n/2 * (2a + (n-1)d). Here, S_8 = 8/2 * (20 + 35) = 4 * 55 = 220.
Correct Answer:
C
— 140
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