POST UTME DELSU 2017 Mathematics | Objective

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Question 1 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
A. \(\frac{1}{2}\)
B. ( 3 )
C. ( 4 )
Correct D. ( 6 )

Correct Answer: D

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Question 2 View Details
Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\).
A. \(x = -1\)
Correct B. \(x = 3\)
C. \(x = -3\)
D. \(x = 1\)

Correct Answer: B

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Question 3 View Details
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?
A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
Correct C. \(\frac{3}{4}\)
D. \(\frac{2}{3}\)

Correct Answer: C

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Question 4 View Details
Find the value of ( x ) in the equation \(2^x + 5^x = 10^x\).
A. \(x = 2\)
B. \(x = 3\)
Correct C. \(x = 4\)
D. \(x = 5\)

Correct Answer: C

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Question 5 View Details
A company produces 200 units of a product per day. If the cost of production is ( C(x) = \(2x^2 + 5x - 3\) ), where ( x ) is the number of units produced, find the \\(cost of production is ( C(x) = \((2x^2 + 5x - 3\)\cost of producing 250 units.
A. ₦1250
B. ₦1500
Correct C. ₦1750
D. ₦2000

Correct Answer: C

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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. ( 22 )
B. ( 24 )
C. ( 26 )
D. ( 28 )

Correct Answer: A

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Question 7 View Details
A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 80% of the scores fall within 2 standard deviations of the mean, what percentage of the scores fall within 1 standard deviation of the mean?
Correct A. ( 68 )
B. ( 72 )
C. ( 76 )
D. ( 80 )

Correct Answer: A

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Question 8 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{2}\)\\()x^2 + 3x - 2\) ) using the chain rule.
Correct A. \(x + 3\)
B. \(x^2 + 3\)
C. \(x^2 + 3x - 2\)
D. \(x^2 + 3x + 2\)

Correct Answer: A

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Question 9 View Details
A set of numbers has a mean of 50 and a standard deviation of 5. If 80% of the numbers fall within 2 standard deviations of the mean, what percentage of the numbers fall within 1 standard deviation of the mean?
Correct A. ( 68 )
B. ( 72 )
C. ( 76 )
D. ( 80 )

Correct Answer: A

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Question 10 View Details
Find the equation of the circle with center ( (3, 4) ) and radius 5.
Correct A. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 25\) )
B. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 25\) )
C. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 30\) )
D. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 30\) )

Correct Answer: A

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Question 11 View Details
In a random sample of 25 students, the mean height is 175 cm with a standard deviation of 5 cm. If the mean height of the entire population is 180 cm, calculate the standard error of the mean.
A. 2.5 cm
Correct B. 3.5 cm
C. 4.5 cm
D. 5.5 cm

Correct Answer: B

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Question 12 View Details
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 1240
B. 1245
Correct C. 1250
D. 1255

Correct Answer: C

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Question 13 View Details
In the diagram below, the circle has a radius of 4 cm. Find the area of the shaded region.
Correct A. 50.24 \(cm^2\)
B. 50.53 \(cm^2\)
C. 50.73 \(cm^2\)
D. 50.93 \(cm^2\)

Correct Answer: A

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Question 14 View Details
Find the derivative of the function f(x) = \(3x^2 + 2x - 5\) using the chain rule.
Correct A. 6x + 2
B. 6x + 3
C. 6x - 2
D. 6x - 3

Correct Answer: A

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Question 15 View Details
Evaluate the definite integral \int_\(0^2\) \(2x + 1\) dx.
A. 5
B. 6
Correct C. 7
D. 8

Correct Answer: C

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Question 16 View Details
In a geometric sequence with first term \(a\) and common ratio \(r\), the sum of the first (n\) terms is given by the formula \(S_n = \\((n) terms is given by the formula \frac{a 1 - r^n}{1 - r}). If \(a = 2\),\(r =\)\\(). If (a = 2\(\frac{1}{2}\)\)\), and (n = 5\), find the value of \(S_n\\((n = 5), find the value of\).
Correct A. 15
B. 16
C. 17
D. 18

Correct Answer: A

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Question 17 View Details
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.
Correct A. 256\pi
B. 512\pi
C. 768\pi
D. 1024\pi

Correct Answer: A

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Question 18 View Details
If \((x^2 + 4x + 4\) = 0\), find the value of \(x\\((x^2 + 4x + 4 = 0), find the value of\).
Correct A. -2
B. -1
C. 1
D. 2

Correct Answer: A

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Question 19 View Details
A circle has a radius of 6 cm. Find the area of the circle.
Correct A. 36\pi
B. 72\pi
C. 108\pi
D. 144\pi

Correct Answer: A

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Question 20 View Details
If (x + \(\frac{1}{x}\(= 2\)\)\), find the value of \\((x + frac{1}{x} = 2\(x^2 + \frac{1}{x^2}\).
A. 3
B. 4
C. 5
Correct D. 6

Correct Answer: D

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Question 21 View Details
Find the volume of the frustum of a cone with height 10cm, lower base radius 6cm, and upper base radius 4cm.
A. 200\pi \(cm^3\)
Correct B. 300\pi \(cm^3\)
C. 400\pi \(cm^3\)
D. 500\pi \(cm^3\)

Correct Answer: B

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Question 22 View Details
Solve for x in the equation \(\log_{10} x^2 \\)\(= 4\)\).
Correct A. 2
B. 4
C. 10
D. 20

Correct Answer: A

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Question 23 View Details
A set of 5 consecutive integers has a median of 10. Find the sum of the integers.
A. 100
B. 150
Correct C. 200
D. 250

Correct Answer: C

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Question 24 View Details
Find the surface area of the sphere with radius 5cm.
A. 50\pi \(cm^2\)
Correct B. 100\pi \(cm^2\)
C. 150\pi \(cm^2\)
D. 200\pi \(cm^2\)

Correct Answer: B

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Question 25 View Details
A company produces 300 units of a product per day. If the production rate is increased by 20%, find the new production rate.
A. 360 \(units/day\)
B. 400 \(units/day\)
Correct C. 420 \(units/day\)
D. 440 \(units/day\)

Correct Answer: C

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