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POST UTME ESUT 2017 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 2 View Details

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

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

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

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

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

Correct Answer: A

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Question 3 View Details

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

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

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

C. \(f'(x) = \frac{x}{x^2 + 1 ^2}\)

D. \(f'(x) = \frac{-x}{x^2 + 1 ^2}\)

Correct Answer: A

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Question 4 View Details

Solve the system of equations \(x + y = 2\) and \(x - y = 1\).

Correct A. \(x = \frac{3}{2}, y = \frac{1}{2}\)

B. \(x = \frac{1}{2}, y = \frac{3}{2}\)

C. \(x = 1, y = 1\)

D. \(x = 2, y = 0\)

Correct Answer: A

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Question 5 View Details

Find the equation of the circle with center \((2, 3)\) and radius \(4\).

Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\) \)

B. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\) \)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\) \)

D. \(x - 3\)^2 + \(y - 2\)^\(2 = 9\) \)

Correct Answer: A

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Question 6 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 24πcm³

Correct B. 48πcm³

C. 96πcm³

D. 192πcm³

Correct Answer: B

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Question 7 View Details

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

Correct A. \(-∞, -1\) ∪ [3, ∞)

B. \(-∞, -3\) ∪ [1, ∞)

C. \(-∞, -3\) \cup \(-1, ∞\)\)

D. \(-∞, 3\) ∪ [1, ∞)

Correct Answer: A

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Question 8 View Details

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

A. 1040

Correct B. 1080

C. 1120

D. 1160

Correct Answer: B

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Question 9 View Details

Solve the system of equations \(x + y = 4\) and x - 2y = -3.

Correct A. (1, 3)

B. (3, 1)

C. \(-1, -3\)

D. \(3, -1\)

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).

A. 9

Correct B. 10

C. 11

D. 12

Correct Answer: B

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Question 11 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \(x^2 + y^2 - 12x - 16y + 40 = 0\)

B. \(x^2 + y^2 - 10x - 12y + 20 = 0\)

C. \(x^2 + y^2 - 14x - 20y + 60 = 0\)

D. \(x^2 + y^2 - 12x - 14y + 30 = 0\)

Correct Answer: A

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Question 12 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. x in \( -infty, -3 \ cup (3, infty) )

B. x in \( -infty, -3 \ cup (3, infty) cup {0} )

C. x in \( -infty, -3 \ cup (3, infty) cup {0, 2} )

D. x in \( -infty, -3 \ cup (3, infty) cup {0, 2, 4} )

Correct Answer: A

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Question 13 View Details

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

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

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

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

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

Correct Answer: C

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Question 14 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\) and the line \(y = 2x\\((y = x^2) and the line\) about the x-axis.

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

B. \(\frac{8}{3} \pi\)

Correct C. \(\frac{16}{3} \pi\)

D. \(\frac{32}{3} \pi\)

Correct Answer: C

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Question 15 View Details

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

Correct A. \(-1\)

B. ( 0 )

C. ( 1 )

D. ( 2 )

Correct Answer: A

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Question 16 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 5.5 \cdot \(10^6\)

B. 1.6 \cdot \(10^7\)

Correct C. 3.2 \cdot \(10^7\)

D. 6.3 \cdot \(10^7\)

Correct Answer: C

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4x + 3}{x^2 - 2x - 3}\)\)\\() > 0.\)

A. \left\(-\infty, -1 \right\) \cup \left\(1, \infty \right\)

B. \left\(-\infty, -3 \right\) \cup \left\(1, \infty \right\)

Correct C. \left\(-\infty, -3 \right\) \cup \left\(-1, 1 \right\) \cup \left\(1, \infty \right\)

D. \left\(-\infty, -3 \right\) \cup \left\(1, \infty \right\)

Correct Answer: C

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Question 18 View Details

Find the equation of the tangent line to the curve \(y = x\^2 + 2x - 3\\(tangent line to the curve (y = x\) at the point (1, 2).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 19 View Details

Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}.

Correct A. \left\(1, 1 \right\)

B. \left\(1, -1 \right\)

C. \left\(-1, 1 \right\)

D. \left\(-1, -1 \right\)

Correct Answer: A

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Question 20 View Details

Find the derivative of the function f(x) = \(x^3 - 2x^2 + x - 1\).

Correct A. \(3x^2 - 4x + 1\)

B. \(3x^2 - 4x - 1\)

C. \(3x^2 + 4x - 1\)

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

Correct Answer: A

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Question 21 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 \cdot \(\frac{3^{10} - 1}{3 - 1}\)\)

B. 2 \cdot \(\frac{3^{11} - 1}{3 - 1}\)\)

C. 2 \cdot \(\frac{3^{12} - 1}{3 - 1}\)\)

D. 2 \cdot \(\frac{3^{13} - 1}{3 - 1}\)\)

Correct Answer: A

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Question 22 View Details

Solve the system of equations using matrices: \begin{align*} x + y + z &= 6, \ x + 2y + 3z &= 11, \ x + 3y + 6z &= 16. \end{align*}

A. \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{bmatrix}

B. \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 6 \ 1 & 6 & 11 \end{bmatrix}

Correct C. \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{bmatrix}^{-1}

D. \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 6 \ 1 & 6 & 11 \end{bmatrix}^{-1}

Correct Answer: C

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Question 23 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x + 2\)^2 + \(y - 3\)^\(2 = 16\)

B. \(x - 2\)^2 + \(y + 3\)^\(2 = 16\)

C. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

Correct Answer: A

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Question 24 View Details

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

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

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

C. \(\frac{1}{6}\)\)

D. \(\frac{1}{12}\)\)

Correct Answer: B

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Question 25 View Details

Find the magnitude of the vector \begin{bmatrix} 3 \ 4 \end{bmatrix}.

Correct A. \(\sqrt{25}\)

B. \(\sqrt{26}\)

C. \(\sqrt{27}\)

D. \(\sqrt{28}\)

Correct Answer: A

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