Post Utme Mathematics Past Questions and Answers

Question 461:

The indefinite integral of the function \(f(x)=x \cos x\) for any constant \(k\). is

A. \(-\cos x+\sin x+k\)
B. \(x \sin x-\cos x\)
C. \(x \sin x\) for any constant k
D. \(x+\sin x+\cos x+k\)

Question 462:

Evaluate the integral \(\int_{1}^{2}\left(x^{2}+\frac{1}{x}\right) d x\).

A. \(\frac{8}{3}+\ln 2\)
B. \(\frac{7}{3}+\ln 2\)
C. \(\frac{7}{3}-\ln 3\)
D. \(\frac{8}{3}\)

Question 463:

The trigonometric expression \(\cos 2 A +\sin 2 A\) can be written as

A. \(\cos A(\cos A-\sin A)\)
B. \(\cos ^{2} A+\sin 2-2 \sin A \cos A\)
C. \(2 \sin A \cos A +\cos ^{2} A +\sin ^{2} A\)
D. \(\cos ^{2} A +\sin ^{2} A -2 \sin A \cos A\)

Question 464:

Suppose \(D, E\) and \(P\) are subset of a universal set U. Let \(U\) be the set of natural numbers not greater than 10 , while \(D, E\) and \(P\) are respectively the set of odd numbers, even numbers and prime numbers. For any set \(X\), its complement \(X\) and \(Q\) denote the empty set.

Display the set \(D \cap P\)

A. \(\{3.5 .7\}\)
B. \(\{2\}\)
C. \(\{4.6 .8 .10\}\)
D. \(\{2.3 .5 .7\}\)

Question 465:

Find \(D \cap E\)

A. \(\{2\}\)
B. \(\{3.5 ;\)
C. \(\{1,2.3 .4 .5 \cdot 6.7 .8 .9 .10\}\)
D. \(\varnothing\)