JAMB Mathematics Past Questions & Answers - Page 281

1,401.

The derivative of cosec x is

A.

tan x cosec x

B.

-cot x cosec x

C.

tan x sec x

D.

-cot x sec x

Correct answer is B

\(\csc x = \frac{1}{\sin x}\)

Using the quotient rule,

\(\frac{\mathrm d y}{\mathrm d x} = \frac{vdu - udv}{v^{2}}\)

= \(\frac{\sin x (0) - 1 (\cos x)}{(\sin x)^{2}}\)

= \(\frac{- \cos x}{\sin^{2} x}\)

= \((\frac{- \cos x}{\sin x}) (\frac{1}{\sin x})\)

= \(- \cot x \csc x\)

1,403.

P is on the locus of points equidiatant from two given points X and Y. UV is a straight line throuh Y parallel to the locus. If < PYU is 40°, find < XPY.

A.

100o

B.

80 o

C.

50 o

D.

40 o

Correct answer is B

< PYU = < YPQ = 40°(Alternative) = PQ\(\parallel\)UV

< XPQ = < YPQ = 40°, Since QX = QY

therefore < XPY = 80°

1,404.

Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x - 2y + 4 = 0, find the equation of QR

A.

x + 2y - 1= -0

B.

2x + y - 3 = 0

C.

x - 2y - 3 = 0

D.

2x + y - 1 = 0

Correct answer is D

Line PQ : x - 2y + 4 = 0

2y = x + 4 \(\implies y = \frac{x}{2} + 2 \)

Slope = \(\frac{1}{2}\)

Slope of the perpendicular line QR: \(\frac{-1}{\frac{1}{2}} = -2\)

Line QR: \(y = mx + b\)

\(y = -2x + b\) 

Point of intersection: (1, -1)

\(-1 = -2(1) + b \implies b = -1 + 2 = 1\)

\(y = -2x + 1 \implies y + 2x - 1 = 0\)

\(QR: 2x + y - 1 = 0\)

1,405.

Find the distance between two towns P(45°N, 30°W) and Q(15°S, 30°W) if the radius of the earth is 7000km. [\(\pi = \frac{22}{7}\)]

A.

\(\frac{1100}{3}\)km

B.

\(\frac{2200}{3}\)km

C.

\(\frac{22000}{3}\)km

D.

\(\frac{1100}{3}\)km

Correct answer is C

Angular difference = 45° + 15° = 60°.

\(D = \frac{60°}{360°} \times 2 \times \frac{22}{7} \times 7000\)

= \(\frac{22000}{3} km\)