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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2023 Mathematics | Objective

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Question 1

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

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.8 & \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

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

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

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

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

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

A vector \( \vec{a} \) has magnitude 5 units and direction 30° north of east. Find the magnitude of the vector \( \vec{a} \) 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

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

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

Find the equation of the circle pas\sing 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

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

Find the derivative of the function f(x) = \( 2x^2 + 3x - 1 \) / \( x^2 - 4x + 3 \) u\sing 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

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

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

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing 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

A circle has a radius of 5 units. Find the area of the circle u\sing 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

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

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

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

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 21

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

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

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

Question 24

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

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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