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POST UTME LAUTECH 2023 Mathematics | Objective

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Question 1 View Details

Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 2 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 3 View Details

Solve for x in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}\).

A. \(x = 3\)

B. \(x = 4\)

Correct C. \(x = 5\)

D. \(x = 6\)

Correct Answer: C

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Question 4 View Details

Find the surface area of the sphere with radius 5 cm.

A. 50π cm²

B. 100π cm²

Correct C. 150π cm²

D. 200π cm²

Correct Answer: C

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Question 5 View Details

Determine the number of terms in the sequence 1, 2, 4, 8, ...

A. 5

B. 6

C. 7

Correct D. 8

Correct Answer: D

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Question 6 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7 View Details

Find the value of y in the equation \(y = \frac{1}{2} 3x + 5 \\) ) when \(x = 4\).

A. 8

Correct B. 9

C. 10

D. 11

Correct Answer: B

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Question 8 View Details

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. 25π

B. 50π

C. 75π

D. 100π

Correct Answer: A

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Question 9 View Details

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

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 10 View Details

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

A. 9

B. 11

Correct C. 13

D. 15

Correct Answer: C

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Question 11 View Details

In the diagram below, the equation of the circle is given by \(x - 2 \\)^2 + \(y - 3)^\(2 = 4\) ). Find the equation of the \\\\((()^(2\) = 4\)\tangent line to the circle at the point ( (5, 7) ).

Correct A. \(y = -x + 12\)

B. \(y = x - 1\)

C. \(y = -x + 11\)

D. \(y = x + 1\)

Correct Answer: A

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Question 12 View Details

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

Correct A. \(egin{pmatrix} 1.6 \ 2.4 \end{pmatrix}\)

B. \(egin{pmatrix} 2.4 \ 3.6 \end{pmatrix}\)

C. \(egin{pmatrix} 3.2 \ 4.8 \end{pmatrix}\)

D. \(egin{pmatrix} 4.8 \ 7.2 \end{pmatrix}\)

Correct Answer: A

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Question 13 View Details

A random variable ( X ) has a probability distribution given by \(P X = x \\) = egin{cases} 0.2 & \text{if } \(x = 1\) \ 0.3 & \text{if } \(x = 2\) \ 0.5 & \text{if } \(x = 3\) \end{cases} ). Find the probability that ( X ) takes on a value greater than 2.

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 14 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 15 View Details

Find the value of (\(12\theta\) given that \\((\)12theta\(\(1\theta = \frac{3}{5}\) and 1\\(theta =\)\(\frac{4}{5}\)\).

Correct A. \(\frac{24}{25}\)

B. \(\frac{16}{25}\)

C. \(\frac{20}{25}\)

D. \(\frac{12}{25}\)

Correct Answer: A

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Question 16 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\frac{1}{2}\\()x^2 + 1\)\), the \\((y = frac{1}{2}x^2 + 1\(x)-axis, and the line \(x = 2\) about the \\()-axis, and the line (x = 2\(x\)-axis.

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

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

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

D. \(\frac{64\pi}{3}\)

Correct Answer: A

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Question 17 View Details

Solve the inequality \(|x^2 - 4x + 3| \geq 2\).

Correct A. \(x \leq -1\) or ( x geq 3 )

B. ( x leq 1 ) or ( x geq 3 )

C. \(x \leq -1\) or ( x geq 2 )

D. ( x leq 1 ) or ( x geq 2 )

Correct Answer: A

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Question 18 View Details

Find the equation of the circle passing through the points \(-2, 3\)\), \(1, -2\)\), and \((4, 5)\).

Correct A. \(x^2 + y^2 - 6x + 10y + 11 = 0\)

B. \(x^2 + y^2 - 4x - 2y + 3 = 0\)

C. \(x^2 + y^2 + 2x - 4y - 5 = 0\)

D. \(x^2 + y^2 - 2x + 4y - 7 = 0\)

Correct Answer: A

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Question 19 View Details

A right circular cone has a height of 8 cm and a base radius of 5 cm. Find the volume of the cone.

A. ( 100pi ) cm\(^3\)

B. ( 200pi ) cm\(^3\)

Correct C. ( 300pi ) cm\(^3\)

D. ( 400pi ) cm\(^3\)

Correct Answer: C

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Question 20 View Details

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

A. \(x = 1\)

B. \(x = 2\)

Correct C. \(x = 3\)

D. \(x = 6\)

Correct Answer: C

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Question 21 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} > 0\) for ( x in mathbb{R} ).

Correct A. \(x < -2\) or \(x > 2\)

B. \(x > -2\) or \(x < 2\)

C. \(x = -2\) or \(x = 2\)

D. \(x = -2\) and \(x = 2\)

Correct Answer: A

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Question 22 View Details

Find the value of ( k ) such that the function ( f(x) = \(\frac{kx^2 - 2x + 1}{x^2 - 4}\)\)\) ) is continuous at \(x = 1\).

Correct A. \(k = 3\)

B. \(k = 2\)

C. \(k = 1\)

D. \(k = 0\)

Correct Answer: A

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Question 23 View Details

Solve the system of equations \(egin{cases} x^2 + y^2 = 4 \ x - 2y = -1 \end{cases}\).

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

B. \(x = 2, y = 1\)

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

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

Correct Answer: A

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Question 24 View Details

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

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

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

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

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

Correct Answer: A

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Question 25 View Details

Find the sum of the first 5 terms of the geometric series \(2 + 6 + 18 + ldots\).

Correct A. ( 62 )

B. ( 64 )

C. ( 66 )

D. ( 68 )

Correct Answer: A

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