JAMB Mathematics Past Questions & Answers - Page 372

1,856.

A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)

A.

\(\frac{-8}{15}\)

B.

\(\frac{8}{15}\)

C.

\(\frac{17}{15}\)

D.

\(\frac{-17}{15}\)

Correct answer is A

p>\(x \ast y = \frac{x^2 - y^2}{2xy}\\
=\frac{(x+y)(x-y)}{2xy}\\
-5 \ast 3 =\frac{(-5+3)(-5-3)}{2(-5\times3)}\\
=\frac{-2 \times -8}{2(-5\times3)}\\
=\frac{-8}{15}\)

 

1,857.

If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?

A.

p varies directly as r3

B.

p varies inversely as r6

C.

p varies inversely as 6√P

D.

p varies directly as r6

Correct answer is C

P ∝ 1/q3
P = K/q3
q3 = K/P
q = K/p1/3
But q ∝ r2
q = Kr2
K/p1/3 = Kr2
r2 = K/p1/3 x 1/K
r2 = 1/p1/3
r = (1/p1/3)2
r = 1/p1/6
r ∝ 1/p1/6
∴ r varies inversely as 6√P

1,858.

A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6

A.

1/12

B.

10/3

C.

1/20

D.

9/5

Correct answer is D

x ⊕ y = xy/6 = xe/6 = x
xe = 6x
e = 6
x ⊕ y = xx1/6 where x1 = 20
x x 20/6 = 6
x = 36/20
x = 9/5

1,859.

If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals

A.

NQ

B.

1/4NQ

C.

2NQ

D.

1/2NQ

Correct answer is A

No explanation has been provided for this answer.

1,860.

PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS

A.

120o

B.

90o

C.

30o

D.

60o

Correct answer is D

No explanation has been provided for this answer.