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POST UTME UI 2020 Mathematics | Objective

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Question 1 View Details

A cylindrical \tank with a radius of 7m and a height of 10m is filled with water. Find the volume of water in the \tank.

Correct A. 490π m³

B. 4900π m³

C. 49000π m³

D. 490000π m³

Correct Answer: A

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Question 2 View Details

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

A. $x = -1$

Correct B. $x = 1$

C. $x = -3$

D. $x = 3$

Correct Answer: B

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Question 3 View Details

In a right-angled triangle, the length of the hypotenuse is 10cm and one of the other sides is 6cm. Find the length of the third side.

A. 8cm

Correct B. 12cm

C. 14cm

D. 16cm

Correct Answer: B

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Question 4 View Details

A car travels from city A to city B at an average speed of $(60km/h$\) and returns at an average speed of $40km/h\\((60km/h) and returns at an average speed of$. What is the average speed for the round trip?

A. $45km/h$

B. $50km/h$

Correct C. $55km/h$

D. $60km/h$

Correct Answer: C

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Question 5 View Details

A set of 5 coins contains 2 nickels and 3 dimes. If a coin is selected at random, what is the probability that it is a nickel?

A. 0.2

Correct B. 0.3

C. 0.4

D. 0.5

Correct Answer: B

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Question 6 View Details

Find the value of x in the equation $2x^2 + 5x - 3 = 0$.

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 7 View Details

Solve for y in the equation $\frac{y}{2} + 3 = 7$.

Correct A. 8

B. 10

C. 12

D. 14

Correct Answer: A

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Question 8 View Details

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

A. 50.24

Correct B. 100.48

C. 200.96

D. 251.2

Correct Answer: B

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Question 9 View Details

A line passes through the points (2, 3) and (4, 5). Find the equation of the line.

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = 3x - 1$

D. $y = 3x + 1$

Correct Answer: A

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Question 10 View Details

A random experiment has two possible outcomes: heads or tails. If the probability of getting heads is 0.4, find the probability of getting tails.

Correct A. 0.3

B. 0.4

C. 0.5

D. 0.6

Correct Answer: A

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Question 11 View Details

Solve the inequality ($\frac{x}{x-2}\(> 1$\) for \$(frac{x}{x-2} > 1\(x > 2$\).

A. $x > 2$

Correct B. $x > 4$

C. $x < 2$

D. $x < 4$

Correct Answer: B

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Question 12 View Details

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

Correct A. 6x \sin x + $3x^2$ \cos x

B. 6x \cos x + $3x^2$ \sin x

C. 6x \sin x - $3x^2$ \cos x

D. 6x \cos x - $3x^2$ \sin x

Correct Answer: A

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Question 13 View Details

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

A. $\frac{1}{3}$\)

Correct B. $\frac{2}{3}$\)

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

D. 1

Correct Answer: B

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Question 14 View Details

The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 15 View Details

Solve the system of equations using matrices: $\begin{array}{ccc} x + y + z & = & 6 2x + 3y + z & = & 11 x + 2y + 3z & = & 7 \end{array}$

Correct A. \begin{array}{ccc} x & = & 1 \ y & = & 2 \ z & = & 3 \end{array}

B. \begin{array}{ccc} x & = & 2 \ y & = & 1 \ z & = & 3 \end{array}

C. \begin{array}{ccc} x & = & 1 \ y & = & 3 \ z & = & 2 \end{array}

D. \begin{array}{ccc} x & = & 3 \ y & = & 2 \ z & = & 1 \end{array}

Correct Answer: A

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Question 16 View Details

Determine the number of terms in the series $sum_{n = 1$}^{infty} $\frac{1}{n n+1 \}$\) ) that satisfy $\frac{1}{n n+1 \}$\) < $\frac{1}{100}$\) ).

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 17 View Details

Find the value of lim_{x \to 0} $\frac{$1x}{x}$\) using L'Hopital's rule.

Correct A. 1

B. 0

C. -1

D. ∞

Correct Answer: A

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Question 18 View Details

Solve the matrix equation $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}$ for ( x ) and ( y ).

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

B. $x = 2, y = 3$

C. $x = 3, y = 4$

D. $x = 4, y = 5$

Correct Answer: A

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Question 19 View Details

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

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 20 View Details

Find the area of the region bounded by the curves $y = x^2$ and $y = 4x$.

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 21 View Details

In a base 8 number system, what is the value of the digit (x\) in the number $x_{8} = 105_{10}\\((x) in the number$?

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 22 View Details

Let (S\) be the set of all positive integers $n\\((S) be the set of all positive integers$ such that (n\) is divisible by $5\\((n) is divisible by$ and (n\) is a perfect square. What is the sum of the elements of $S\\((n) is a perfect square. What is the sum of the elements of$?

A. 50

Correct B. 100

C. 150

D. 200

Correct Answer: B

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Question 23 View Details

Find the sum of the infinite geometric series $\sum_{n = 1}^\infty \frac{2}{3^n}$.

A. $\frac{2}{3}$\)

Correct B. $\frac{4}{9}$\)

C. $\frac{6}{9}$\)

D. $\frac{8}{9}$\)

Correct Answer: B

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Question 24 View Details

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

A. $\frac{16}{3}$\)\pi

Correct B. $\frac{32}{3}$\)\pi

C. $\frac{64}{3}$\)\pi

D. $\frac{128}{3}$\)\pi

Correct Answer: B

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Question 25 View Details

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ using the chain rule.

Correct A. -$\frac{2x}{x^2 + 1$ ^2}\)\)

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

C. $\frac{2x}{x^2 + 1$ ^2}\)\)

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

Correct Answer: A

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