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POST UTME LASU 2022 Mathematics | Objective

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Question 1 View Details

Find the value of \(\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx\).

Correct A. \(\frac{\pi}{2}\)\)

B. \(\frac{\pi}{4}\)\)

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

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

Correct Answer: A

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Question 2 View Details

Solve the inequality \(\frac{x^2-4x-5}{x^2-4x+4} > 0\).

Correct A. \(-\infty, -1\) \cup \(1, \infty\)

B. \(-\infty, -1\) \cup (1, 2)

C. \(-\infty, 1\) \cup \(2, \infty\)

D. \(-\infty, 1\) \cup \(2, \infty\)

Correct Answer: A

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Question 3 View Details

Find the area of the region bounded by the curves \(y = x^2\) and \(y = 2x\).

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

B. \(\frac{2}{3}\)\)

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

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

Correct Answer: A

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Question 4 View Details

A right circular cone has a height of 20 cm and a base radius of 10 cm. Find the volume of the cone.

Correct A. 2000\pi

B. 1000\pi

C. 500\pi

D. 2500\pi

Correct Answer: A

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Question 5 View Details

A company produces two products, A and B. The profit on product A is (\(\frac{1}{2}\)\) x and the profit on product B is \\((frac{1}{2}\(frac{1}{3}\) x. If the total profit is \(\\(frac{1}{3}) x. If the total profit is \frac{5}{6}\) x, find the value of x.

Correct A. 30

B. 60

C. 90

D. 120

Correct Answer: A

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Question 6 View Details

A circle has a radius of 5 cm. Find the area of the circle using 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 7 View Details

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

Correct A. \(x < -1\) or \(x > \frac{3}{2}\)

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

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

D. \(x > -1\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 8 View Details

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

Correct A. \(y = \frac{1}{2}x + \frac{5}{2}\)

B. \(y = \frac{1}{2}x - \frac{5}{2}\)

C. \(y = 2x - 1\)

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

Correct Answer: A

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Question 9 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.

Correct A. 72

B. 96

C. 108

D. 120

Correct Answer: A

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Question 10 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 11 View Details

Find the value of x in the equation \(\frac{x}{2} + 5 = 11\).

Correct A. 8

B. 10

C. 12

D. 14

Correct Answer: A

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Question 12 View Details

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

A. 0

Correct B. -2

C. -4

D. 2

Correct Answer: B

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Question 13 View Details

Find the value of sin(2θ) given that \sin(θ) = \(3/5\\(sin(2θ) given that sin(θ) =\).

A. \(12/25\)

Correct B. \(24/25\)

C. \(36/25\)

D. \(48/25\)

Correct Answer: B

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Question 14 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 15 View Details

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?

A. \(1/5\)

B. \(1/8\)

Correct C. \(3/8\)

D. \(5/8\)

Correct Answer: C

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Question 16 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 17 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.68

B. 0.73

Correct C. 0.83

D. 0.93

Correct Answer: C

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Question 18 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 19 View Details

Find the derivative of the function [\(f(x) =\)\(3x^2 + 2x - 5\) ] using the power rule.

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

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

Correct Answer: A

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Question 20 View Details

A binary operation [ ast ] is defined as [ a ast \(b = a\^2 + b^2\) ]. Find the value of [ 2 ast 3 ].

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 21 View Details

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

Correct A. \(x^2\) + \\((y^2 - 10x - 12y + 35\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 12x - 10y + 35\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 8x - 14y + 25\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 14x - 8y + 25\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

Solve the inequality \\((3x^2 - 2x - 1\)\(> 0.\)\)

Correct A. \(x <\)\(-1/3\) or \(x > 1/3\)\)

B. \(x <\)\(-1/3\) or \(x < 1/3\)\)

C. \(x >\)\(-1/3\) or \(x < 1/3\)\)

D. \(x >\)\(-1/3\) or \(x > 1/3\)\)

Correct Answer: A

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Question 23 View Details

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

A. 55

Correct B. 60

C. 65

D. 70

Correct Answer: B

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Question 24 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 25 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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