TRICKY QUESTION

A STRAIGHT HIGHWAY LEADS TO THE FOOT OF A TOWER. A MAN STANDING AT THE TOP OF THE TOWER OBSERVES A CAR AT AN ANGLE OF DEPRESSION OF 30 deg, WHICH IS APPROACHING THE FOOT OF THE TOWER WITH A UNIFORM SPEED. SIX SECONDS LATER, THE ANGLE OF THE DEPRESSION OF THE CAR IS FOUND TO BE 60 deg. FIND THE TIME TAKEN BY THE CAR TO REACH THE FOOT OF THE TOWER FROM THIS POINT.

TAKE DB = x,

SO,

AB = 6 + x,

TAN 30 = BC / AB

1 / sqrt(3) = BC / 6 +x

BC = (6 + x) / sqrt(3).....................(i)

THEN,

TAN 60 = BC / DB

sqrt(3) = BC / x

BC = x * sqrt(3)............................(ii)

BY (i) AND (ii) WE GET,

x * sqrt(3) = (6 + x) / sqrt(3)

x * sqrt(3) * sqrt(3) = 6 + x

x * 3 = 6 + x

3x = 6 + x

3x - x = 6

2x = 6

x = 3sec

A CUBE OF EDGE 6 cm IS PAINTED ON ALL SIDES AND THEN CUT INTO UNIT CUBES. THE NUMBER OF UNIT CUBES  WITH NO SIDES PAINTED IS,

USUALLY THIS QUESTION TAKES LOT OF TIME IN THE EXAM UP TO 2 MINUTES

BUT THIS THE TRICK BY WHICH YOU CAN DO THIS QUESTION IN MAXIMUM 20 SECONDS

VOLUME OF BIGGER CUBE = 216 cu. cm

VOLUME OF UNIT CUBE = 1 * 1 * 1 = 1 cu. cm

NUMBER OF UNCOLOURED CUBE  = 4 * 4 * 4 = 64

BECAUSE EDGE OF UNCOLOURED CUBE IS 4 cm

IN WHAT RATIO DOES THE POINT T (3 , 0) DIVIDE THE SEGMENT JOINING THE POINTS S (4 , -2) AND U (1 , 4)

LET THE POINT T DIVIDE LINE SEGMENT "SU" IN THE RATIO k : 1

IF THE CO ORDINATES OF POINT T BE (x , y) AND THAT OF POINTS S AN U BE (x1 , y1)

AND (x2 , y2) RESPECTIVELY THEN

x = (k*x2 + x1)/(k + 1)............(i)

y = (ky2 + y1)/(k + 1).............(ii)

THEREFORE,

IN EQUATION (i)

3 = (k*1 + 1*4)/(k + 1)

 3k + 3 = k + 4

3k - k = 4 - 3

k = 1/2

IF YOU WANT TO PUT IN (ii) EQUATION YOU CAN PUT IN THAT EQUATION THE

ANSWER WILL COME SAME....