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POST UTME UNILAG 2021 Mathematics | Objective

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Question 1 View Details

Let X be a random variable with probability density function f(x) = \begin{cases} 2x & $0 < x$$< 1$\ 0 & \text{otherwise} \end{cases}. Find the probability that X is greater than \$0 & text{otherwise} \(1/2$.

A. $1/4$

B. $1/2$

Correct C. $3/4$

D. 1

Correct Answer: C

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Question 2 View Details

Solve the differential equation \$\frac{dy}{dx}$\) = \$\frac{y}{x}$\) using the chain rule.

Correct A. $y = x\^2$

B. $y = x\^3$

C. $y = x\^2 + 1$

D. $y = x\^3 + 1$

Correct Answer: A

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Question 3 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 4 View Details

Let A and B be two events such that P(A) = $1/4$ and P(B) = $1/2$. Find P$A \cap B$ if A and B are independent.

Correct A. $1/8$

B. $1/4$

C. $1/2$

D. $3/4$

Correct Answer: A

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Question 5 View Details

Solve the equation $x^3$ + \$(2x^2 - 7x + 12$$= 0.$\)

A. $x = -3$

B. $x = -1$

Correct C. $x = 3$

D. $x = 4$

Correct Answer: C

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Question 6 View Details

In the diagram below, the graph of $y = \frac{1}{2} $12x$ is shown. What is the amplitude of the graph?

A. 1

Correct B. 0.5

C. 2

D. 0.25

Correct Answer: B

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Question 7 View Details

If ( f(x) = $\frac{1}{x^2 + 1}$\)) ), find $f -x \\\() ), find (f -x$ ).

A. $f -x \$ = $\frac{1}{x^2 - 1}$\)\) )

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

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

D. $f -x \$ = $\frac{1}{x^2 - 1}$\)\) )

Correct Answer: B

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Question 8 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x > \frac{3}{2}$

D. $x > -1$ or $x < \frac{3}{2}$

Correct Answer: A

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Question 9 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 10 View Details

If $x^2 + 2x - 3 = 0$, find the value of ( x ).

A. $x = -3$

Correct B. $x = 1$

C. $x = -1$

D. $x = 3$

Correct Answer: B

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Question 11 View Details

Find the equation of the circle with centre $-2, 3$ and radius 4.

Correct A. text{Equation: } $x + 2$^2 + \$text{Equation:} (x + 2\(y - 3$^$2 = 16$

B. text{Equation: } $x - 2$^2 + \$text{Equation:} (x - 2\(y + 3$^$2 = 16$

C. text{Equation: } $x + 2$^2 + \$text{Equation:} (x + 2\(y + 3$^$2 = 16$

D. text{Equation: } $x - 2$^2 + \$text{Equation:} (x - 2\(y - 3$^$2 = 16$

Correct Answer: A

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Question 12 View Details

Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \end{bmatrix}.

Correct A. \text{Solution: } $x = 1$, $y = 2$

B. \text{Solution: } $x = 2$, $y = 1$

C. \text{Solution: } $x = 3$, $y = 4$

D. \text{Solution: } $x = 4$, $y = 3$

Correct Answer: A

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Question 13 View Details

Find the value of sin 2x if \$sin x =$$\\(sin 2x if sin x = \frac{3}{5}$\).

Correct A. $\frac{12}{25}$\)

B. $\frac{24}{25}$\)

C. $\frac{36}{25}$\)

D. $\frac{48}{25}$\)

Correct Answer: A

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Question 14 View Details

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

Correct A. \text{Solution: }$x = -2$

B. \text{Solution: }$x = -1$

C. \text{Solution: } $x = 0$

D. \text{Solution: } $x = 1$

Correct Answer: A

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Question 15 View Details

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

Correct A. 124

B. 126

C. 128

D. 130

Correct Answer: A

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Question 16 View Details

Determine the value of x in the equation $\log_{10} x^2 \$$= 4 ).$

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 17 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 2x$ about the x-axis.

A. $\frac{16}{15}$\)\pi

B. $\frac{32}{15}$\)\pi

Correct C. $\frac{64}{15}$\)\pi

D. $\frac{128}{15}$\)\pi

Correct Answer: C

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Question 18 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

A. $-\infty, -1$ \cup $3, \infty$

B. $-\infty, -3$ \cup $1, \infty$

Correct C. $-\infty, -1$ \cup $1, \infty$

D. $-\infty, -3$ \cup $3, \infty$

Correct Answer: C

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Question 19 View Details

Find the equation of the tangent line to the curve $y = x^3 - 6x^2 + 9x + 2$ at the point \$tangent line to the curve (y = x^3 - 6x^2 + 9x + 2\(1, -4 \$ ).

Correct A. $y = -3x + 1$

B. $y = -3x - 1$

C. $y = 3x - 1$

D. $y = 3x + 1$

Correct Answer: A

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Question 20 View Details

A right circular cone has a height of 12 cm and a base radius of 4 cm. Find the volume of the cone.

A. 192\pi

B. 384\pi

Correct C. 576\pi

D. 768\pi

Correct Answer: C

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Question 21 View Details

In the circle with equation $x - 1 \$^2 + $y - 2)^\(2 = 4$ ), find the equation of the \$)^(2 = 4\tangent line at the point where it intersects the line \(y = x + 1$.

Correct A. $y = -x + 3$

B. $y = x - 3$

C. $y = -x + 1$

D. $y = x + 1$

Correct Answer: A

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Question 22 View Details

A right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.

Correct A. ( 288pi ) $cm^3$

B. ( 288pi ) $m^3$

C. ( 288pi ) in^3

D. ( 288pi ) $ft^3$

Correct Answer: A

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Question 23 View Details

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

Correct A. ( 10494 )

B. ( 10494.5 )

C. ( 10494.9 )

D. ( 10495 )

Correct Answer: A

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Question 24 View Details

A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the mean becomes 12. Find the sum of the original 5 numbers.

Correct A. ( 40 )

B. ( 45 )

C. ( 50 )

D. ( 55 )

Correct Answer: A

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Question 25 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x > \frac{3}{2}$

D. $x > -1$ or $x < \frac{3}{2}$

Correct Answer: A

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