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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

cscx=1sinx

Using the quotient rule,

dydx=vduudvv2

= sinx(0)1(cosx)(sinx)2

= cosxsin2x

= (cosxsinx)(1sinx)

= cotxcscx

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) = PQUV

< 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 y=x2+2

Slope = 12

Slope of the perpendicular line QR: 112=2

Line QR: y=mx+b

y=2x+b 

Point of intersection: (1, -1)

1=2(1)+bb=1+2=1

y=2x+1y+2x1=0

QR:2x+y1=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. [π=227]

A.

11003km

B.

22003km

C.

220003km

D.

11003km

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