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POST UTME CHRISTOPHER UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Find the area under the curve \(y = \frac{1}{x^2}\) from \(x = 1\) to \(x = 2\).

Correct A. \(\frac{1}{2}\)

B. \(\frac{1}{3}\)

C. \(\frac{1}{4}\)

D. \(\frac{1}{5}\)

Correct Answer: A

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Question 2 View Details

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 3 View Details

A sequence is defined by \(a_n = \frac{1}{n}\). Find the sum of the first five terms of the sequence.

Correct A. \(\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}\)

B. \(\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}\)

C. \(\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}\)

D. \(\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7}\)

Correct Answer: A

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Question 4 View Details

A histogram is constructed with the following data: \(egin{array}{|c|c|} hline \text{Class} & \text{Frequency} \ hline 0-10 & 5 \ 10-20 & 8 \ 20-30 & 12 \ 30-40 & 15 \ 40-50 & 10 \ hline \end{array}\). Find the mean of the data.

A. 25

B. 30

Correct C. 35

D. 40

Correct Answer: C

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Question 5 View Details

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

Correct A. \(\pi \times 4^2 \times 10\)

B. \(\pi \times 4^2 \times 5\)

C. \(\pi \times 4^2 \times 10^2\)

D. \(\pi \times 4^2 \times 10^3\)

Correct Answer: A

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Question 6 View Details

Find the value of 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 7 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula.

Correct A. x = -2 or x = -3

B. x = -1 or x = -6

C. \(x = 2\) or \(x = 3\)

D. \(x = 1\) or \(x = 6\)

Correct Answer: A

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Question 8 View Details

A binary operation * is defined as (a * b = ab + 5\). Find the value of \(2 * 3\\((a * b = ab + 5). Find the value of\).

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 9 View Details

A particle moves in a straight line with a velocity of \(v = 2t + 5\) \(m/s\). Find the acceleration of the particle after 3 seconds.

A. 4 \(m/s\^2\)

B. 6 \(m/s\^2\)

Correct C. 8 \(m/s\^2\)

D. 10 \(m/s\^2\)

Correct Answer: C

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Question 10 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. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 11 View Details

A random variable X is uniformly distributed over the interval [0, 1]. Find the probability that \(X^2\) + \\((Y^2\)\(> 1\)\), where Y is an independent random variable uniformly distributed over the interval [0, 1].

A. 0

B. \(\frac{1}{2}\)\)

Correct C. \(\frac{2}{3}\)\)

D. \(\frac{3}{4}\)\)

Correct Answer: C

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Question 12 View Details

Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 13 View Details

A solid cylinder of radius 4 cm and height 10 cm has a hole drilled through it with a radius of 2 cm. Find the volume of the remaining solid.

A. 100\pi

Correct B. 200\pi

C. 300\pi

D. 400\pi

Correct Answer: B

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Question 14 View Details

The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 35

B. 40

C. 45

D. 50

Correct Answer: A

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Question 15 View Details

Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + \cdots\).

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 16 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find ( AB ) if it exists.

Correct A. \(\begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix}\)

B. \(\begin{bmatrix} 11 & 14 \\ 23 & 28 \end{bmatrix}\)

C. \(\begin{bmatrix} 3 & 4 \\ 9 & 12 \end{bmatrix}\)

D. \(\begin{bmatrix} 7 & 8 \\ 15 & 18 \end{bmatrix}\)

Correct Answer: A

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Question 17 View Details

Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, 54, ... ).

Correct A. \(10494\)

B. \(10494.5\)

C. \(10495\)

D. \(10496\)

Correct Answer: A

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Question 18 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for \(x \\\() for (x\) in the interval \([0, 2\pi] \\).

A. \(\frac{\pi}{2}\)

Correct B. \(\frac{\pi}{4}\)

C. \(\frac{3\pi}{4}\)

D. \(\frac{5\pi}{4}\)

Correct Answer: B

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Question 19 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) \) using the chain rule.

Correct A. \(-\frac{2x}{x^2 + 1 ^2}\)

B. \(\frac{2x}{x^2 + 1 ^2}\)

C. \(-\frac{2}{x^2 + 1 ^2}\)

D. \(\frac{2}{x^2 + 1 ^2}\)

Correct Answer: A

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Question 20 View Details

Find the equation of the circle with center ( (3, 4) \) and radius 5.

Correct A. \(x - 3\)^2 + \(y - 4\)^\(2 = 25\)\)

B. \(x - 4\)^2 + \(y - 3\)^\(2 = 25\)\)

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 30\)\)

D. \(x - 4\)^2 + \(y - 3\)^\(2 = 30\)\)

Correct Answer: A

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Question 21 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 22 View Details

Solve for ( x ) in the equation \(2^x = 16\).

A. ( 2 )

Correct B. ( 4 )

C. ( 8 )

D. ( 16 )

Correct Answer: B

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Question 23 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).

Correct A. \(6x + 2\)

B. \(6x - 2\)

C. \(6x + 2x - 2\)

D. \(6x + 2x + 2\)

Correct Answer: A

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Question 24 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(x < -1\) or \(x > \frac{3}{2}\)

B. \(x < -1\) or \(x < \frac{3}{2}\)

C. \(x > -1\) or \(x > \frac{3}{2}\)

D. \(x > -1\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 25 View Details

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. ( 6 )

B. ( 12 )

Correct C. ( 18 )

D. ( 24 )

Correct Answer: C

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