SSC TRICKS FOR MATHS

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

IF a = 997, b = 998, c = 999, THEN, FIND, a^3 + b^3 + c^3 - 3abc WITH THE FORMULA OF, a^3 + b^3 + c^3 - 3abc = (a + b + c)/2{(a-b)^2 + (b - c)^2 + (c - a)^2} (997 + 998 + 999)/2{(997 - 998)^2 + (998 - 999)^2 + (999 - 997)^2} 2994/2 * 1 + 1+ 4 2994/2 * 6 2994 * 3 8982