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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2 View Details

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & text{if } \(X = 1\) \\(text{if} (X = 1\ 0.8 & text{if} \(X = 2\) \\(text{if}\((X = 2\)\ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 1.

Correct A. 0.2

B. 0.8

C. 1

D. 0.6

Correct Answer: A

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Question 3 View Details

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

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 4 View Details

Solve the equation \(2^x + 2^x = 64\).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 5 View Details

A circuit consists of a 12V battery, a 4Ω resistor, and a 6Ω resistor connected in series. Find the current flowing through the circuit.

A. 1.5A

Correct B. 2A

C. 2.5A

D. 3A

Correct Answer: B

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Question 6 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 64\pi \(cm^3\)

B. 128\pi \(cm^3\)

Correct C. 192\pi \(cm^3\)

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

Correct Answer: C

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Question 7 View Details

Solve for x in the equation \(\log_{10} x^2\)\(= 4\)\).

A. \(10^4\)

B. \(10^8\)

Correct C. \(10^12\)

D. \(10^16\)

Correct Answer: C

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Question 8 View Details

A vector (\(\vec{a}\)\) has magnitude 5 units and direction 30° north of east. Find the magnitude of the vector \\((vec{a}\(\vec{a}\) if it is rotated 60° counterclockwise.

Correct A. 5\sqrt{3} units

B. 10 units

C. 5\sqrt{2} units

D. 5 units

Correct Answer: A

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Question 9 View Details

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

Correct A. \(x \leq -1\) or \(x \geq \frac{3}{2}\)

B. \(x \leq 1\) or \(x \geq -3\)

C. \(x \leq -3\) or \(x \geq 1\)

D. \(x \leq \frac{3}{2}\) or \(x \geq -1\)

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices \(A(0, 0), B(3, 0), C(1, 2)\).

A. 3 square units

Correct B. 6 square units

C. 9 square units

D. 12 square units

Correct Answer: B

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Question 11 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and (6, 7).

Correct A. \(x^2\) + \\((y^2 + 4x + 6y - 11\)\(= 0\)\)

B. \(x^2\) + \\((y^2 + 2x + 4y - 9\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 6x + 2y - 13\)\(= 0\)\)

D. \(x^2\) + \\((y^2 + 8x + 10y - 15\)\(= 0\)\)

Correct Answer: A

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Question 12 View Details

A random variable X has a probability distribution given by P\(X = 1 = 1/4\), P\(X = 2 = 1/2\), P\(X = 3 = 1/4\). Find the probability that X is greater than 2.

A. \(1/2\)

Correct B. \(3/4\)

C. \(1/4\)

D. \(3/8\)

Correct Answer: B

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Question 13 View Details

Find the derivative of the function f(x) = \(2x^2 + 3x - 1\) / \(x^2 - 4x + 3\) using the quotient rule.

Correct A. \(4x^2 - 2x - 3\) / \(x^2 - 4x + 3\)^2

B. \(4x^2 + 2x - 3\) / \(x^2 - 4x + 3\)^2

C. \(4x^2 - 2x + 3\) / \(x^2 - 4x + 3\)^2

D. \(4x^2 + 2x + 3\) / \(x^2 - 4x + 3\)^2

Correct Answer: A

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Question 14 View Details

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A.

Correct A. 32

B. 16

C. 8

D. 4

Correct Answer: A

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Question 15 View Details

Find the sum of the infinite geometric series 1 + \(1/2\) + \(1/4\) + ...

Correct A. 2

B. 4

C. 8

D. 16

Correct Answer: A

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Question 16 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

A. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

B. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct C. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

D. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct Answer: C

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Question 17 View Details

A circle has a radius of 5 units. Find the area of the circle using the formula \(A = \pi r^2\).

Correct A. 25\pi

B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: A

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Question 18 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x ).

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

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

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

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

Correct Answer: B

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Question 19 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20 View Details

A curve has the equation (y = \(x^2 + 2x - 3\)\). Find the area under the curve between \(x = 0\\((y = x^2 + 2x - 3). Find the area under the curve between\) and \(x = 2\).

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 21 View Details

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

Correct A. \(x < -3\)

B. \(x > -3\)

C. \(x < 3\)

D. \(x > 3\)

Correct Answer: A

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Question 22 View Details

A right-angled triangle has a hypotenuse of length 10 units and one leg of length 6 units. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 23 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Question 24 View Details

In a binary number system, what is the value of the digit in the 5th position from the right in the number 1011011101?

A. 1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 25 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/5\)

D. \(3/8\)

Correct Answer: A

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