POST UTME LAUTECH 2020 Mathematics | Objective

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Question 1 View Details
Solve for x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\).
A. \(x = -10\)
Correct B. \(x = 2\)
C. \(x = -6\)
D. \(x = 6\)

Correct Answer: B

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Question 2 View Details
Find the value of \(\log_{10} x^2 \\) ) given that \(\log_{10} x = 2\).
Correct A. 4
B. 2
C. 6
D. 8

Correct Answer: A

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Question 3 View Details
A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(6, 7) ). Find the equation of the circle.
Correct A. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )
B. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )
C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 36\) )
D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 49\) )

Correct Answer: A

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Question 4 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. x < -1 or \(x > 3\)
B. \(x < 1\) or \(x > 3\)
C. x < -1 or \(x < 3\)
D. \(x > 1\) or \(x < 3\)

Correct Answer: A

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Question 5 View Details
A vector ( vec{a} ) has components \(a_x = 2\) and \(a_y = 3\). Find the magnitude of the vector.
A. 5
Correct B. 10
C. 15
D. 20

Correct Answer: B

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Question 6 View Details
In the diagram below, a right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the two legs is 3:4, find the area of the triangle.
Correct A. 24
B. 30
C. 40
D. 50

Correct Answer: A

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Question 7 View Details
A random variable X has a probability distribution given by (P(X) = \begin{cases} 0.2 & \text{if}\(X = 1\), \\((P(X) = begin{cases} 0.2 & \ 0.3 & \text{if} X = 2, \\\( 0.3 & text{if} X = 2, \ 0.5 & \text{if} X = 3. \end{cases}\) Find the expected value of X.
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 8 View Details
Solve the inequality \(2x^2 + 5x - 3 \geq 0\).
Correct A. x \in \left[ -3, \(\frac{1}{2}\)\) \right]
B. x \in \left[ -3, \infty \right]
C. x \in \left[ -3, 0 \right]
D. x \in \left[ 0, \(\frac{1}{2}\)\) \right]

Correct Answer: A

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Question 9 View Details
Find the area under the curve \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).
Correct A. \(\frac{1}{2}\)\) \ln 2
B. \(\frac{1}{2}\)\) \ln 1
C. \(\frac{1}{2}\)\) \ln 3
D. \(\frac{1}{2}\)\) \ln 4

Correct Answer: A

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Question 10 View Details
A histogram of exam scores is shown below. If the mean score is 60, find the value of k.
Correct A. 20
B. 30
C. 40
D. 50

Correct Answer: A

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Question 11 View Details
In a quadratic equation of the form \((ax^2 + bx + c\) = 0\), if the sum of the roots is 6 and the product of the roots is 12, find the value of ( a ) if \(b = 3\\((ax^2 + bx + c = 0), if the sum of the roots is 6 and the product of the roots is 12, find the value of ( a ) if\).
Correct A. -2
B. 2
C. 4
D. 6

Correct Answer: A

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Question 12 View Details
A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, find the volume of water in the \tank in cubic meters.
A. 120π
Correct B. 240π
C. 360π
D. 480π

Correct Answer: B

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Question 13 View Details
A curve is defined by the equation (y = \(\frac{\(2x^2 - 3x + 1}{x^2 - 4x + 3}\)\)\). Find the derivative of the curve at the point where \\((y = frac{2x^2 - 3x + 1}{x^2 - 4x + 3}\(x = 1\).
A. -1
Correct B. 1
C. 2
D. 3

Correct Answer: B

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Question 14 View Details
A polynomial function is defined by the equation ( f(x) = \((x^3 - 2x^2 + 3x - 1\)\) ). Find the value of \(f -2 \\((x^3 - 2x^2 + 3x - 1) ). Find the value of \\) ).
Correct A. -11
B. -9
C. -7
D. -5

Correct Answer: A

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Question 15 View Details
A quadratic equation is defined by the equation \(x^2 + 4x + 4 = 0\). Find the roots of the equation.
Correct A. -2
B. -1
C. 1
D. 2

Correct Answer: A

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