POST UTME NILE UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \( \begin{cases} x + y = 4 \ x - 2y = -3 \end{cases} \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 2
Solve the equation \( \sin\( x \ \) = \frac{1}{2} ) for ( x ) in the interval ( [0, 2pi] ).
A. \( \frac{pi}{6} \)
B. \( \frac{pi}{3} \)
C. \( \frac{5pi}{6} \)
D. \( \frac{7pi}{6} \)
Question 3
Solve for x in the equation \[ \begin{array}{rcl} 2x + 5 &=& 11 \ 3x - 2 &=& 7 \ \hline \end{array} \]
A. 3
B. 4
C. 5
D. 6
Question 4
Find the area of the circle with radius \( r = 4 \) u\sing the formula for the area of a circle.
A. A = 16\pi
B. A = 32\pi
C. A = 64\pi
D. A = 128\pi
Question 5
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \) u\sing integration by substitution.
A. π/4
B. π/2
C. π/3
D. π/6
Question 6
Solve the system of equations \( x + y = 3, x - y = 1 \) u\sing the method of substitution.
A. x = 2, y = 1
B. x = 2, y = 2
C. x = 1, y = 2
D. x = 1, y = 1
Question 7
A right circular cylinder has a height of 10 cm and a radius of 5 cm. What is its volume?
A. 500\pi
B. 1000\pi
C. 2000\pi
D. 5000\pi
Question 8
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. 10
B. 12
C. 14
D. 16
Question 9
Let ( S ) be the set of all real numbers ( x ) such that \( x^2 + 2x - 3 = 0 \). Find the probability that a randomly selected element from ( S ) is greater than 1.
A. 1/2
B. 1/3
C. 2/3
D. 3/4
Question 10
Find the surface area of the sphere with radius 5 cm.
A. 100\pi cm^2
B. 150\pi cm^2
C. 200\pi cm^2
D. 250\pi cm^2
Question 11
Solve the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) u\sing the chain rule.
A. y = x^2
B. y = x^3
C. y = x^4
D. y = x^5
Question 12
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
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}
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 + x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( 1 + x^2 \)^{3/2}}
B. f'(x) = \frac{x}{\( 1 + x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 + x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 + x^2 \)^{3/2}}
Question 15
Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.
A. f'(x) = 2x \sin x + x^2 \cos x
B. f'(x) = 2x \sin x - x^2 \cos x
C. f'(x) = x^2 \sin x - 2x \cos x
D. f'(x) = x^2 \sin x + 2x \cos x

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