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POST UTME BSU 2023 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\)

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2 View Details

A random variable X has a probability distribution given by ( P(X) = begin{cases} 0.2 & \text{if } \(X = 1\\(begin{cases} 0.2 & text{if}\) \ 0.8 & \text{if } \\(0.8 & \(X = 2\) \\ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 1.

A. 0.2

B. 0.8

Correct C. 0.6

D. 0.4

Correct Answer: C

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Question 3 View Details

The mean of a set of numbers is 15, and the standard deviation is 3. If the largest number in the set is 21, what is the smallest number?

Correct A. 9

B. 12

C. 15

D. 18

Correct Answer: A

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Question 4 View Details

Solve the equation \(2^x + 3^x = 5^x\) for x.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 5 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 6 View Details

In the diagram below, the circle has a radius of 4 cm. Find the area of the sector OAB, where ∠\(AOB = 60\)°.

A. 10π \(cm^2\)

Correct B. 20π \(cm^2\)

C. 30π \(cm^2\)

D. 40π \(cm^2\)

Correct Answer: B

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Question 7 View Details

A sequence is defined by the recurrence relation a_\(n = 2a\)_(n-1\) + 1, where \(a_1 = 3\\((n-1) + 1, where\). Find the sum of the first 5 terms of the sequence.

Correct A. 3 + 7 + 15 + 31 + 63

B. 3 + 5 + 11 + 23 + 47

C. 3 + 7 + 13 + 25 + 51

D. 3 + 9 + 17 + 33 + 65

Correct Answer: A

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Question 8 View Details

In a game of chance, a player rolls a fair six-sided die. If the player rolls an even number, they win twice the amount they bet. If the player rolls an odd number, they lose their bet. What is the expected value of the game?

Correct A. 0

B. \(1/6\)

C. \(1/3\)

D. \(2/3\)

Correct Answer: A

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Question 9 View Details

Solve the system of equations: \(x + y = 4\) and \(x^2\) + \\((y^2\)\(= 16.\)\)

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

Correct B. \(x = 2\), \(y = 4\)

C. \(x = 4\), \(y = 2\)

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

Correct Answer: B

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Question 10 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 2\) about the x-axis.

A. 16π/3

Correct B. 32π/3

C. 64π/3

D. 128π/3

Correct Answer: B

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Question 11 View Details

Solve the inequality \(\frac{x}{x+2} > \frac{3}{x-1}\) for x in \(-\infty, -2 \ cup -2, 1\) cup (1, infty) ).

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

B. \(x > -2\) and \(x < 1\)

C. \(x < -2\) or \(x = 1\)

D. \(x > -2\) and \(x > 1\)

Correct Answer: A

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Question 12 View Details

Find the volume of the solid formed by rotating the region bounded by \(y = x^2\) and \(y = 4 - x\) about the x-axis.

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

Correct B. \(\frac{64}{3} \pi\)

C. \(\frac{128}{3} \pi\)

D. \(\frac{256}{3} \pi\)

Correct Answer: B

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Question 13 View Details

Solve the system of equations \(egin{cases} x + y + z = 6 \ 2x + 3y + z = 12 \ x + 2y + 3z = 10 \end{cases}\).

Correct A. \(x = 1, y = 2, z = 3\)

B. \(x = 2, y = 1, z = 3\)

C. \(x = 3, y = 1, z = 2\)

D. \(x = 1, y = 3, z = 2\)

Correct Answer: A

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Question 14 View Details

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ).

A. ( 5 )

B. ( 10 )

Correct C. ( 15 )

D. ( 20 )

Correct Answer: C

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Question 15 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\).

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

B. \(x = -1, x = -6\)

C. \(x = 1, x = 6\)

D. \(x = 2, x = 3\)

Correct Answer: A

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Question 16 View Details

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

Correct A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation \(2^x + 2^{x+1} = 3 \cdot 2^{x+1}\).

A. \(x = -1\)

Correct B. \(x = 0\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: B

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Question 18 View Details

Find the sum of the first 10 terms of the geometric series \(2 + 4 + 8 + ldots\).

Correct A. ( 2047 )

B. ( 2048 )

C. ( 2049 )

D. ( 2050 )

Correct Answer: A

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Question 19 View Details

A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly 3 elements.

A. ( 10 )

Correct B. ( 15 )

C. ( 20 )

D. ( 25 )

Correct Answer: B

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Question 20 View Details

Find the equation of the tangent line to the curve \(y = x^2 - 4x + 3\) at the point \\(tangent line to the curve (y = x^2 - 4x + 3\(1, -2 \\) ).

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

B. \(y = x - 3\)

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

D. \(y = x + 1\)

Correct Answer: A

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Question 21 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

Correct A. -120

B. 120

C. 0

D. -60

Correct Answer: A

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Question 22 View Details

If the function [\(f(x) =\)\(\frac{1}{x^2 + 1}\)\)\) \] has a local maximum at [ \(x = a\) \], find the value of [ a \].

A. -1

Correct B. 0

C. 1

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

Correct Answer: B

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Question 23 View Details

The histogram below shows the distribution of exam scores. Find the mean of the scores.

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 24 View Details

Find the sum of the infinite geometric series [ \sum_{\(n = 1\)}^\infty \(\frac{1}{2^n}\)\)\) \].

A. 1

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

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

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

Correct Answer: C

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Question 25 View Details

The sequence [ \{ 1, 2, 4, 8, \ldots \} \] is a geometric sequence. Find the next term in the sequence.

A. 16

B. 32

C. 64

Correct D. 128

Correct Answer: D

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