POST UTME CHRISTOPHER UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details
Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 + \(x^2}}\)\) ) using the chain rule.
Correct A. f'\((x) =\)\(\frac{-x}\){ 1 + \(x^2\) \)^{\(3/2\)}}\)
B. f'\((x) =\)\(\frac{x}\){ 1 + \(x^2\) \)^{\(3/2\)}}\)
C. f'\((x) =\)\(\frac{1}\){ 1 + \(x^2\) \)^{\(3/2\)}}\)
D. f'\((x) =\)\(\frac{-1}\){ 1 + \(x^2\) \)^{\(3/2\)}}\)

Correct Answer: A

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Question 2 View Details
A random experiment has two independent events, A and B. If P(A) = 0.4 and P(B) = 0.6, find the probability that both events occur.
Correct A. 0.24
B. 0.48
C. 0.64
D. 0.8

Correct Answer: A

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Question 3 View Details
Simplify the expression \(\frac{2x^2 \sqrt{3x}}{x^3 \sqrt{2x}}\).
Correct A. 2 \(\sqrt{\(\frac{3}{2}\)\)}\)
B. 2 \(\sqrt{\(\frac{2}{3}\)\)}\)
C. 2 \(\sqrt{\(\frac{3}{2}\)\)}\) \(\sqrt{x}\)
D. 2 \(\sqrt{\(\frac{2}{3}\)\)}\) \(\sqrt{x}\)

Correct Answer: A

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Question 4 View Details
Find the equation of the line passing through the points (2, 3) and (4, 5).
Correct A. \(y = 2x - 1\)
B. \(y = 2x + 1\)
C. \(y = x + 2\)
D. \(y = x - 2\)

Correct Answer: A

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Question 5 View Details
A binary operation (*\) on the set of real numbers is defined as \(a * b = a^2 + b^2\\((*) on the set of real numbers is defined as\). Find the value of \(2 * 3\).
Correct A. 13
B. 5
C. 7
D. 9

Correct Answer: A

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Question 6 View Details
Let ( X ) and ( Y ) be independent random variables with probability density functions \(f_X x \\) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \(f_Y y \\) = egin{cases} \(3y^2\), & 0 leq y leq 1 \ 0, & text{otherwise} \end{cases} ). Find the probability that \(X + Y \\(text{otherwise} end{cases} ). Find the probability that \leq 1\).
Correct A. \(\frac{1}{2}\)\)
B. \(\frac{1}{3}\)\)
C. \(\frac{2}{3}\)\)
D. \(\frac{3}{4}\)\)

Correct Answer: A

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Question 7 View Details
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) in the form \(x - h \\)^2 + \(y - k\)^\(2 = r\^2\) ).
Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)
B. \(x + 2\)^2 + \(y - 3\)^\(2 = 16\)
C. \(x - 2\)^2 + \(y + 3\)^\(2 = 16\)
D. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)

Correct Answer: A

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Question 8 View Details
Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).
A. \(x = 2\)
Correct B. \(x = 3\)
C. \(x = 4\)
D. \(x = 5\)

Correct Answer: B

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Question 9 View Details
Find the sum of the first 10 terms of the geometric series \(2, 4, 8, 16, \ldots\).
A. 1023
Correct B. 1024
C. 1025
D. 1026

Correct Answer: B

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Question 10 View Details
Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).
Correct A. \(y = 2x - 1\)
B. \(y = 2x + 1\)
C. \(y = 2x - 2\)
D. \(y = 2x + 2\)

Correct Answer: A

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Question 11 View Details
Let X be a random variable with probability density function f(x) = \(\frac{1}{2}e^{-|x|}\) for -∞\(< x\)< ∞. Find the probability that X is greater than 1.
Correct A. 0.5
B. 0.6
C. 0.7
D. 0.8

Correct Answer: A

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Question 12 View Details
Solve for x in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 13 View Details
Find the surface area of the solid formed by rotating the region bounded by \(y = x\^2\) and \(y = 4 - x\^2\) about the x-axis.
A. 16π
Correct B. 32π
C. 48π
D. 64π

Correct Answer: B

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Question 14 View Details
Let A be a 3x3 matrix with elements a_{ij}. Find the determinant of A.
Correct A. a_{11}a_{22}a_{33} - a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32}
B. a_{11}a_{22}a_{33} - a_{12}a_{23}a_{31} - a_{13}a_{21}a_{32}
C. a_{11}a_{22}a_{33} + a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32}
D. a_{11}a_{22}a_{33} + a_{12}a_{23}a_{31} - a_{13}a_{21}a_{32}

Correct Answer: A

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Question 15 View Details
Find the sum of the infinite geometric series with first term 1 and common ratio \(\frac{1}{2}\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 16 View Details
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].
A. -3
Correct B. 0
C. 3
D. 6

Correct Answer: B

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Question 17 View Details
Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
A. 10
B. 100
C. 1000
Correct D. 10000

Correct Answer: D

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Question 18 View Details
Find the volume of the sphere with radius 5 cm.
A. 500\pi
B. 1000\pi
Correct C. 2000\pi
D. 5000\pi

Correct Answer: C

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Question 19 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
A. \(-\infty, -1\) \cup \(3, \infty\)
B. \(-\infty, -3\) \cup \(1, \infty\)
Correct C. \(-\infty, -1\) \cup \(1, \infty\)
D. \(-\infty, -3\) \cup \(3, \infty\)

Correct Answer: C

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Question 20 View Details
Find the surface area of the cylinder with radius 4 cm and height 10 cm.
A. 160\pi
B. 320\pi
Correct C. 400\pi
D. 800\pi

Correct Answer: C

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Question 21 View Details
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism in cubic centimeters.
Correct A. 30
B. 40
C. 50
D. 60

Correct Answer: A

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Question 22 View Details
Solve for x in the equation: \(2^x = 64\).
A. 5
Correct B. 6
C. 7
D. 8

Correct Answer: B

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Question 23 View Details
A circle has a radius of 4 cm. Find the area of the circle in square centimeters.
Correct A. 50.24
B. 50.26
C. 50.28
D. 50.30

Correct Answer: A

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Question 24 View Details
A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the prism in square centimeters.
A. 104
Correct B. 108
C. 112
D. 116

Correct Answer: B

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Question 25 View Details
Solve for x in the equation: \(x^2 + 4x + 4 = 0\).
Correct A. -2
B. -1
C. 0
D. 1

Correct Answer: A

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