Mathematics Past Questions and Answers

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

Question 27:

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

Question 28:

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 100^o
B 80 ^o
C 50 ^o
D 40 ^o

Question 29:

A school boy lying on the ground 30m away from the foot of a water tank tower observes that the angle of elevation of the top of the tank 60^o. Calculate the height of the water tank.

A 60m
B 30 \(\sqrt{3}\)m
C 20 \(\sqrt{3}\)m
D 10 \(\sqrt{3}\)m

Question 30:

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