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POST UTME DELSU 2021 Mathematics | Objective

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Question 1 View Details

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 200\pitext{ cm}^3

Correct B. 300\pitext{ cm}^3

C. 400\pitext{ cm}^3

D. 500\pitext{ cm}^3

Correct Answer: B

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Question 2 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.135

B. 0.225

Correct C. 0.315

D. 0.405

Correct Answer: C

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Question 3 View Details

Solve for x in the equation \(2x^2 + 5x - 3 = 0\).

A. -1

Correct B. 1

C. -3

D. 2

Correct Answer: B

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Question 4 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 5 View Details

A vector ( mathbf{a} ) has a magnitude of 5 and is directed at an angle of 30° to the x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. \(\mathbf{a} = 4.33\mathbf{i} + 2.5\mathbf{j}\)

B. \(\mathbf{a} = 2.5\mathbf{i} + 4.33\mathbf{j}\)

C. \(\mathbf{a} = 3.54\mathbf{i} + 2.5\mathbf{j}\)

D. \(\mathbf{a} = 2.5\mathbf{i} + 3.54\mathbf{j}\)

Correct Answer: A

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Question 6 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 + 2\)

C. \(\frac{1}{2} \times 4^2 - 3 \times 4 - 2\)

D. \(\frac{1}{2} \times 4^2 - 3 \times 4 + 2\)

Correct Answer: A

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Question 7 View Details

A particle moves along the curve (y = \(x^2 - 2x + 1\)\) with a velocity of \(\\((y = x^2 - 2x + 1) with a velocity of \frac{dy}{dx} = 2x - 2\). Find the acceleration at the point where \(x = 2\).

Correct A. \(2 \times 2 - 2\)

B. \(2 \times 2 + 2\)

C. \(2 \times 2 - 4\)

D. \(2 \times 2 + 4\)

Correct Answer: A

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Question 8 View Details

Solve for ( x ) in the equation \(2^x = 32\).

A. \(x = 5\)

Correct B. \(x = 6\)

C. \(x = 7\)

D. \(x = 8\)

Correct Answer: B

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Question 9 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

Correct B. \(\frac{3}{8}\)

C. \(\frac{1}{4}\)

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

Correct Answer: B

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Question 10 View Details

Find the volume of the solid formed by revolving the area under the curve (y = \(x^2 - 2x + 1\)\) about the x-axis from \(x = 0\\((y = x^2 - 2x + 1) about the x-axis from\) to \(x = 2\).

A. \(\frac{1}{3} \pi \times 2^3\)

B. \(\frac{1}{3} \pi \times 3^3\)

Correct C. \(\frac{1}{3} \pi \times 4^3\)

D. \(\frac{1}{3} \pi \times 5^3\)

Correct Answer: C

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Question 11 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 12 View Details

Find the value of \(\frac{d}{dx} x^3 - 6x^2 + 11x - 6 \\) ).

Correct A. \(3x^2 - 12x + 11\)

B. \(3x^2 - 12x + 6\)

C. \(3x^2 - 12x - 11\)

D. \(3x^2 - 12x + 5\)

Correct Answer: A

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Question 13 View Details

Solve the system of equations \(egin{cases} x + y = 2 \ x - y = 0 \end{cases}\).

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

B. \(x = 1\), \(y = 0\)

C. \(x = 0\), \(y = 1\)

D. \(x = 0\), \(y = 0\)

Correct Answer: A

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Question 14 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. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 3\)^2 + \(y - 2\)^\(2 = 9\)

Correct Answer: A

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Question 15 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).

A. \(x = 0\)

Correct B. \(x = 90\)

C. \(x = 180\)

D. \(x = 270\)

Correct Answer: B

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Question 16 View Details

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

A. \(x = -1\)

B. \(x = 0\)

Correct C. \(x = 1\)

D. \(x = 2\)

Correct Answer: C

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Question 17 View Details

Find the value of \(\log_{10} x^2 \\) ) given that \(\log_{10} x = 2\).

Correct A. ( 4 )

B. ( 6 )

C. ( 8 )

D. ( 10 )

Correct Answer: A

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Question 18 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 \(x < \frac{1}{2}\)

Correct Answer: A

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Question 19 View Details

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

Correct A. ( 1 )

B. \(-1\)

C. ( 0 )

D. ( 2 )

Correct Answer: A

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Question 20 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 0\)

C. \(x = 2\)

D. \(x = -1\)

Correct Answer: A

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Question 21 View Details

Given that ( f(x) = \(\frac{1}{x^2 + 1}\)\)) ), find lim_{x \to infty} f\( x \\() ), find lim_{x to infty} f\ ).

Correct A. 0

B. 1

C. ∞

D. undefined

Correct Answer: A

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Question 22 View Details

Solve the inequality \(|2x - 1| \geq 3\).

Correct A. \(-∞, -2] \cup [4, ∞\)

B. \(-∞, -1] \cup [2, ∞\)

C. \(-∞, -3] \cup [1, ∞\)

D. \(-∞, -4] \cup [3, ∞\)

Correct Answer: A

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Question 23 View Details

Find the equation of the \tangent line to the curve \(y = x^2 - 2x + 1\) at the point ( (1, 0) ).

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

B. \(y = x + 1\)

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

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

Correct Answer: A

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Question 24 View Details

A random variable ( X ) has a probability density function ( f(x) = egin{cases} 2x & \(0 < x\)\(< 1\)\ 0 & \text{otherwise} end{cases} ). Find \(E X^2 \\\(end{cases} ). Find (E X^2\) ).

Correct A. \(1/3\)

B. \(1/2\)

C. \(2/3\)

D. 1

Correct Answer: A

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Question 25 View Details

The polynomial ( P(x) = \(x^3 - 6x^2 + 11x - 6\) ) has a root at \(x = 1\). Find the other two roots.

Correct A. 2, 3

B. 1, 2

C. 1, 3

D. 2, 4

Correct Answer: A

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