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POST UTME CALEB UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) )

B. \(\frac{1}{2} \left \frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right \\) )

C. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) + \(\frac{1}{2}\)\) left\(\frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right\) )

D. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) - \(\frac{1}{2}\)\) left\(\frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right\) )

Correct Answer: A

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Question 2 View Details

Solve the inequality \(\left| x - 2 \right| \geq 3\).

Correct A. \(x \leq -1\) or ( x geq 5 )

B. ( x leq 1 ) or ( x geq 5 )

C. \(x \leq -1\) or ( x geq 4 )

D. ( x leq 1 ) or ( x geq 4 )

Correct Answer: A

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Question 3 View Details

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?

Correct A. \(\frac{3}{8}\)

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

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

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

Correct Answer: A

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Question 4 View Details

Solve the equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\) or \(x = -3\)

D. \(x = 1\) or \(x = 3\)

Correct Answer: A

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Question 5 View Details

Find the value of ( x ) in the equation \(2^x = 16\).

A. \(x = 2\)

Correct B. \(x = 4\)

C. \(x = 1\)

D. \(x = 3\)

Correct Answer: B

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Question 6 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find ( AB ) using the rule of Sarrus.

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

B. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}

C. \begin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix}

D. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}

Correct Answer: A

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Question 7 View Details

A random experiment has two possible outcomes: A and B. The probability of outcome A is 0.4, and the probability of outcome B is 0.6. If outcome A occurs, there is a 0.7 probability that outcome C will occur. If outcome B occurs, there is a 0.8 probability that outcome C will occur. What is the probability that outcome C will occur?

Correct A. 0.28

B. 0.56

C. 0.84

D. 0.96

Correct Answer: A

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Question 8 View Details

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

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

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

C. \(\frac{-2x}{x^2 + 1\) ^3}\)\)

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

Correct Answer: B

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Question 9 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 3\) with initial term \(a_1 = 2\). Find the sum of the first five terms of the sequence.

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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Question 10 View Details

Find the area of the triangle formed by the points ( (0, 0) ), ( (3, 4) ), and ( (6, 0) ).

Correct A. 12

B. 15

C. 18

D. 20

Correct Answer: A

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Question 11 View Details

Let ( f(x) = \(\frac{1}{x^2 + 1}\)\)) ). Find lim_{x \to infty} f\( x \\() ). Find lim_{x to infty} f\ ).

Correct A. 0

B. 1

C. ∞

D. undefined

Correct Answer: A

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Question 12 View Details

A set ( A ) contains 5 elements. If ( A ) has 3 subsets, what is the number of elements in the power set of ( A )?

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 13 View Details

A sequence (a_n\) is defined as \(a_n = \\((a_n) is defined as \frac{1}{n}\). Find the sum of the first 5 terms of the sequence.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 14 View Details

A histogram has a mean of 20 and a standard deviation of 5. If the histogram has 10 bars, what is the range of the histogram?

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 15 View Details

Two events ( A ) and ( B ) are independent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), what is the probability that both events occur?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 16 View Details

A vector ( mathbf{a} ) has a magnitude of 5 and a direction of 30°. If a vector ( mathbf{b} ) has a magnitude of 3 and a direction of 60°, what is the magnitude of the sum of the two vectors?

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 17 View Details

A binary operation ( ast ) is defined as (a ast b = \(a^2 + b^2\)\). If \(a = 2\\((a ast b = a^2 + b^2). If\) and \(b = 3\), what is the result of the operation?

A. 13

B. 14

C. 15

Correct D. 16

Correct Answer: D

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Question 18 View Details

A set ( A ) contains 3 elements. If ( A ) has 2 subsets, what is the number of elements in the power set of ( A )?

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 19 View Details

A sequence (a_n\) is defined as \(a_n = \\((a_n) is defined as \frac{1}{n^2}\). Find the sum of the first 4 terms of the sequence.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 20 View Details

A histogram has a mean of 25 and a standard deviation of 6. If the histogram has 12 bars, what is the range of the histogram?

A. 20

B. 30

C. 40

D. 50

Correct Answer: VIEW ANSWER

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Question 21 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and \(-1, 2\).

Correct A. \(x^2\) + \\((y^2 + 6x - 4y - 12\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 6x + 4y - 12\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 4x - 6y - 12\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 4x + 6y - 12\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

Solve the system of equations using matrices: \begin{align*} x + 2y - z &= 4 \ 2x - 3y + z &= 3 \ -x + y + 2z &= -2 \end{align*}

Correct A. \(x = 1\), \(y = 2\), \(z = 3\)

B. \(x = 2\), \(y = 1\), \(z = 3\)

C. \(x = 1\), \(y = 3\), \(z = 2\)

D. \(x = 3\), \(y = 2\), \(z = 1\)

Correct Answer: A

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Question 23 View Details

A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.

A. 256\pi \(cm^3\)

Correct B. 512\pi \(cm^3\)

C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: B

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Question 24 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 25 View Details

Solve the polynomial equation: \(x^3\) - \\((6x^2 + 11x - 6\)\(= 0.\)\)

Correct A. \(x = 1\), 2, 3

B. \(x = 1\), 2, -3

C. \(x = 1\), -2, 3

D. \(x = 2\), -1, 3

Correct Answer: A

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