JAMB Mathematics Past Questions & Answers - Page 149

741.

If x4 - kx3 + 10x2 + 1x - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and 1

A.

k = -7, 1 = -15

B.

k = -15, 1 = -7

C.

k = \(\frac{15}{3}\) , 1 = -7

D.

k = \(\frac{7}{3}\) , 1 = -17

Correct answer is A

If k = -7 is put as -15, the equation x4 - kx3 + 10x2 + 1x - 3 becomes x4 - (7x3) + 10x2 + (15)-3 = x4 + 7x3 + 10x2 - 15x - 3

This equation is divisible by (x - 1) and (x + 2) with the remainder as 27

k = -7, 1 = -15

742.

Simplify \(\frac{(a^2 - \frac{1}{a}) (a^{\frac{4}{3}} + a^{\frac{2}{3}})}{a^2 - \frac{1}{a}^2}\)

A.

a\(\frac{2}{3}\)

B.

a-\(\frac{1}{3}\)

C.

\(a^{2}\) + 1

D.

a

E.

a\(\frac{1}{3}\)

Correct answer is E

\(\frac{(a^2 - \frac{1}{a})(a^{\frac{4}{3}} + a^{\frac{2}{3}})}{a^2 - \frac{1}{a}^2}\)

= \(\frac{(\frac{a^2 - 1}{a})(\frac{a^2 + 1}{a^{\frac{2}{3}}})}{a^{4} - \frac{1}{a^2}}\)

= \(\frac{a^4 - 1}{a^{\frac{5}{3}}}\) x \(\frac{a^2}{a^4 - 1}\)

= a\(\frac{1}{3}\)

743.

Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)

A.

-3

B.

3

C.

\(\frac{3}{5}\)

D.

\(\frac{-3}{2}\)

E.

1n 6 - 2 1n 5

Correct answer is C

No explanation has been provided for this answer.

744.

The locus of all points having a distance of 1 unit from each of the two fixed points a and b is

A.

A line parallel to the line ab

B.

A line perpendicular to the line ab through the mid-point of ab

C.

A circle through a and b with centre at the mid-point of ab

D.

A circle with centre at a and passes through b

E.

A circle in a plane perpendicular to ab and centre at the mid-point of the line ab

Correct answer is B

The locus of all points having a distance of 1 unit from each of the two fixed points. a and b is: a perpendicular to the (ab) through the mid-points ab

745.

If (25)x - 1 = 64(\(\frac{5}{2}\))6, then x has the value

A.

7

B.

4

C.

32

D.

64

E.

5

Correct answer is B

(25)x - 1 = 64(\(\frac{5}{2}\))6

(\(\frac{5}{2}\))6 = (\(\frac{5^6}{64}\))

25x - 1 = 64 x (\(\frac{5^6}{64}\))

52x - 2 = 56

2x - 2 = 6x

= \(\frac{8}{2}\)

= 4