POST UTME REDEEMERS UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A curve is defined by the equation \( y = \frac{1}{x^2 + 1} \). Find the equation of the \tangent line at the point \( 1, \frac{1}{2} \ \) ).
A. \( y = x - \frac{1}{2} \)
B. \( y = x + \frac{1}{2} \)
C. \( y = -x + \frac{1}{2} \)
D. \( y = x + \frac{1}{2} \)
Question 2
A cylindrical \tank has a height of 10 m and a radius of 4 m. If the \tank is filled with water to a height of 8 m, what is the volume of water in the \tank?
A. 200π
B. 400π
C. 600π
D. 800π
Question 3
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \ \) or \( x = -3 \ \)
B. \( x = 2 \ \) or \( x = 3 \ \)
C. \( x = -3 \ \) or \( x = 2 \ \)
D. \( x = 3 \ \) or \( x = -2 \ \)
Question 4
A company produces two products, A and B. The profit on product A is ₦50 per unit and the profit on product B is ₦75 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. ₦12500
B. ₦15000
C. ₦17500
D. ₦20000
Question 5
A set A contains 5 elements, and a set B contains 3 elements. Find the number of elements in the union of sets A and B.
A. 8
B. 10
C. 12
D. 15
Question 6
If \( \tan A = \frac{1}{3} \) and \( \tan B = \frac{1}{4} \), find \( \tan \( A + B \ \) )
A. \frac{25}{37}
B. \frac{37}{25}
C. \frac{12}{5}
D. \frac{5}{12}
Question 7
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).
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 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
C. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x > \frac{1}{2} \)
Question 9
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?
A. 8
B. 6
C. 10
D. 12
Question 10
Solve for x in the equation \( egin{vmatrix} 2 & 3 \ 4 & 5 \end{vmatrix} = x \)
A. 7
B. 10
C. 12
D. 15
Question 11
Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).
A. 0.24
B. 0.36
C. 0.48
D. 0.60
Question 12
Solve the equation [ 2x + 5 = 11 ].
A. 3
B. 2
C. 4
D. 5
Question 13
Solve the equation \( 2^x + 3^x = 5^x \)
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 14
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 62
B. 64
C. 66
D. 68
Question 15
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)

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