POST UTME RSU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \ \).
A. 0
B. 1
C. -1
D. 2
Question 2
Find the magnitude of the vector [2, 3, 4].
A. 5
B. 6
C. 7
D. 8
Question 3
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 4
In a binary system, what is the value of the number 1011 in base 10?
A. 11
B. 13
C. 15
D. 17
Question 5
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \ 0.1 & \text{if } x = 4 \end{cases} ). Find the expected value of ( X ).
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 6
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 7
A particle moves along the x-axis with the equation of motion ( x(t) = 2t^2 - 5t + 1 ). Find the velocity of the particle at time \( t = 2 \).
A. ( v(2) = -1 \)
B. ( v(2) = 1 \)
C. ( v(2) = 3 \)
D. ( v(2) = 5 \)
Question 8
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 9
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 10
Let ( f(x) = \sin x ). Find the area under the curve \( y = f\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \ \)
B. \( \frac{pi}{2} \ \)
C. \( \frac{pi}{4} \ \)
D. \( \frac{pi}{6} \ \)
Question 11
Find the equation of the circle with center \( -2, 3 \) and radius 4.
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
Question 12
Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ).
A. 6x - 2
B. 6x + 2
C. 3x^2 - 2
D. 3x^2 + 2
Question 13
Find the derivative of the function f(x) = 3x^2 + 2x - 1
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 14
A random variable ( X ) has a probability density function ( f(x) = \begin{cases} 2x & 0 < x < 1 \ 0 & \text{otherwise} \end{cases} \). Find the expected value of ( X ).
A. ( E(X) = \frac{1}{2} \)
B. ( E(X) = \frac{1}{4} \)
C. ( E(X) = \frac{1}{3} \)
D. ( E(X) = \frac{1}{6} \)
Question 15
Solve for x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4

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