Q. If z = 2(cos(π/3) + i sin(π/3)), what is z in rectangular form? (2022)
A.
1 + √3i
B.
2 + √3i
C.
1 + 2i
D.
2 + 2i
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Solution
Using Euler's formula, z = 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + √3i.
Correct Answer: A — 1 + √3i
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Q. If z = 3 + 4i, what is the modulus of z? (2021)
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Solution
The modulus of z is given by |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Correct Answer: A — 5
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Q. If z = 4 - 3i, find the conjugate of z. (2023)
A.
4 + 3i
B.
4 - 3i
C.
-4 + 3i
D.
-4 - 3i
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Solution
The conjugate of z = 4 - 3i is z* = 4 + 3i.
Correct Answer: A — 4 + 3i
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Q. If z = 5 + 12i, find the argument of z. (2020)
A.
arctan(12/5)
B.
arctan(5/12)
C.
π/2
D.
0
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Solution
The argument of z = 5 + 12i is θ = arctan(12/5).
Correct Answer: A — arctan(12/5)
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Q. If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)
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Solution
z1 * z2 = (2 + 2i)(2 - 2i) = 4 - 4i^2 = 4 + 4 = 8.
Correct Answer: A — 8
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Q. If z1 = 2 + 2i and z2 = 3 - i, find z1 + z2. (2023)
A.
5 + i
B.
5 + 3i
C.
1 + i
D.
1 - i
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Solution
z1 + z2 = (2 + 2i) + (3 - i) = 5 + i.
Correct Answer: A — 5 + i
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Q. In a class of 15 students, their ages are: 14, 15, 16, 14, 15, 16, 17, 18, 19, 20, 14, 15, 16, 17, 18. What is the median age? (2023)
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Solution
Arranging the ages: 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 20. The median is the 8th number, which is 16.
Correct Answer: B — 16
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Q. In a class of 30 students, 18 are boys and 12 are girls. If one student is selected at random, what is the probability that the student is a girl?
A.
2/5
B.
1/3
C.
1/2
D.
3/5
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Solution
Probability = Number of girls / Total students = 12/30 = 2/5.
Correct Answer: A — 2/5
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Q. In a class of 30 students, the marks obtained are as follows: 45, 50, 50, 55, 60, 60, 60, 70, 75. What is the mode of the marks? (2019)
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Solution
The number 60 appears most frequently (3 times), so the mode is 60.
Correct Answer: B — 60
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Q. In a class, the marks obtained by students are: 45, 55, 45, 60, 70, 55, 55. What is the mode of the marks?
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Solution
The mode is 55, as it appears three times in the data set.
Correct Answer: B — 55
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Q. In a class, the number of pets owned by students is recorded as follows: 0, 1, 2, 1, 3, 1, 2. What is the mode?
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Solution
The mode is 1, which appears 3 times in the data set.
Correct Answer: B — 1
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Q. In a class, the number of students who scored the following grades: A, A, B, B, B, C, C, D. What is the mode?
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Solution
The mode is B, as it appears most frequently (3 times) in the data set.
Correct Answer: B — B
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Q. In a data set of 10 numbers, if the numbers are arranged in ascending order, what is the median? (2020)
A.
Average of 5th and 6th
B.
5th number
C.
6th number
D.
Average of 1st and 10th
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Solution
For an even number of observations, the median is the average of the two middle numbers, which are the 5th and 6th numbers.
Correct Answer: A — Average of 5th and 6th
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Q. In a data set of 10 numbers, the mode is 5. If the number 5 is replaced by 7, what will be the new mode? (2021)
A.
5
B.
7
C.
No mode
D.
Cannot be determined
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Solution
Replacing 5 with 7 removes the most frequent number, so the new mode is 7.
Correct Answer: B — 7
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Q. In a data set of 10 numbers, the numbers are: 2, 3, 4, 4, 5, 5, 5, 6, 7, 8. What is the mode of this data set?
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Solution
The mode is the number that appears most frequently. Here, 5 appears 3 times, which is more than any other number.
Correct Answer: C — 5
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Q. In a data set of 12 values: 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, what is the mode? (2023)
A.
1
B.
2
C.
5
D.
No mode
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Solution
The number 5 appears most frequently (3 times), so the mode is 5.
Correct Answer: C — 5
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Q. In a data set, the numbers 3, 7, 7, 2, 5, 7, 8, 9, 2, 3 are given. What is the mode of this data set?
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Solution
The mode is the number that appears most frequently. Here, 7 appears 3 times, which is more than any other number.
Correct Answer: C — 7
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Q. In a data set, the numbers are 3, 7, 7, 2, 5, 7, 4. What is the mode of this data set?
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Solution
The mode is the number that appears most frequently. Here, 7 appears three times, which is more than any other number.
Correct Answer: D — 7
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Q. In a data set, the numbers are 3, 7, 7, 2, 5, 7, 8, 9. What is the mode of the data set?
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Solution
The mode is the number that appears most frequently. Here, 7 appears three times, which is more than any other number.
Correct Answer: C — 7
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Q. In a frequency distribution, the following data is given: 1 (2 times), 2 (3 times), 3 (3 times), 4 (1 time). What is the mode? (2020)
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Solution
Both 2 and 3 appear 3 times, but since 2 is the smallest, the mode is 2.
Correct Answer: B — 2
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Q. In a group of 15 people, the ages are: 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29. What is the mode of the ages? (2022)
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Solution
The age 22 appears 3 times, which is more than any other age, so the mode is 22.
Correct Answer: C — 25
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Q. In a group of friends, the number of games played is: 3, 3, 4, 4, 4, 5, 6. What is the mode of the games played?
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Solution
The mode is 4, as it appears most frequently (3 times) in the data set.
Correct Answer: B — 4
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Q. In a lottery, the probability of winning is 0.2. What is the probability of losing?
A.
0.2
B.
0.5
C.
0.8
D.
0.1
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Solution
Probability of losing = 1 - P(winning) = 1 - 0.2 = 0.8.
Correct Answer: C — 0.8
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Q. In a pair of vertically opposite angles, if one angle measures 120 degrees, what is the measure of the other angle? (2021)
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
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Solution
Vertically opposite angles are equal. Therefore, if one angle measures 120 degrees, the other angle also measures 120 degrees.
Correct Answer: B — 120 degrees
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Q. In a parallelogram, if one angle is 70 degrees, what is the measure of the opposite angle? (2019)
A.
70 degrees
B.
110 degrees
C.
90 degrees
D.
80 degrees
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Solution
In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.
Correct Answer: A — 70 degrees
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Q. In a parallelogram, if the base is 8 cm and the height is 5 cm, what is the area? (2021)
A.
40 cm²
B.
30 cm²
C.
50 cm²
D.
20 cm²
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Solution
Area = base * height = 8 * 5 = 40 cm²
Correct Answer: A — 40 cm²
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Q. In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
A.
5 cm
B.
10 cm
C.
8 cm
D.
7 cm
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Solution
Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.
Correct Answer: A — 5 cm
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Q. In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees angles? (2019)
A.
1:√3
B.
1:2
C.
√3:1
D.
2:1
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Solution
In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees angles are in the ratio 1:√3.
Correct Answer: A — 1:√3
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Q. In a set of numbers: 10, 20, 30, 40, 50, what is the median? (2023)
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Solution
The numbers are in order. The median is the average of the 3rd and 4th numbers: (30 + 40) / 2 = 35.
Correct Answer: B — 30
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Q. In a set of numbers: 5, 6, 7, 5, 8, 5, 9, 6, what is the mode?
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Solution
The mode is 5, as it appears four times in the data set.
Correct Answer: A — 5
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