Q. In a class of 50 students, 20 study Mathematics, 25 study Science, and 10 study both. How many students study only Science?
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Solution
The number of students who study only Science is 25 - 10 = 15.
Correct Answer: A — 15
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Q. In a class of 50 students, 25 study English, 20 study Hindi, and 5 study both. How many students study only one language?
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Solution
The number of students studying only English is 25 - 5 = 20, and only Hindi is 20 - 5 = 15. Thus, total studying only one language is 20 + 15 = 35.
Correct Answer: D — 35
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Q. In a class of 50 students, 30 study English, 25 study Mathematics, and 10 study both. How many study only Mathematics?
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Solution
Only Mathematics = Total Mathematics - Both = 25 - 10 = 15.
Correct Answer: A — 15
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Q. In a class of 50 students, 40% are girls. How many boys are there in the class? (2023)
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Solution
Number of girls = 40% of 50 = 20. Therefore, number of boys = 50 - 20 = 30.
Correct Answer: B — 30
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Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 5, what will be the new ratio of boys to girls? (2023)
A.
4:3
B.
5:2
C.
3:2
D.
2:3
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Solution
Initially, there are 36 boys and 24 girls. After increasing boys by 5, there will be 41 boys and 24 girls, giving a new ratio of 41:24, which simplifies to approximately 4:3.
Correct Answer: A — 4:3
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Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 10 and the number of girls is decreased by 5, what will be the new ratio of boys to girls? (2023)
A.
2:3
B.
3:2
C.
5:3
D.
4:3
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Solution
Initially, there are 36 boys and 24 girls. After the changes, there will be 46 boys and 19 girls. The new ratio is 46:19, which simplifies to approximately 4:3.
Correct Answer: D — 4:3
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Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 10, what will be the new ratio of boys to girls? (2023)
A.
4:3
B.
5:2
C.
3:2
D.
2:3
Show solution
Solution
Initially, there are 36 boys and 24 girls. After increasing the boys by 10, there will be 46 boys and 24 girls, giving a new ratio of 46:24, which simplifies to 4:3.
Correct Answer: A — 4:3
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Q. In a class of 80 students, 50 like English, 30 like Hindi, and 10 like both. How many students like only Hindi?
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Solution
The number of students who like only Hindi is 30 - 10 = 20.
Correct Answer: A — 20
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Q. In a class of 80 students, 50 like history, 30 like geography, and 10 like both. How many students like only geography?
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Solution
The number of students who like only geography is 30 - 10 = 20.
Correct Answer: A — 20
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Q. In a class of 80 students, 50 study English, 40 study Hindi, and 20 study both. How many students study only Hindi?
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Solution
The number of students studying only Hindi is 40 - 20 = 20.
Correct Answer: A — 20
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Q. In a class of students, the ratio of boys to girls is 3:2. If the total number of students is 50, how many boys are there? (2023)
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Solution
Let the number of boys be 3x and girls be 2x. Then, 3x + 2x = 50, which gives x = 10. Therefore, boys = 3x = 30.
Correct Answer: B — 30
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Q. In a class, 12 students play cricket, 10 play football, and 5 play both. How many students play only cricket?
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Solution
Only cricket players = Total cricket players - Both = 12 - 5 = 7.
Correct Answer: B — 7
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Q. In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?
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Solution
Using inclusion-exclusion, the number of students who play either sport is: (Cricket + Football - Both) = 12 + 15 - 5 = 22.
Correct Answer: A — 22
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Q. In a class, 25 students play cricket, 20 play football, and 5 play neither. How many students play at least one sport?
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Solution
Total students = 25 + 20 - (students who play both) + students who play neither. Since 5 play neither, 30 play at least one sport.
Correct Answer: C — 30
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Q. In a class, 25 students study English, 20 study Hindi, and 5 study both. What is the number of students studying only Hindi?
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Solution
The number of students studying only Hindi is calculated as: Hindi only = Total Hindi - Both = 20 - 5 = 15.
Correct Answer: A — 15
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Q. In a class, 30% of the students are girls. If there are 120 students in total, how many boys are there?
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Solution
Number of girls = 30% of 120 = 36. Therefore, number of boys = 120 - 36 = 84.
Correct Answer: B — 80
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Q. In a class, 40% of the students are girls. If there are 30 girls in the class, how many students are there in total? (2023)
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Solution
Let the total number of students be x. Then, 40% of x = 30. Therefore, x = 30 / 0.4 = 75.
Correct Answer: A — 60
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Q. In a classroom, if every student has either 2 or 3 pencils, and the total number of pencils is 30, which of the following could be the number of students with 2 pencils?
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Solution
If there are 10 students with 2 pencils, then there are 10 students with 3 pencils, totaling 30 pencils.
Correct Answer: A — 10
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Q. In a classroom, the teacher wants to arrange chairs in rows such that each row has the same number of chairs. If there are 48 chairs and the number of rows must be a factor of 48, which of the following is NOT a possible number of rows?
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Solution
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. 10 is not a factor of 48.
Correct Answer: D — 10
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Q. In a classroom, the teacher wants to arrange students in rows such that each row has the same number of students. If there are 24 students, which of the following arrangements is NOT possible?
A.
6 rows of 4 students
B.
8 rows of 3 students
C.
12 rows of 2 students
D.
5 rows of 5 students
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Solution
5 rows of 5 students would require 25 students, which is not possible with only 24 students.
Correct Answer: D — 5 rows of 5 students
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Q. In a clock system, if it is currently 3 o'clock, what time will it be in 10 hours?
A.
1 o'clock
B.
2 o'clock
C.
3 o'clock
D.
4 o'clock
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Solution
In a 12-hour clock, 3 + 10 = 13, and 13 mod 12 = 1.
Correct Answer: B — 2 o'clock
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Q. In a clock system, if it is currently 9 o'clock, what time will it be in 15 hours?
A.
12 o'clock
B.
11 o'clock
C.
1 o'clock
D.
10 o'clock
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Solution
15 hours from 9 o'clock is calculated as (9 + 15) mod 12 = 24 mod 12 = 0, which is 12 o'clock.
Correct Answer: C — 1 o'clock
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Q. In a coordinate plane, if the point A(2, 3) is reflected across the x-axis, what are the coordinates of the reflected point?
A.
(2, -3)
B.
(3, 2)
C.
(-2, 3)
D.
(3, -2)
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Solution
Reflecting a point across the x-axis changes the sign of the y-coordinate. Thus, A(2, 3) becomes (2, -3).
Correct Answer: A — (2, -3)
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Q. In a coordinate plane, if the point A(2, 3) is reflected over the x-axis, what are the coordinates of the reflected point?
A.
(2, -3)
B.
(3, 2)
C.
(-2, 3)
D.
(-3, -2)
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Solution
Reflecting a point (x, y) over the x-axis results in (x, -y). Therefore, A(2, 3) becomes (2, -3).
Correct Answer: A — (2, -3)
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Q. In a cyclic quadrilateral, if one angle is 80 degrees, what is the maximum possible measure of the opposite angle?
A.
100 degrees
B.
80 degrees
C.
180 degrees
D.
90 degrees
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Solution
In a cyclic quadrilateral, opposite angles are supplementary. Therefore, if one angle is 80 degrees, the opposite angle can be 100 degrees.
Correct Answer: A — 100 degrees
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Q. In a cyclic quadrilateral, the opposite angles are related in which way? (2023)
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are independent.
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Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer: B — They are supplementary.
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Q. In a cyclic quadrilateral, which of the following is true?
A.
The opposite angles are supplementary
B.
All sides are equal
C.
The diagonals are equal
D.
It has at least one right angle
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Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer: A — The opposite angles are supplementary
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Q. In a cyclic quadrilateral, which of the following properties holds true?
A.
The sum of opposite angles is 180 degrees.
B.
All sides are equal.
C.
It has at least one right angle.
D.
The diagonals are equal.
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Solution
In a cyclic quadrilateral, the sum of opposite angles is always 180 degrees.
Correct Answer: A — The sum of opposite angles is 180 degrees.
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Q. In a cyclic quadrilateral, which of the following statements is true?
A.
The opposite angles are supplementary.
B.
All sides are equal.
C.
It has at least one right angle.
D.
It can only be a square.
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Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer: A — The opposite angles are supplementary.
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Q. In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?
A.
The graph opens upwards.
B.
The graph opens downwards.
C.
The graph is a straight line.
D.
The graph is a constant function.
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Solution
When a > 0 in a quadratic function, the graph opens upwards, indicating that the vertex is the minimum point.
Correct Answer: A — The graph opens upwards.
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