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POST UTME REDEEMERS UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Find 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

A random variable X has a probability distribution given by the following table:

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 3 View Details

If ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ), find ( f'(x) ).

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

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

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

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

Correct Answer: B

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Question 4 View Details

Solve the system of equations:

Correct A. \(x = 2, y = 3\)

B. \(x = 3, y = 2\)

C. \(x = 1, y = 4\)

D. \(x = 4, y = 1\)

Correct Answer: A

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Question 5 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 6 View Details

Find the area under the curve y = \sin(x) from \(x = 0\) to x = π/2.

A. 1

Correct B. \(1/2\)

C. π/2

D. π

Correct Answer: B

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Question 7 View Details

Solve the equation \(\frac{1}{x}\)\) + \(\frac{1}{y}\)\) = \(\frac{1}{2}\)\) for x in terms of y.

Correct A. \(x = 2y\)/\(y-2\)

B. \(x = 2y\)/\(y+2\)

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

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

Correct Answer: A

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Question 8 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 9 View Details

Find the value of x in the equation \log_{10} \(x^2 = 4\).

A. \(10^4\)

Correct B. \(10^8\)

C. \(10^2\)

D. \(10^6\)

Correct Answer: B

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Question 10 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16π

B. 32π

C. 64π

D. 128π

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. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 12 View Details

In the circle with equation \(x^2 + y^2 - 6x + 4y - 12 = 0\), find the equation of the \tangent at the point ( (2, 3) ).

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

B. \(y = x - 1\)

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

D. \(y = x + 2\)

Correct Answer: A

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Question 13 View Details

Find the sum of the first 10 terms of the geometric progression with first term 2 and common ratio 3.

A. 3210

B. 3220

Correct C. 3230

D. 3240

Correct Answer: C

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Question 14 View Details

Find the area under the curve \(y = x^2 + 2x - 3\) from \(x = 1\) to \(x = 3\).

A. 20

B. 30

Correct C. 40

D. 50

Correct Answer: C

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Question 15 View Details

In the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(5, 6) ), find the equation of the median from vertex ( A ) to side ( BC ).

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

B. \(y = x - 1\)

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

D. \(y = x + 2\)

Correct Answer: A

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Question 16 View Details

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

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 17 View Details

A rectangular solid has a length of 10cm, a width of 5cm, and a height of 8cm. Find its surface area.

A. \(240cm^2\)

Correct B. \(250cm^2\)

C. \(260cm^2\)

D. \(270cm^2\)

Correct Answer: B

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Question 18 View Details

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

A. 50

B. 55

Correct C. 60

D. 65

Correct Answer: C

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Question 19 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 20 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or \(x > 3/2\)\)

C. x < -1 or \(x < 3/2\)\)

D. \(x > 1\) or \(x > 3/2\)\)

Correct Answer: A

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Question 21 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}\). Find the vector \(\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}\) using the determinant method.

Correct A. \(egin{pmatrix} 6 \ -2 \end{pmatrix}\)

B. \(egin{pmatrix} -6 \ 2 \end{pmatrix}\)

C. \(egin{pmatrix} 2 \ -6 \end{pmatrix}\)

D. \(egin{pmatrix} -2 \ 6 \end{pmatrix}\)

Correct Answer: A

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Question 22 View Details

A random experiment has two independent events, A and B, with probabilities ( P(A) = 0.4 ) and ( P(B) = 0.6 ). Find the probability that both events occur.

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 23 View Details

Find the determinant of the matrix \(egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix}\).

Correct A. -1

B. 1

C. 2

D. 4

Correct Answer: A

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Question 24 View Details

The equation of a circle is \(x^2 + y^2 - 4x + 6y + 4 = 0\). Find the center and radius of the circle.

Correct A. Center: \(2, -3 \\) ), Radius: 1

B. Center: \(2, -3 \\) ), Radius: 2

C. Center: \(2, -3 \\) ), Radius: 3

D. Center: \(2, -3 \\) ), Radius: 4

Correct Answer: A

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Question 25 View Details

Solve the quadratic 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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