Mathematics (Core), 2012, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2012

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

31 - 40 of 48 Questions

#	Question	Ans
31.	Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\) A. 1 B. 2 C. 3 D. 4 Show Content Detailed Solution \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\) = \([\tan \theta]_{0} ^{\frac{\pi}{4}}\) = \(\tan \frac{\pi}{4} - \tan 0\) = \(1 - 0\) = 1. There is an explanation video available below.	A
32.	The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number. A. 126 B. 180 C. 216 D. 224 Show Content Detailed Solution \(\frac{x}{7} = \frac{96}{1}\) ==> \(\frac{672 + x}{8} = 112\) Therefore x = 224	D
33.	Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5 A. 9 B. 8 C. 7 D. 4 Show Content Detailed Solution There is an explanation video available below.	D
34.	Find the range of 4,9,6,3,2,8,10 and 11 A. 11 B. 9 C. 8 D. 4 Show Content Detailed Solution There is an explanation video available below.	B
35.	Find the standard deviation of 2,3,8,10 and 12 A. 3.9 B. 4.9 C. 5.9 D. 6.9 Show Content Detailed Solution There is an explanation video available below.	A
36.	Evaluate ⁿ⁺¹C_n-2 If n =15 A. 3630 B. 3360 C. 1120 D. 560 Show Content Detailed Solution There is an explanation video available below.	D
37.	In how many ways can the letters of the word TOTALITY be arranged? A. 6720 B. 6270 C. 6207 D. 6027 Show Content Detailed Solution There is an explanation video available below.	A
38.	The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests? A. \(\frac{2}{27}\) B. \(\frac{3}{27}\) C. \(\frac{4}{27}\) D. \(\frac{5}{3}\) Show Content Detailed Solution There is an explanation video available below.	C
39.	The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years A. \(\frac{2}{15}\) B. \(\frac{3}{15}\) C. \(\frac{7}{15}\) D. \(\frac{13}{15}\) Show Content Detailed Solution Man lives = \(\frac{2}{3}\) not live = \(\frac{1}{3}\) Wife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\) P(at least one lives to 80 years) = P(man lives to 80 not woman) + P(woman lives to 80 and not man) + P(both live to 80) \(P = (\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\) = \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\) = \(\frac{13}{15}\) There is an explanation video available below.	D
40.	The shaded region above is represented by the equation A. y ≤ 4x + 2 B. y ≥ 4x + 2 C. y ≤ -4x + 4 D. y ≤ 4x + 4 Show Content Detailed Solution Equation of the line \(\frac{y - 4}{x - 0} = \frac{0 - 4}{1 - 0}\) \(\frac{y - 4}{x} = \frac{-4}{1}\) \(\therefore -4x = y - 4\) \(y = -4x + 4\) \(\therefore \text{The shaded portion = } y \leq -4x + 4\) There is an explanation video available below.	C

31.	Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\) A. 1 B. 2 C. 3 D. 4 Show Content Detailed Solution \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\) = \([\tan \theta]_{0} ^{\frac{\pi}{4}}\) = \(\tan \frac{\pi}{4} - \tan 0\) = \(1 - 0\) = 1. There is an explanation video available below.	A
32.	The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number. A. 126 B. 180 C. 216 D. 224 Show Content Detailed Solution \(\frac{x}{7} = \frac{96}{1}\) ==> \(\frac{672 + x}{8} = 112\) Therefore x = 224	D
33.	Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5 A. 9 B. 8 C. 7 D. 4 Show Content Detailed Solution There is an explanation video available below.	D
34.	Find the range of 4,9,6,3,2,8,10 and 11 A. 11 B. 9 C. 8 D. 4 Show Content Detailed Solution There is an explanation video available below.	B
35.	Find the standard deviation of 2,3,8,10 and 12 A. 3.9 B. 4.9 C. 5.9 D. 6.9 Show Content Detailed Solution There is an explanation video available below.	A

36.	Evaluate ⁿ⁺¹C_n-2 If n =15 A. 3630 B. 3360 C. 1120 D. 560 Show Content Detailed Solution There is an explanation video available below.	D
37.	In how many ways can the letters of the word TOTALITY be arranged? A. 6720 B. 6270 C. 6207 D. 6027 Show Content Detailed Solution There is an explanation video available below.	A
38.	The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests? A. \(\frac{2}{27}\) B. \(\frac{3}{27}\) C. \(\frac{4}{27}\) D. \(\frac{5}{3}\) Show Content Detailed Solution There is an explanation video available below.	C
39.	The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years A. \(\frac{2}{15}\) B. \(\frac{3}{15}\) C. \(\frac{7}{15}\) D. \(\frac{13}{15}\) Show Content Detailed Solution Man lives = \(\frac{2}{3}\) not live = \(\frac{1}{3}\) Wife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\) P(at least one lives to 80 years) = P(man lives to 80 not woman) + P(woman lives to 80 and not man) + P(both live to 80) \(P = (\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\) = \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\) = \(\frac{13}{15}\) There is an explanation video available below.	D
40.	The shaded region above is represented by the equation A. y ≤ 4x + 2 B. y ≥ 4x + 2 C. y ≤ -4x + 4 D. y ≤ 4x + 4 Show Content Detailed Solution Equation of the line \(\frac{y - 4}{x - 0} = \frac{0 - 4}{1 - 0}\) \(\frac{y - 4}{x} = \frac{-4}{1}\) \(\therefore -4x = y - 4\) \(y = -4x + 4\) \(\therefore \text{The shaded portion = } y \leq -4x + 4\) There is an explanation video available below.	C