POST UTME UNIBEN 2021 Mathematics | Objective

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Question 1 View Details
Determine the value of x in the equation \(\sin^2 x + \cos^2 x = 1\) if \($1x = \frac{3}{5}\).
Correct A. \(\frac{\pi}{4}\)
B. \(\frac{\pi}{3}\)
C. \(\frac{\pi}{2}\)
D. \(\frac{\pi}{6}\)

Correct Answer: A

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Question 2 View Details
Solve the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\).
Correct A. \(x = 1, y = 2\)
B. \(x = 2, y = 1\)
C. \(x = 1, y = 1\)
D. \(x = 2, y = 2\)

Correct Answer: A

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Question 3 View Details
A particle moves in a straight line with a velocity of ( v(t) = 2t + 1 ) \((m/s\)\). Find the acceleration of the particle at time \(t = 2\\((m/s). Find the acceleration of the particle at time\) s.
Correct A. ( 4 ) \(m/s\^2\)
B. ( 2 ) \(m/s\^2\)
C. ( 1 ) \(m/s\^2\)
D. ( 3 ) \(m/s\^2\)

Correct Answer: A

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Question 4 View Details
A fair six-sided die is rolled. What is the probability that the number appearing is a multiple of 3?
A. \(\frac{1}{6}\)
Correct B. \(\frac{1}{3}\)
C. \(\frac{2}{3}\)
D. \(\frac{5}{6}\)

Correct Answer: B

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Question 5 View Details
Solve the trigonometric equation \($1x = \frac{1}{\sqrt{3}}\) for ( x ) in the interval ( [0, 2pi) ).
Correct A. \(\frac{\pi}{6}\)
B. \(\frac{\pi}{3}\)
C. \(\frac{\pi}{2}\)
D. \(\frac{2\pi}{3}\)

Correct Answer: A

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Question 6 View Details
Find the volume of the frustum of a cone with height (h = 5\) and radii of the bases \(r_1 = 3\\((h = 5) and radii of the bases\) and \(r_2 = 2\).
Correct A. \(\frac{1}{3}\)\)\pi (5) \(3^2 + 2^2 + 3 \cdot 2\)
B. \(\frac{1}{3}\)\)\pi (5) \(3^2 - 2^2 + 3 \cdot 2\)
C. \(\frac{1}{3}\)\)\pi (5) \(3^2 + 2^2 - 3 \cdot 2\)
D. \(\frac{1}{3}\)\)\pi (5) \(3^2 - 2^2 - 3 \cdot 2\)

Correct Answer: A

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Question 7 View Details
Solve the inequality \(\frac{x}{x-1} > 0\).
Correct A. \(x < 0\) \text{ or } \(x > 1\)
B. \(x < 1\)
C. \(x > 1\)
D. \(x > 0\)

Correct Answer: A

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Question 8 View Details
Find the derivative of the function \(f(x) = \frac{1}{x^2 + 1}\).
Correct A. f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\)
B. f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\)
C. f'\((x) =\)\(\frac{x}{x^2 + 1\) ^2}\)\)
D. f'\((x) =\)\(\frac{-x}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 9 View Details
Solve the equation \(\sin^2 x + \cos^2 x = 1\).
A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{\pi}{2}\)\)
C. \(x =\)\(\frac{3\pi}{4}\)\)
Correct D. \(x =\)\(\frac{\pi}{2}\)\) \text{ or }\(x =\)\(\frac{3\pi}{4}\)\)

Correct Answer: D

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Question 10 View Details
Find the area of the triangle with vertices \(A(0, 0)\), \(B(3, 0)\), and \(C(0, 4)\).
Correct A. \(\frac{1}{2}\)\) (3) (4)
B. \(\frac{1}{2}\)\) (3) (5)
C. \(\frac{1}{2}\)\) (4) (5)
D. \(\frac{1}{2}\)\) (3) (6)

Correct Answer: A

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Question 11 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 12 View Details
Solve the system of equations using matrices:\n\(egin{cases} 2x + 3y = 7 \ 4x - 2y = -2 \end{cases}\)
Correct A. \(x = 1, y = 2\)
B. \(x = 2, y = 1\)
C. \(x = 3, y = 4\)
D. \(x = 4, y = 3\)

Correct Answer: A

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Question 13 View Details
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?
A. 200
Correct B. 250
C. 300
D. 350

Correct Answer: B

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Question 14 View Details
Find the area under the curve \(y = x^2 + 2x - 3\) from \(x = 0\) to \(x = 3\).
A. 27
B. 30
Correct C. 33
D. 36

Correct Answer: C

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Question 15 View Details
Simplify the expression \(\frac{1}{2} \log_2 x^2 + 1 \\) + \(\frac{3}{2}\)\) \log_2 \(x^2 - 1\) ).
A. \(\log_2 x^2 + 1 \\) )
B. \(\log_2 x^2 - 1 \\) )
C. \(\log_2 x^2 + 1 \\) + \log_2 \(x^2 - 1\) )
Correct D. \(\log_2 x^2 + 1 \\) - \log_2 \(x^2 - 1\) )

Correct Answer: D

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Question 16 View Details
Find the value of 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 17 View Details
A set A contains 5 elements. If we select 2 elements from set A, what is the number of ways to do this?
A. 10
B. 15
Correct C. 20
D. 25

Correct Answer: C

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Question 18 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
A. 16
B. 32
Correct C. 64
D. 128

Correct Answer: C

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Question 19 View Details
A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
Correct C. 35
D. 45

Correct Answer: C

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Question 20 View Details
A histogram is shown below. What is the mean of the data?
A. 5
B. 10
Correct C. 15
D. 20

Correct Answer: C

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Question 21 View Details
A set A contains 5 elements. If we select 2 elements from set A, what is the number of ways to do this?
A. 10
B. 15
Correct C. 20
D. 25

Correct Answer: C

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Question 22 View Details
Find the value of 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 23 View Details
A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
Correct C. 35
D. 45

Correct Answer: C

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Question 24 View Details
A histogram is shown below. What is the mean of the data?
A. 5
B. 10
Correct C. 15
D. 20

Correct Answer: C

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Question 25 View Details
A set A contains 5 elements. If we select 2 elements from set A, what is the number of ways to do this?
A. 10
B. 15
C. 20
D. 25

Correct Answer: VIEW ANSWER

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