SSC TRICKS FOR MATHS

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 QUESTIO

10^(3x) = 125 THEN,  10^(-2x) = ? SOLUTION: 10^(3x) CAN BE WRITTEN AS {10^(x)}^3 AND 125 CAN BE WRITTEN AS 5^3 SO, {10^(x)}^3 = 5^3 POWERS ARE SAME ON BOTH THE SIDES WITH DIFFERENT BASE WE ONLY TAKE THE BASE i.e., 10^x = 5 SQUARING BOTH THE SIDES BUT PUT A "minus" SIGN WITH POWER {10^(x)}^(-2) = 5^(-2) THEN, {10^(x)}^(-2) CAN BE WRITTEN AS 10^(-2x) = 5^(-2) SO ANSWER OF 10^(-2x) IS 1/25 AS 5^(-2) IS 1/25

A COMPANY HIRES SOME EMPLOYEES IN A FIX PATTERN. ON THE 1ST DAY IT HIRED 1 MORE PERSON AND ON 3RD 1 MORE AND 1 MORE PERSON INCREASING IN THIS GROUP IN THIS SEQUENCE. THE CAPACITY OF EACH PERSON WAS SAME. IF COMPANY COMPLETE THE PROJECT IN 24TH DAY, THEN OUT OF TOTAL RS 50,000 MAXIMUM EARNING OF A PERSON IS? K+2K+3K+4K+________+24K = 50,000 K(1+2+3+4+5+________24) = 50,000 K * {(24 * 25)/2} = 50,000 K = 500/3 IS MINIMUM AND 500/3 * 24 = 4000 IS MAXIMUM