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POST UTME EKSU 2024 Mathematics | Objective

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Question 1 View Details

Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value between 0.5 and 1.

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

Correct B. $\frac{3}{4}$\)

C. $\frac{5}{8}$\)

D. $\frac{7}{16}$\)

Correct Answer: B

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Question 2 View Details

Find the area under the curve $y = x^2 $1x \$ ) from $x = 0$ to $x = \frac{\pi}{2}$.

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

B. $\frac{\pi}{4}$\)

Correct C. $\frac{\pi}{2}$\)

D. $\frac{3\pi}{4}$\)

Correct Answer: C

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Question 3 View Details

Solve the system of linear equations: $\begin{cases} x + y + z = 6 \ x + 2y + 3z = 14 \ 2x + 3y + 4z = 20 \end{cases}$

Correct A. \{ (1, 2, 3) \}

B. \{ (2, 3, 1) \}

C. \{ (3, 1, 2) \}

D. \{ (1, 3, 2) \}

Correct Answer: A

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Question 4 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 + $y + 3$^$2 = 16$

D. $x - 3$^2 + $y + 2$^$2 = 16$

Correct Answer: A

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Question 5 View Details

Find the sum of the first 10 terms of the geometric series with first term $a = 2$ and common ratio $r = \frac{1}{2}$.

Correct A. $\frac{1023}{512}$\)

B. $\frac{1024}{512}$\)

C. $\frac{1025}{512}$\)

D. $\frac{1026}{512}$\)

Correct Answer: A

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Question 6 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 7 View Details

A sequence is defined as [ $a_n = 2n\^2 + 3n - 1$ ]. Find the sum of the first 5 terms of the sequence.

Correct A. 105

B. 115

C. 125

D. 135

Correct Answer: A

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Question 8 View Details

Find the derivative of the function [$f(x) =$$3x^2$ \sin (2x) ] using the product rule.

Correct A. $6x^2$ \sin (2x) + 12x \cos (2x)

B. $6x^2$ \sin (2x) - 12x \cos (2x)

C. $12x^2$ \sin (2x) + 6x \cos (2x)

D. $12x^2$ \sin (2x) - 6x \cos (2x)

Correct Answer: A

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Question 9 View Details

In the diagram below, [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ] is a matrix. Find the determinant of the matrix.

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 10 View Details

A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 11 View Details

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

Correct A. $\frac{-1}{2x^{3/2}}$

B. $\frac{1}{2x^{3/2}}$

C. $\frac{1}{x^{3/2}}$

D. $\frac{-1}{x^{3/2}}$

Correct Answer: A

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Question 12 View Details

Solve the matrix equation $egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}$ for ( x ) and ( y ).

A. $x = 1, y = 2$

Correct B. $x = 2, y = 1$

C. $x = 1, y = 1$

D. $x = 2, y = 2$

Correct Answer: B

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Question 13 View Details

A random variable ( X ) has a probability distribution given by $P X = x \$ = $frac{1}{2}$\) ) for \$frac{1}{2})\(x = 1, 2, 3, 4$. Find the probability that ( X ) is greater than 2.

A. $\frac{1}{4}$

B. $\frac{1}{2}$

Correct C. $\frac{3}{4}$

D. $\frac{1}{2}$

Correct Answer: C

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Question 14 View Details

Solve the inequality $\log_{10} x^2 \$ > 4 ) for ( x ).

Correct A. $x > 10$

B. $x < -10$

C. $x > -10$

D. $x < 10$

Correct Answer: A

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Question 15 View Details

Find the derivative of the function ( f(x) = \sin $x^2$ ) using the chain rule.

Correct A. $2x $1x^2 \$ )

B. $2x $1x^2 \$ )

C. $$1x^2 \$ )

D. $$1x^2 \$ )

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 the equation $\log_{10} x^2 \$ = 4 ) for ( x ).

Correct A. $x = 10^4$

B. $x = 10^{-4}$

C. $x = 10^2$

D. $x = 10^{-2}$

Correct Answer: A

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Question 18 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 19 View Details

Solve the inequality $x^2 - 4x + 4 \geq 0$.

Correct A. ( x leq 2 )

B. ( x geq 2 )

C. $x < 2$

D. $x > 2$

Correct Answer: A

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Question 20 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using the chain rule.

Correct A. $2 \(1x$1x\)

B. $\cos^2 x$

C. $\sin^2 x$

D. $$1x$

Correct Answer: A

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Question 21 View Details

Solve the inequality $\frac{x^2 - 4x - 5}{x^2 - 4x + 4} > 0$ for ( x in mathbb{R} ).

Correct A. $-∞, -1$ ∪ (1, ∞)

B. $-∞, -1$ ∪ (1, 2)

C. $-∞, -1$ ∪ (2, ∞)

D. $-∞, 1$ ∪ (2, ∞)

Correct Answer: A

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Question 22 View Details

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

Correct A. 16π/3

B. 16π/5

C. 16π/7

D. 16π/9

Correct Answer: A

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Question 23 View Details

Find the equation of the circle with center at ( (2, 3) ) and radius 4.

Correct A. $x - 2$^2 + $y - 3$^$2 = 16$

B. $x - 2$^2 + $y - 3$^$2 = 20$

C. $x - 2$^2 + $y - 3$^$2 = 24$

D. $x - 2$^2 + $y - 3$^$2 = 28$

Correct Answer: A

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Question 24 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 25 View Details

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

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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