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POST UTME VERITAS UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $$1x = \frac{1}{\sqrt{3}}$ if ( x ) lies in the first quadrant.

Correct A. $\frac{\pi}{6}$

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

C. $\frac{\pi}{3}$

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

Correct Answer: A

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Question 2 View Details

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

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 3 View Details

A random experiment has two independent events, A and B. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

A. 0.2

Correct B. 0.24

C. 0.3

D. 0.36

Correct Answer: B

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Question 4 View Details

Solve the equation $x^2 + 4x + 4 = 0$.

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 5 View Details

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 6 View Details

Solve the inequality ($\frac{x}{x+2}\(> 0$\) for x in \$(frac{x}{x+2}\(> 0$$-infty$, infty \ ).

A. $-2, ∞$

Correct B. $-∞, -2$ cup (0, ∞)

C. $-∞, -2$ cup (2, ∞)

D. $-∞, 0$ cup (2, ∞)

Correct Answer: B

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Question 7 View Details

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

A. $\frac{\pi^3}{3}$\)\)

Correct B. $\frac{\pi^3}{6}$\)\)

C. $\frac{\pi^3}{12}$\)\)

D. $\frac{\pi^3}{24}$\)\)

Correct Answer: B

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Question 8 View Details

Solve the system of equations $x^2 + y^2 = 4$ and $xy = 2$.

Correct A. \left\{(2, 1), (-2, -1)\right\}

B. \left\{(1, 2), (-1, -2)\right\}

C. \left\{ 2, -1 , (-2, 1)\right\}

D. \left\{ 1, -2 , (-1, 2)\right\}

Correct Answer: A

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Question 9 View Details

Find the value of ( x ) in the equation $x^3 - 6x^2 + 11x - 6 = 0$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 10 View Details

Solve the inequality $x^2 - 4x + 3 > 0$.

Correct A. $-∞, 1$ cup (3, ∞)

B. $-∞, 3$ cup (1, ∞)

C. $-∞, ∞$ \setminus \{1, 3\}

D. $-∞, ∞$

Correct Answer: A

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Question 11 View Details

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 12 View Details

Solve the system of linear equations using the method of substitution: $2x + 3y = 7$ and $x - 2y = -3$.

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 binary operation ( odot ) is defined as $a odot b = ab + 2$. Find the value of ( 3 odot 4 ).

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 14 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $1/6$

B. $1/3$

C. $1/2$

Correct D. $2/3$

Correct Answer: D

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Question 15 View Details

Find the derivative of the function ( f(x) = $3x^2 + 2x - 5$ ) using the power rule.

Correct A. 6x + 2

B. 6x - 2

C. $3x^2 + 2$

D. $3x^2 - 2$

Correct Answer: A

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_$X(x) = 2x$, $0 < x$ < 1 and f_$Y(y) =$$3y^2$,$(0 < y$\) < 1. Find the probability that $X + Y < 1\\((0 < y) < 1. Find the probability that$.

Correct A. $1/4$

B. $1/2$

C. $3/4$

D. 1

Correct Answer: A

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Question 17 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 18 View Details

Find the mean and standard deviation of the data set: 2, 4, 6, 8, 10.

Correct A. 4, 2

B. 6, 3

C. 8, 4

D. 10, 5

Correct Answer: A

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Question 19 View Details

Let A = [2, 4, 6] and B = [1, 3, 5]. Find the dot product of A and B.

Correct A. 32

B. 36

C. 40

D. 44

Correct Answer: A

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Question 20 View Details

Solve the polynomial equation $x^3$ - \$(6x^2 + 11x - 6$$= 0.$\)

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 21 View Details

Solve the inequality ($\frac{\(x^2 - 4}{x + 2}$$> 0$\) for x in \$(frac{x^2 - 4}{x + 2} > 0\(-\infty, -2 \ cup -2, \infty$ )\).

Correct A. $-2, -1$ ∪ (1, ∞)

B. $-∞, -2$ ∪ (2, ∞)

C. $-∞, -1$ ∪ (1, ∞)

D. $-∞, -2$ \cup $-1, ∞$\)

Correct Answer: A

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Question 22 View Details

Find the sum of the first 10 terms of the arithmetic sequence with first term $a = 3$ and common difference $d = 2$.

Correct A. 60

B. 70

C. 80

D. 90

Correct Answer: A

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Question 23 View Details

Solve the quadratic equation $x^2 + 4x + 4 = 0$ using the quadratic formula.

A. 0

Correct B. -2

C. 1

D. -1

Correct Answer: B

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Question 24 View Details

Find the equation of the circle with center $C -2, 3 \$ ) and radius $r = 4$.

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 25 View Details

Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1$ for ( x in [0, 2pi] ).

Correct A. 0, $\frac{\pi}{2}$\), \pi, $\frac{3\pi}{2}$\)

B. 0, \pi, 2pi

C. $\frac{\pi}{2}$\), \pi, $\frac{3\pi}{2}$\)

D. 0, $\frac{\pi}{2}$\), \pi, $\frac{3\pi}{2}$\)

Correct Answer: A

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