Q. In a survey of favorite fruits, the responses were: Apple, Banana, Banana, Cherry, Cherry, Cherry, Date. What is the mode?
A.
Apple
B.
Banana
C.
Cherry
D.
Date
Show solution
Solution
The mode is Cherry, as it appears most frequently (3 times) in the data set.
Correct Answer: C — Cherry
Learn More →
Q. In a survey, 60% of people prefer tea over coffee. If 200 people were surveyed, how many prefer tea? (2019)
A.
120
B.
100
C.
80
D.
60
Show solution
Solution
Number of people preferring tea = 60% of 200 = 0.6 * 200 = 120.
Correct Answer: A — 120
Learn More →
Q. In a survey, 70% of people prefer tea over coffee. If 200 people were surveyed, how many prefer tea? (2019)
A.
140
B.
150
C.
160
D.
170
Show solution
Solution
Number of people preferring tea = 70% of 200 = 0.7 * 200 = 140.
Correct Answer: A — 140
Learn More →
Q. In a survey, the ages of 15 participants are: 22, 23, 23, 24, 25, 25, 25, 26, 27, 28, 28, 29, 30, 30, 30. What is the mode of the ages?
Show solution
Solution
The mode is 30, as it appears most frequently (3 times) in the data set.
Correct Answer: D — 30
Learn More →
Q. In a survey, the number of languages spoken by individuals is recorded as follows: 1, 2, 2, 3, 3, 3, 4. What is the mode?
Show solution
Solution
The mode is 3, as it appears three times in the data set.
Correct Answer: C — 3
Learn More →
Q. In a survey, the number of languages spoken by participants is recorded as follows: 1, 2, 2, 3, 3, 3, 4, 5. What is the mode?
Show solution
Solution
The mode is 3, as it appears 3 times, more than any other number.
Correct Answer: C — 3
Learn More →
Q. In a survey, the number of siblings reported by participants is: 0, 1, 2, 1, 2, 2, 3. What is the mode?
Show solution
Solution
The mode is 2, which appears 3 times in the data set.
Correct Answer: C — 2
Learn More →
Q. In a triangle, if one angle is 45 degrees and the other is 45 degrees, what is the measure of the third angle? (2020)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.
Correct Answer: A — 90 degrees
Learn More →
Q. In a triangle, if one angle is 50 degrees and another is 60 degrees, what is the measure of the third angle?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.
Correct Answer: A — 70 degrees
Learn More →
Q. In a triangle, if one angle measures 60 degrees and another measures 80 degrees, what is the measure of the third angle? (2019)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - 60 - 80 = 40 degrees.
Correct Answer: A — 40 degrees
Learn More →
Q. In a triangle, if two sides are 7 cm and 10 cm, what is the maximum possible length of the third side? (2019)
A.
16 cm
B.
17 cm
C.
18 cm
D.
19 cm
Show solution
Solution
The maximum length of the third side = sum of the other two sides - 1 = 7 + 10 - 1 = 16 cm.
Correct Answer: B — 17 cm
Learn More →
Q. In the data set 1, 2, 2, 3, 4, 4, 4, 5, 5, what is the mode?
Show solution
Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer: C — 4
Learn More →
Q. In the data set: 2, 3, 3, 4, 4, 5, 5, 5, what is the mode?
Show solution
Solution
The mode is 5, as it appears most frequently (three times) in the data set.
Correct Answer: D — 5
Learn More →
Q. In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
Show solution
Solution
The discriminant is 0, which indicates that the roots are real and equal.
Correct Answer: B — Real and equal
Learn More →
Q. In the expansion of (2 + 3x)^5, what is the coefficient of x?
Show solution
Solution
The coefficient of x is given by C(5, 1) * (2)^4 * (3) = 5 * 16 * 3 = 240.
Correct Answer: A — 15
Learn More →
Q. In the expansion of (2x - 3)^4, what is the coefficient of x^3? (2023)
A.
-108
B.
-72
C.
72
D.
108
Show solution
Solution
The coefficient of x^3 in (2x - 3)^4 is given by 4C1 * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96. The coefficient is -108.
Correct Answer: A — -108
Learn More →
Q. In the expansion of (2x - 3y)^5, what is the coefficient of x^3y^2?
A.
-720
B.
-540
C.
540
D.
720
Show solution
Solution
The coefficient is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = 720.
Correct Answer: C — 540
Learn More →
Q. In the expansion of (3x - 4)^7, what is the coefficient of x^5? (1920)
A.
1260
B.
1440
C.
1680
D.
1920
Show solution
Solution
Using the binomial theorem, the coefficient of x^5 in (3x - 4)^7 is given by 7C5 * (3)^5 * (-4)^2 = 21 * 243 * 16 = 21 * 3888 = 81588.
Correct Answer: A — 1260
Learn More →
Q. In the expansion of (a + b)^n, if the coefficient of a^3b^2 is 60, what is the value of n?
Show solution
Solution
C(n,3) * b^2 = 60. For n = 5, C(5,3) = 10, which does not satisfy. For n = 6, C(6,3) = 20, which does not satisfy. For n = 7, C(7,3) = 35, which does not satisfy. For n = 8, C(8,3) = 56, which satisfies.
Correct Answer: B — 6
Learn More →
Q. In the expansion of (x + 3)^5, what is the coefficient of x^3?
A.
60
B.
90
C.
100
D.
120
Show solution
Solution
Using the binomial theorem, the coefficient of x^3 in (x + 3)^5 is given by 5C3 * (3)^2 = 10 * 9 = 90.
Correct Answer: B — 90
Learn More →
Q. In the expansion of (x + 3)^6, what is the coefficient of x^4?
A.
540
B.
720
C.
810
D.
900
Show solution
Solution
Using the binomial theorem, the coefficient of x^4 in (x + 3)^6 is given by 6C4 * (3)^2 = 15 * 9 = 135.
Correct Answer: B — 720
Learn More →
Q. In the expansion of (x - 1)^8, what is the coefficient of x^5?
Show solution
Solution
The coefficient of x^5 in (x - 1)^8 is C(8,5) * (-1)^3 = 56 * (-1) = -56.
Correct Answer: A — -56
Learn More →
Q. In the expansion of (x - 2)^6, what is the term containing x^2?
A.
-60x^2
B.
90x^2
C.
-80x^2
D.
80x^2
Show solution
Solution
The term containing x^2 is given by C(6, 2) * (x)^2 * (-2)^(6-2) = 15 * x^2 * 16 = 240x^2, so the term is -80x^2.
Correct Answer: C — -80x^2
Learn More →
Q. In the following data set: 1, 2, 2, 3, 3, 4, 4, 4, what is the mode?
Show solution
Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer: D — 4
Learn More →
Q. In the following data set: 4, 4, 4, 5, 5, 6, 7, 8, what is the mode?
Show solution
Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer: A — 4
Learn More →
Q. In triangle ABC, if angle A = 30 degrees and angle B = 60 degrees, what is the measure of angle C? (2021)
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.
Correct Answer: C — 90 degrees
Learn More →
Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the type of triangle? (2020)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer: B — Isosceles
Learn More →
Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what type of triangle is DEF? (2021)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer: B — Isosceles
Learn More →
Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Correct Answer: A — Yes
Learn More →
Q. In triangle GHI, if angle G = 30 degrees and side GH = 10 cm, what is the length of side HI if angle H = 60 degrees? (2023)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.
Correct Answer: C — 15 cm
Learn More →
Showing 451 to 480 of 793 (27 Pages)
