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POST UTME UNN 2025 Mathematics | Objective

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Question 1 View Details

Solve the inequality \(2x^2 - 3x - 2 > 0\) and select the correct solution set.

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

B. No solution

C. \( x > 2 \)

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

Correct Answer: A

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Question 2 View Details

Find the volume of the solid generated by rotating the region bounded by \(y = \sqrt{x}\), the x‑axis and \(x = 4\) about the x‑axis.

A. 4\pi

B. 32\pi

Correct C. 8\pi

D. 16\pi

Correct Answer: C

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Question 3 View Details

A box contains 4 red, 5 blue and 6 green balls. Two balls are drawn successively without replacement. What is the probability that the first ball is red and the second ball is green?

A. 2/7

Correct B. 4/35

C. 6/35

D. 1/5

Correct Answer: B

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Question 4 View Details

Given the polynomial \(f(x)=x^{3}-3x+1\), what is the sum of all real roots of the equation \(f(x)=0\)?

A. 1

B. 3

C. -1

Correct D. 0

Correct Answer: D

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Question 5 View Details

Let \(S = \{ a_n \mid a_n = 3n + 2, \ n \in \mathbb{N}, \ 1 \le n \le 5 \}\). Which statement about \(S\) is correct?

A. S is a geometric progression.

Correct B. S is an arithmetic progression.

C. The sum of the elements of S is 65.

D. The cardinality of S is 4.

Correct Answer: B

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Question 6 View Details

If\( f(x) = 2x^3 - 5x^2 + kx - 12 \)has a remainder of 4 when divided by\( x-2 \)and a remainder of -3 when divided by\( x+1 \), find the value of\( k \).

A. 10

Correct B. No such value

C. -16

D. 5

Correct Answer: B

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Question 7 View Details

The histogram below shows the distribution of scores of 40 students in a test. The class intervals are 0-9, 10-19, 20-29, 30-39, 40-49 with respective frequencies 4, 8, 12, 10, 6. Compute the mean score (to one decimal place).

A. 25.0

B. 24.5

Correct C. 26.0

D. 25.5

Correct Answer: C

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Question 8 View Details

In the diagram, vectors\( \vec{A} \)and\( \vec{B} \)are represented as arrows\( OA \)and\( OB \)from the origin O. Vector\( \vec{C}=3\vec{A}-2\vec{B} \). If\( \vec{A}=(1,2) \)and\( \vec{B}=(0,0.5) \), find the magnitude of\( \vec{C} \)(to two decimal places).

A. \( \sqrt{29} \)

Correct B. \( \sqrt{34} \)

C. \( \sqrt{41} \)

D. \( \sqrt{50} \)

Correct Answer: B

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Question 9 View Details

If\( 2^{x}=5 \)and\( \log_{10}(x)=y \), find the value of\( y \)correct to three decimal places.

Correct A. 0.366

B. 0.368

C. 0.367

D. 0.365

Correct Answer: A

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Question 10 View Details

Simplify\( \sqrt{81}+\log_{3}27-\frac{1}{2}\log_{2}16 \).

A. 9

Correct B. 10

C. 11

D. 12

Correct Answer: B

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Question 11 View Details

The binary number 101101₂ is divided by the fraction 3/5. Express the result in base 2, rounded to four binary places after the binary point.

A. 1001100.0000

B. 1001010.1111

C. 1001011.1111

Correct D. 1001011.0000

Correct Answer: D

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Question 12 View Details

Let S = { x ∈ ℚ | x can be expressed as a terminating fraction in base 8 }. Which of the following numbers belongs to S?

Correct A. 0.5

B. 0.4

C. 0.3

D. 0.2

Correct Answer: A

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Question 13 View Details

The sum of the first n terms of a geometric progression is given by S_n = 5(1-(-2)^n)/3. What is the 5th term of the progression?

Correct A. 80

B. -80

C. 40

D. -40

Correct Answer: A

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Question 14 View Details

Consider the polynomial f(x)=x³−6x²+9x+4. Which interval contains a local maximum of f?

Correct A. (0,2)

B. (4,\infty)

C. (2,4)

D. (-\infty,0)

Correct Answer: A

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Question 15 View Details

In right‑angled triangle ABC with ∠C = 90°, the legs have lengths 3 and 4. Let θ be the acute angle opposite the side of length 3. Compute sin θ + cos θ.

A. 1

B. 0

Correct C. 7/5

D. 5/7

Correct Answer: C

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Question 16 View Details

Find the area enclosed between the curves y = x^{2} and y = 2x + 3.

Correct A. 32/3

B. 28/3

C. 10/3

D. 34/3

Correct Answer: A

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Question 17 View Details

Two circles are given by (x-1)^2 + (y-2)^2 = 9 and (x+3)^2 + (y-2)^2 = 4. Determine the equation of the line that passes through their points of intersection and is perpendicular to the line joining their centres.

Correct A. x = -\frac{13}{8}

B. x = -1

C. x = -2

D. x = 0

Correct Answer: A

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Question 18 View Details

A bag contains 3 white, 4 black and 5 yellow balls. Two balls are drawn sequentially without replacement. What is the probability that the second ball is yellow given that the first ball drawn was not yellow?

A. \frac{5}{10}

B. \frac{4}{11}

C. \frac{5}{12}

Correct D. \frac{5}{11}

Correct Answer: D

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Question 19 View Details

If 254_{6} is multiplied by 13_{6}, what is the product expressed in base 6?

A. 4320_{6}

Correct B. 4230_{6}

C. 4210_{6}

D. 4240_{6}

Correct Answer: B

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Question 20 View Details

Given vectors \vec{a}=3\hat{i}-2\hat{j}+\hat{k} and \vec{b}=-\hat{i}+4\hat{j}-2\hat{k}, compute the magnitude of \vec{a}\times(\vec{b}\times\vec{a}).

A. 14\sqrt{5}

B. 7\sqrt{10}

C. 10\sqrt{7}

Correct D. 5\sqrt{70}

Correct Answer: D

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Question 21 View Details

A solid is formed by rotating the region bounded by \( y=\sqrt{x} \), \( y=0 \) and \( x=4 \) about the x‑axis. Find its total surface area.

A. \( \frac{\pi}{4}\bigl(17\sqrt{17}-1\bigr) \)

Correct B. \( \frac{\pi}{6}\bigl(17\sqrt{17}-1\bigr) \)

C. \( \frac{\pi}{3}\bigl(17\sqrt{17}-1\bigr) \)

D. \( \frac{\pi}{6}\bigl(16\sqrt{16}-1\bigr) \)

Correct Answer: B

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Question 22 View Details

Find the coordinates of the point(s) of intersection between the line \( 2x - y + 3 = 0 \) and the circle \( (x-1)^2 + (y+2)^2 = 9 \).

A. \( 4,5 \)

B. \( 1, -5 \)

Correct C. No real intersection

D. \( 2, -1 \)

Correct Answer: C

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Question 23 View Details

Evaluate the derivative of \( f(x) = \sqrt{\ln (5x^2 + 1)} \) at \( x = 1 \).

Correct A. \( \frac{5}{6\sqrt{\ln 6}} \)

B. \( \frac{5}{3\sqrt{\ln 6}} \)

C. \( \frac{10}{6\sqrt{\ln 6}} \)

D. \( \frac{5}{6\ln 6} \)

Correct Answer: A

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Question 24 View Details

Find the area enclosed between the curve \( y = x^3 - 3x \) and the x‑axis between its successive real roots.

Correct A. 9/2

B. 3

C. 9

D. 6

Correct Answer: A

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Question 25 View Details

In base‑5, the number \( (132)_5 \) is multiplied by \( (23)_5 \). Express the product in base‑5.

A. (4231)_5

B. (4321)_5

Correct C. (4141)_5

D. (4411)_5

Correct Answer: C

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