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POST UTME ESUT 2020 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\)

Correct A. 2

B. -3

C. 4

D. -2

Correct Answer: A

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Question 2 View Details

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

Correct A. \(10^4\)

B. \(10^2\)

C. \(10^8\)

D. \(10^6\)

Correct Answer: A

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Question 3 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 4 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 5 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24

B. 100.48

C. 200.96

D. 50.72

Correct Answer: A

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Question 6 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 - 6x - 4y + 11\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 8x - 6y + 15\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 10x - 8y + 19\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 12x - 10y + 23\)\(= 0\)\)

Correct Answer: A

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Question 7 View Details

Solve the differential equation \(\frac{dy}{dx} = \frac{2x}{y}\) with the initial condition y(1) = 2.

Correct A. \(y = x\^2 + 1\)

B. \(y = x\^2 - 1\)

C. \(y = x\^2 + 2x + 1\)

D. \(y = x\^2 - 2x + 1\)

Correct Answer: A

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Question 8 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 4\).

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 9 View Details

A sequence is defined by the recurrence relation a_\(n = 2a\)_\(n-1\) + 1, with \(a_1 = 3\). Find the value of a_5.

A. 33

B. 35

Correct C. 37

D. 39

Correct Answer: C

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Question 10 View Details

A circle has a radius of 4 cm and passes through the point (0, 3). Find the equation of the circle.

Correct A. \(x^2\) + \\((y^2 - 8x - 12y + 16\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 12x - 8y + 16\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 16x - 12y + 16\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 20x - 15y + 16\)\(= 0\)\)

Correct Answer: A

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Question 11 View Details

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

Correct A. \boxed{ 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 12 View Details

Solve the inequality \(\frac{x - 2}{x + 1}\)\\() > 0.\)

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

B. \(x < -1\)\text{ or } \(x < 2\)

C. \(x > -1\)\text{ or } \(x > 2\)

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

Correct Answer: A

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Question 13 View Details

Find the value of \sum_{\(n = 1\)}^{5} \(n^2\).

Correct A. \boxed{55}

B. 50

C. 60

D. 70

Correct Answer: A

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Question 14 View Details

A set of 5 numbers has a mean of 10. Find the sum of the numbers.

Correct A. \boxed{50}

B. 40

C. 60

D. 70

Correct Answer: A

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Question 15 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. \boxed{0.24}

B. 0.3

C. 0.4

D. 0.5

Correct Answer: A

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Question 16 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. \boxed{50.24}

B. 40.96

C. 60.48

D. 70.72

Correct Answer: A

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Question 17 View Details

Solve the equation \(\frac{1}{x + 1}\)\) + \(\frac{1}{x - 1}\)\) = \(\frac{2}{x^2 - 1}\)\)\).

Correct A. \boxed{\(x = 2\)}

B. \(x = -2\)

C. \(x = 1\)

D. \(x = -1\)

Correct Answer: A

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Question 18 View Details

A set of 4 numbers has a median of 10. Find the sum of the numbers.

Correct A. \boxed{40}

B. 30

C. 50

D. 60

Correct Answer: A

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Question 19 View Details

Two events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.6, find P\(A \cup B\).

Correct A. \boxed{1}

B. 0.8

C. 0.9

D. 0.95

Correct Answer: A

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Question 20 View Details

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

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 21 View Details

Solve the equation \\((2x^2 + 5x - 3\)\(= 0\)\) using the quadratic formula.

A. 1

Correct B. -1

C. -2

D. 2

Correct Answer: B

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Question 22 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 23 View Details

Solve the trigonometric equation \\(sin(x) =\)\cos(x).

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

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

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

D. \(x =\)\\(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 24 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 25 View Details

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

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

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

C. \(x = 2\), \(y = 2\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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