Year :
2002
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
31 - 40 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 31. |
A solid hemisphere has a radius of 7 cm. Find the total surface area. A. 400 cm2 B. 462 cm2 C. 66 cm2 D. 308 cm2 Detailed SolutionTotal surface area of hemisphere = half of TSA of sphere + circumference of circle= \(2\pi r^{2} + \pi r^{2} = 3\pi r^{2}\) = \( 3 \times \frac{22}{7} \times 7^{2} = 462cm^{2}\) |
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| 32. |
Find the value of a if the line 2y - ax + 4 = 0 is perpendicular to the line y + (x/4) - 7 = 0 A. -4 B. 4 C. 8 D. -8 Detailed Solution2y - ax + 4 = 0 \(\implies\) 2y = ax - 4.y + (x/4) - 7 = 0 \(\implies\) y = -x/4 + 7 Slope of line 1 = a/2 Slope of line 2 = -1/4 -1/4 x a/2 = -1 (product of the slope of two perpendicular lines = -1) a/8 = 1 \(\implies\) a = 8. |
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| 33. |
The locus of a point P which is equidistant from two given points S and T is A. the perpendicular bisector of ST B. the angle bisector of PS and ST C. a perpendicular to ST D. a line parallel to ST |
A |
| 34. |
Find the mean of the data: 7, -3, 4, -2, 5, -9, 4, 8, -6, 12 A. 3 B. 4 C. 1 D. 2 Detailed Solution\(Mean: \frac{7 + (-3) + 4 + (-2) + 5 + (-9) + 4 + 8 + (-6) + 12}{10} = \frac{20}{10}\)= 2 |
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| 35. |
The range of the data: k+2, k-3, k+4, k-2, k, k-5, k+3, k-1, and k+6 is A. 10 B. 11 C. 6 D. 8 Detailed SolutionRange = Highest value - Lowest value= (k + 6) - (k - 5) = 11 |
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| 36. |
The probability of a student passing any exam is 2/3. If the student takes three exams, what is the probability that he will not pass any of them? A. 2/3 B. 4/9 C. 8/27 D. 1/27 Detailed SolutionP(not passing exam) = \(1 - \frac{2}{3} = \frac{1}{3}\)P(not passing any of the three exams) = \(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\) = \(\frac{1}{27}\) |
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| 37. |
The acres for rice, pineapple, cassava, cocoa, and palm oil in a certain district are given respectively as 2, 5, 3, 11, and 9. What is the angle sector for cassava in a pie chart? A. 108° B. 180° C. 36° D. 60° Detailed SolutionTotal: 2 + 5 + 3 + 11 + 9 = 30Cassava: \(\frac{3}{30} \times 360° = 36°\) |
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| 38. |
How many three-digit numbers can be formed from 32564 without repeating any of the digits? A. 120 B. 10 C. 20 D. 60 Detailed SolutionTo get the answer, we simply do\(\frac{5!}{(5 - 3)!}\) = \(\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}\) = 60 |
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| 39. |
The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set. A. 105 B. 100 C. 95 D. 110 Detailed SolutionLet the sum of the first five numbers and the sixth number be x and t respectively.\(\frac{x + t}{6} = 60 \implies x + t = 360\) \(\frac{x}{5} = 50 \implies x = 250\) \(\therefore t = 360 - 250 = 110\) |
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| 40. |
Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8. A. 13/6 B. 5/2 C. 7/6 D. 7/3 Detailed SolutionMean : \(\frac{7 + 3 + 14 + 9 + 7 + 8}{6} = \frac{48}{6} = 8\)Mean deviation : \(\frac{\sum |x - \bar{x}|}{n} = \frac{14}{6} = \frac{7}{3}\) |
| 31. |
A solid hemisphere has a radius of 7 cm. Find the total surface area. A. 400 cm2 B. 462 cm2 C. 66 cm2 D. 308 cm2 Detailed SolutionTotal surface area of hemisphere = half of TSA of sphere + circumference of circle= \(2\pi r^{2} + \pi r^{2} = 3\pi r^{2}\) = \( 3 \times \frac{22}{7} \times 7^{2} = 462cm^{2}\) |
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| 32. |
Find the value of a if the line 2y - ax + 4 = 0 is perpendicular to the line y + (x/4) - 7 = 0 A. -4 B. 4 C. 8 D. -8 Detailed Solution2y - ax + 4 = 0 \(\implies\) 2y = ax - 4.y + (x/4) - 7 = 0 \(\implies\) y = -x/4 + 7 Slope of line 1 = a/2 Slope of line 2 = -1/4 -1/4 x a/2 = -1 (product of the slope of two perpendicular lines = -1) a/8 = 1 \(\implies\) a = 8. |
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| 33. |
The locus of a point P which is equidistant from two given points S and T is A. the perpendicular bisector of ST B. the angle bisector of PS and ST C. a perpendicular to ST D. a line parallel to ST |
A |
| 34. |
Find the mean of the data: 7, -3, 4, -2, 5, -9, 4, 8, -6, 12 A. 3 B. 4 C. 1 D. 2 Detailed Solution\(Mean: \frac{7 + (-3) + 4 + (-2) + 5 + (-9) + 4 + 8 + (-6) + 12}{10} = \frac{20}{10}\)= 2 |
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| 35. |
The range of the data: k+2, k-3, k+4, k-2, k, k-5, k+3, k-1, and k+6 is A. 10 B. 11 C. 6 D. 8 Detailed SolutionRange = Highest value - Lowest value= (k + 6) - (k - 5) = 11 |
| 36. |
The probability of a student passing any exam is 2/3. If the student takes three exams, what is the probability that he will not pass any of them? A. 2/3 B. 4/9 C. 8/27 D. 1/27 Detailed SolutionP(not passing exam) = \(1 - \frac{2}{3} = \frac{1}{3}\)P(not passing any of the three exams) = \(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\) = \(\frac{1}{27}\) |
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| 37. |
The acres for rice, pineapple, cassava, cocoa, and palm oil in a certain district are given respectively as 2, 5, 3, 11, and 9. What is the angle sector for cassava in a pie chart? A. 108° B. 180° C. 36° D. 60° Detailed SolutionTotal: 2 + 5 + 3 + 11 + 9 = 30Cassava: \(\frac{3}{30} \times 360° = 36°\) |
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| 38. |
How many three-digit numbers can be formed from 32564 without repeating any of the digits? A. 120 B. 10 C. 20 D. 60 Detailed SolutionTo get the answer, we simply do\(\frac{5!}{(5 - 3)!}\) = \(\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}\) = 60 |
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| 39. |
The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set. A. 105 B. 100 C. 95 D. 110 Detailed SolutionLet the sum of the first five numbers and the sixth number be x and t respectively.\(\frac{x + t}{6} = 60 \implies x + t = 360\) \(\frac{x}{5} = 50 \implies x = 250\) \(\therefore t = 360 - 250 = 110\) |
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| 40. |
Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8. A. 13/6 B. 5/2 C. 7/6 D. 7/3 Detailed SolutionMean : \(\frac{7 + 3 + 14 + 9 + 7 + 8}{6} = \frac{48}{6} = 8\)Mean deviation : \(\frac{\sum |x - \bar{x}|}{n} = \frac{14}{6} = \frac{7}{3}\) |