POST UTME REDEEMERS UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random experiment has two indep\endent events, A and B, with probabilities ( P(A) = 0.4 ) and ( P(B) = 0.6 ). Find the probability that both events occur.
A. 0.24
B. 0.48
C. 0.64
D. 0.76
Question 2
Find the determinant of the matrix \( egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} \).
A. -1
B. 1
C. 2
D. 4
Question 3
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 4
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.
A. \( egin{pmatrix} 6 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} -6 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 2 \ -6 \end{pmatrix} \)
D. \( egin{pmatrix} -2 \ 6 \end{pmatrix} \)
Question 5
Find the area under the curve y = \sin(x) from x = 0 to x = π/2.
A. 1
B. 1/2
C. π/2
D. π
Question 6
Find the value of x in the equation \log_{10} \( x^2 \) = 4.
A. 10^4
B. 10^8
C. 10^2
D. 10^6
Question 7
Solve the equation \frac{1}{x} + \frac{1}{y} = \frac{1}{2} for x in terms of y.
A. x = 2y/\( y-2 \)
B. x = 2y/\( y+2 \)
C. x = 2y/\( y-1 \)
D. x = 2y/\( y+1 \)
Question 8
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x < 1 or x > 3/2
C. x < -1 or x < 3/2
D. x > 1 or x > 3/2
Question 9
A rec\tangular solid has a length of 10cm, a width of 5cm, and a height of 8cm. Find its surface area.
A. 240cm^2
B. 250cm^2
C. 260cm^2
D. 270cm^2
Question 10
The equation of a circle is \( x^2 + y^2 - 4x + 6y + 4 = 0 \). Find the center and radius of the circle.
A. Center: \( 2, -3 \ \) ), Radius: 1
B. Center: \( 2, -3 \ \) ), Radius: 2
C. Center: \( 2, -3 \ \) ), Radius: 3
D. Center: \( 2, -3 \ \) ), Radius: 4
Question 11
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].
A. -1
B. 1
C. 2
D. 3
Question 12
Find the sum of the first 10 terms of the geometric progression with first term 2 and common ratio 3.
A. 3210
B. 3220
C. 3230
D. 3240
Question 13
If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ).
A. \( -\frac{2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( -\frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2}{\( x^2 + 1 \ \)^2} )
Question 14
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot4^2 - 2\cdot4\right \ \) - \frac{1}{2}\left\( 0^3 + 3\cdot0^2 - 2\cdot0\right)\ \)
B. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot4^2 - 2\cdot4\right \ \) + \frac{1}{2}\left\( 0^3 + 3\cdot0^2 - 2\cdot0\right)\ \)
C. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot4^2 - 2\cdot4\right \ \) - \frac{1}{2}\left\( 0^3 + 3\cdot0^2 - 2\cdot0\right)\ \)
D. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot4^2 - 2\cdot4\right \ \) + \frac{1}{2}\left\( 0^3 + 3\cdot0^2 - 2\cdot0\right)\ \)

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