Jamb Question And Answer On Mathematics 2017
2017 JAMB Mathematics Past Questions & Answers - page 1
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1
Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N
Correct Option: D Solution T = {evenn numbers from 1 to 12}
N = {common factors of 6,8 and 12}
Find T ∩ N
T = {2, 4, 6, 8, 10, 12}
N = {2}
T ∩ N = {2} i.e value common to T & N
2
What is the next number in the series 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)...
Correct Option: D Solution 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)..... There are 4 terms in the series Tn = ar\(^{n − 1}\) (formular for geometric series) a = first term = 2 r = common rate = \(\frac{\text{next term}}{\text{previous term}}\) = \(\frac{1}{2}\) n = number of terms T5 = 5th term = ? T5 = ar\(^{5 - 1}\) = ar\(^4\) = 2 × (ar\(^{n − 1}\))4 = 2 × \(\frac{1}{16}\) = \(\frac{1}{8}\)
Therefore the next number will be the 5th term
3
If U = {x : x is an integer and 1 ≤ x ≤ }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
Correct Option: A Solution U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} E1 = {3, 6, 9, 12, 15, 18} E2 = {4, 8, 12, 16, 20} Probability of E2 = \(\frac{5}{20}\) i.e \(\frac{\text{Total number in}E_2}{\text{Entire number in set}}\) Probability of set E2 = 1 − \(\frac{5}{20}\) = \(\frac{15}{20}\) = \(\frac{3}{4}\)
4
The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base
π = \(\frac{22}{7}\)
Correct Option: B Solution Curved surface area of cylinder = 2πrh 110 = 2 × \(\frac{22}{7}\) × r × 5 r = \(\frac{110 \times 7}{44 \times 5}\) = 3.5cm
5
If two graphs Y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q
Correct Option: B Solution Y = Px2 + q Y = 2x2 - 1 Px2 + q = 2x2 - 1 Px2 = 2x2 - 1 - q p = \(\frac{2x^2 - 1 - q}{x^2}\) at x = 2 P = \(\frac{2(2)^2 - 1 - q}{2^2}\) = \(\frac{2(4) - 1 -q}{4}\) = \(\frac{8 - 1 - q}{4}\) P = \(\frac{7 - q}{4}\)
6
Evaluate (\(\sin\)45o + \(\sin\)3o ) in surd form
A
\(\frac{\sqrt{3}}{2\sqrt{2}}\)
D
1 + \(\frac{\sqrt{2}}{2}\)
Correct Option: D Solution hypotenuse \(\sin45 = \frac{1}{\sqrt{2}}\) = \(\frac{2}{2}\) ∴ (sin45 + sin30) = \(\frac{1}{\sqrt{2}} + \frac{1}{2}\) = \(\frac{\sqrt{2}}{2}\) + \(\frac{1}{2}\) = \(\frac{\sqrt{2} + 1}{2}\) = \(\frac{1 + \sqrt{2}}{2}\)
sin = \(\frac{1}{2}\)
7
If y = x Sin x, find \(\frac{dy}{dx}\) when x = \(\frac{\pi}{2}\)
Correct Option: C Solution y = xsinx \(\frac{dy}{dx}\) = \(1 \sin x + x \cos x\) = \(\sin x + x \cos x\) At x = \(\frac{\pi}{2}\) = sin\(\frac{\pi}{r}\) + \(\frac{\pi}{2} \cos {\frac{\pi}{2}}\) = 1 + \(\frac{\pi}{2}\) × 10 = 1
8
If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J
Correct Option: A Solution t ∝ h, t = 20, h t = ? h = 60 t = kh where k is constant 20 = 50k k = \(\frac{20}{50}\) k = \(\frac{2}{5}\) when h = 60, t = ? t = \(\frac{2}{5}\) × 60 t = 24oC
9
Evaluate 1 - (\(\frac{1}{5}\) x \(\frac{2}{3}\)) + ( 5 + \(\frac{2}{3}\))
Correct Option: D No further explanations yet...
10
Given m = N\(\frac{\sqrt{SL}}{T}\) make T the subject of the formula
A
\(\frac{\text{NSL}}{M}\)
Correct Option: B Solution M = \(\frac{\sqrt{SL}}{T}\), make T subject of formula square both sides M2 = \(\frac{N^2SL}{T}\) TM2 = N2SL T = \(\frac{N^2SL}{M^2}\)
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Jamb Question And Answer On Mathematics 2017
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