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POST UTME DELSU 2019 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{1}{3}x + 2 = \frac{1}{6}x - 3\) if x is in base 10.

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 2 View Details

A set A contains 5 elements, and a set B contains 3 elements. If the union of sets A and B is denoted by C, and the intersection of sets A and B is denoted by D, find the number of elements in set C if set D contains 2 elements.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 3 View Details

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

Correct A. \(-∞, -1\) ∪ (1, ∞)

B. \(-∞, -1\) ∪ (2, ∞)

C. \(-∞, 1\) ∪ (2, ∞)

D. \(-∞, 1\) ∪ (2, ∞)

Correct Answer: A

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Question 4 View Details

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

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 5 View Details

A 3x3 matrix is given as \(egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\). Find the determinant of the matrix.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 6 View Details

A random sample of 25 students from a large population has a mean height of 175 cm with a standard deviation of 5 cm. Calculate the probability that a randomly selected student from the same population has a height greater than 180 cm.

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 7 View Details

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

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

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

Correct C. \(f'(x) = \frac{2x x^2 + 1 - 2x^3}{x^2 + 1 ^2}\)

D. \(f'(x) = \frac{2x^3}{x^2 + 1 ^2}\)

Correct Answer: C

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Question 8 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 9 View Details

Find the area under the curve \(y = \frac{1}{x}\) from \(x = 1\) to \(x = 2\) using integration.

Correct A. \(\ln(2) - \ln(1)\)

B. \(\ln(2) - \ln(2)\)

C. \(\ln(1) - \ln(2)\)

D. \(\ln(2) - \ln(2)\)

Correct Answer: A

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Question 10 View Details

Solve the trigonometric equation \(\sin^2(x) + \cos^2(x) = 1\) using trigonometric identities.

Correct A. \(\sin(x) = \pm \sqrt{\frac{1}{2}}\)

B. \(\cos(x) = \pm \sqrt{\frac{1}{2}}\)

C. \(\tan(x) = \pm \sqrt{\frac{1}{2}}\)

D. \(\cot(x) = \pm \sqrt{\frac{1}{2}}\)

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 2cm.

A. 100π cm³

B. 200π cm³

Correct C. 300π cm³

D. 400π cm³

Correct Answer: C

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Question 12 View Details

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

Correct A. x² + y² + \(2x - 6y + 5 = 0\)

B. x² + y² - \(2x + 6y - 5 = 0\)

C. x² + y² + \(4x - 2y - 3 = 0\)

D. x² + y² - \(4x + 2y + 3 = 0\)

Correct Answer: A

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Question 13 View Details

The mean of 5 numbers is 15. If one of the numbers is 10, find the sum of the other 4 numbers.

A. 40

Correct B. 50

C. 60

D. 70

Correct Answer: B

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Question 14 View Details

Find the area under the curve \(y = 2x² + 3x - 4\) from \(x = 0\) to \(x = 2\).

A. 20

B. 30

Correct C. 40

D. 50

Correct Answer: C

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Question 15 View Details

A number in base 8 is represented as 123. Find its equivalent in base 10.

A. 83

B. 93

Correct C. 103

D. 113

Correct Answer: C

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Question 16 View Details

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

Correct A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 18 View Details

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

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

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

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

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

Correct Answer: B

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Question 19 View Details

Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using the chain rule.

Correct A. \(2 \(1x\)1x\)

B. \(\cos^2 x\)

C. \(\(1x\)1x\)

D. \(\sin^2 x\)

Correct Answer: A

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Question 20 View Details

Find the area of the triangle formed by the points ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. ( 12 )

B. ( 16 )

Correct C. ( 20 )

D. ( 24 )

Correct Answer: C

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Question 21 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard deviation of 5 cm. If the height of a student is normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 22 View Details

Solve for x in the equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 3 \ 3 \end{bmatrix}\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?

A. 200

B. 250

Correct C. 300

D. 350

Correct Answer: C

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Question 24 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 25 View Details

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

A. \(x = 0\)

Correct B. \(x = 90\)

C. \(x = 180\)

D. \(x = 270\)

Correct Answer: B

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