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POST UTME LASU 2019 Mathematics | Objective

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Question 1 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is 6, what is the value of the missing number in the data set?

Correct A. 12

B. 14

C. 16

D. 18

Correct Answer: A

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Question 2 View Details

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

Correct A. 59049

B. 59048

C. 59050

D. 59052

Correct Answer: A

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Question 3 View Details

Solve the system of linear equations using matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= -1 \end{align*}

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 4 View Details

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

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 5 View Details

A set of 10 numbers has a mean of 20. If 5 more numbers are added to the set, the mean becomes 22. What is the sum of the original 10 numbers?

A. 200

Correct B. 220

C. 240

D. 260

Correct Answer: B

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Question 6 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{2x^2 + 5x - 3}\)\)\) ) using the quotient rule.

Correct A. \(\frac{-2x + 5}{2x^2 + 5x - 3\) \ ^2}\)\) )

B. \(\frac{2x + 5}{2x^2 + 5x - 3\) \ ^2}\)\) )

C. \(\frac{2x - 5}{2x^2 + 5x - 3\) \ ^2}\)\) )

D. \(\frac{-2x - 5}{2x^2 + 5x - 3\) \ ^2}\)\) )

Correct Answer: A

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Question 7 View Details

A circle with center ( C(2, 3) ) and radius (r = 4\) has equation \(x - 2 \\((r = 4) has equation \\)^2 + \(y - 3\)^\(2 = 16\) ). Find the equation of the line passing through the point ( P(6, 7) ) that is \tangent to the circle.

Correct A. \(y - 7 = \frac{1}{4} x - 6 \\) )

B. \(y - 7 = -\frac{1}{4} x - 6 \\) )

C. \(y - 7 = \frac{1}{2} x - 6 \\) )

D. \(y - 7 = -\frac{1}{2} x - 6 \\) )

Correct Answer: A

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Question 8 View Details

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

Correct A. \(x < -\frac{5}{4}\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > \frac{5}{4}\)

C. \(x < -\frac{3}{2}\) or \(x < \frac{5}{4}\)

D. \(x > -\frac{5}{4}\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 9 View Details

A population of bacteria grows according to the logistic equation \(\frac{dP}{dt} = rP \\(logistic equation (\left 1 - \frac{P}{K} \right \\) ), where \(r = 0.5\) and \(K = 100\). Find the equilibrium population.

A. \(P = 0\)

B. \(P = 50\)

Correct C. \(P = 100\)

D. \(P = 200\)

Correct Answer: C

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Question 10 View Details

A random variable ( X ) has probability density function ( f(x) = \(\frac{1}{2}\)\\()e^{-\)|x|} ). Find the expected value of ( X ).

Correct A. \(( E(X) = 0 )\)

B. \(( E(X) = 1 )\)

C. \(( E(X) = -1 )\)

D. \(( E(X) = 2 )\)

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi \(cm^3\)

B. 128\pi \(cm^3\)

Correct C. 192\pi \(cm^3\)

D. 256\pi \(cm^3\)

Correct Answer: C

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Question 12 View Details

Solve for x in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦2 per loaf, how much profit do they make in a day?

Correct A. ₦500

B. ₦5000

C. ₦50000

D. ₦500000

Correct Answer: A

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Question 14 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 15 View Details

Find the vector projection of vector \(\mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\) onto vector \(\mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}\).

Correct A. egin{pmatrix} 0.8 \ 1 \ 1.2 \end{pmatrix}

B. egin{pmatrix} 1 \ 1.2 \ 1.6 \end{pmatrix}

C. egin{pmatrix} 1.2 \ 1.5 \ 2 \end{pmatrix}

D. egin{pmatrix} 1.5 \ 1.8 \ 2.4 \end{pmatrix}

Correct Answer: A

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Question 16 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 17 View Details

Solve for x in the equation \(2^x + 2^{x+1} = 2^{x+2} + 1\).

A. \(x = -1\)

B. \(x = 0\)

Correct C. \(x = 1\)

D. \(x = 2\)

Correct Answer: C

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Question 18 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is either 1 or 6?

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

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

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

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

Correct Answer: D

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Question 19 View Details

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

Correct A. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 20 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. \(\frac{1}{2}\)

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

C. \(\frac{3}{4}\)

D. \(\frac{4}{5}\)

Correct Answer: B

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Question 21 View Details

Let X be a random variable with probability density function (pdf) given by f(x) = (\(\frac{1}{2}\) \(e^{-\)|x|}\) for -\\((frac{1}{2} e^{-|x|}\(\infty < x < \infty\). Find the probability that X lies between -1 and 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 22 View Details

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

Correct A. \(- \infty, -\frac{3}{2} \\)) (cup) (1, (infty))

B. \(- \infty, -\frac{3}{2} \\)) (cap) (1, (infty))

C. \(- \infty, -\frac{3}{2} \\)) (cup) \(-1, \infty \\))

D. \(- \infty, -\frac{3}{2} \\)) (cap) \(-1, \infty \\))

Correct Answer: A

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Question 23 View Details

Find the area under the curve \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).

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

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

C. \(\frac{2\pi}{3}\)

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

Correct Answer: A

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Question 24 View Details

Let A be a 2x2 matrix given by [\(A =\)egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix}]. Find the determinant of A.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 25 View Details

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

Correct A. 1, 2, 3

B. 1, 2, 4

C. 1, 3, 4

D. 2, 3, 4

Correct Answer: A

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