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POST UTME KSU 2020 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{x}{2} + \frac{3}{4} = \frac{7}{8}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 2 View Details

A binary operation ( oplus ) is defined as \(a oplus b = a^2 + b^2\). Find the value of ( 2 oplus 3 ).

Correct A. 13

B. 14

C. 15

D. 16

Correct Answer: A

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Question 3 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. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 4 View Details

In the circuit below, find the equivalent resistance between points A and B.

A. 2Ω

B. 4Ω

Correct C. 6Ω

D. 8Ω

Correct Answer: C

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Question 5 View Details

A quadratic equation is defined as \(x^2 + 4x + 4 = 0\). Find the value of x.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 6 View Details

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

A. 11,946

B. 12,000

Correct C. 12,054

D. 12,100

Correct Answer: C

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Question 7 View Details

Solve for x in the equation \(\begin{array}{c} 2x + 5y = 11 \ 3x - 2y = -7 \end{array}\) using the method of substitution.

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 8 View Details

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

A. 56

B. 57

Correct C. 58

D. 59

Correct Answer: C

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Question 9 View Details

A rectangular box has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the box.

A. 30

B. 31

Correct C. 32

D. 33

Correct Answer: C

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Question 10 View Details

Find the surface area of the sphere with radius 4 cm.

A. 201

B. 202

Correct C. 203

D. 204

Correct Answer: C

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Question 11 View Details

Find the value of (x\) in the equation \(2^x + 3^x = 5^x\\((x) in the equation\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 12 View Details

Solve the inequality \(\frac{x-2}{x+1} > 0\).

A. \(x<-1\)

Correct B. \(x>-1\)

C. \(x < 2\)

D. \(x > 2\)

Correct Answer: B

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Question 13 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 14 View Details

Find the derivative of \(f(x) = \frac{x^2}{x^2+1}\).

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

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

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

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

Correct Answer: C

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Question 15 View Details

Solve the system of equations \(\begin{cases} x+y = 4 \ x-y = 2 \end{cases}\).

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

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

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

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 16 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3 or 5?

A. \(1/3\)

B. \(1/2\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 17 View Details

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 18 View Details

A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of the vector.

Correct A. \begin{pmatrix} 2.5 \\ 4.33 \end{pmatrix}

B. \begin{pmatrix} 4.33 \\ 2.5 \end{pmatrix}

C. \begin{pmatrix} 5 \\ 0 \end{pmatrix}

D. \begin{pmatrix} 0 \\ 5 \end{pmatrix}

Correct Answer: A

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Question 19 View Details

Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...

Correct A. 59049

B. 59048

C. 59047

D. 59046

Correct Answer: A

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Question 20 View Details

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

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 21 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). What is the expected value of X?

A. 1.1

Correct B. 1.2

C. 1.3

D. 1.4

Correct Answer: B

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Question 22 View Details

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

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 23 View Details

In a set A = {1, 2, 3, 4, 5}, find the number of subsets of A that contain exactly 3 elements.

A. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 24 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 25 View Details

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

Correct A. 2

B. 4

C. 6

D. 8

Correct Answer: A

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