May 2 2018

**INDICES(1). Simplify 125^-1/3 × 49^-1/2 × 10^0(A) 350 (B) 35 (C) 1/ 35 (D) 1 /350Solution :-Using “CASIOfx -991MS /570MS ”When raising a negative fraction to the power put brackets to avoid errors when using the calculator i.e. 125(-1/3) except it is a positive whole number[ON] [1] [2] [5] [^] [(] [(-)] [1] [a b /c] [3] [)] [X] [4] [9] [^] [(] [(-)] [1] [a b /c ] [2] [)] [X] [10] [^] [0] [=] ( 1/ 35 ) Option “C” is the correct answer(2). Simplify 92^x-3 = 3^x+3(A) -3 (B) 3 (C) 2 (D) 5Solution using “CASIO fx -991MS ” calculator when performing calculations raised to the power i.e. 9 2x-3 or 3x+3 put brackets to avoid error i.e. 9 (2x-3) or 3 (x+3) since there is equal sign in the question given make left axis=9 2x-3 , right axis=3 x+3 Note:- left axis must be equal to right axis example a=a, or 31=31.The left axis and the right axis must be the same. To trace the answer in the options given make x = any of the answers given in option A, B, C, D one after the other. If the left axis is equal to the right axis then the option is correct, but if the left axis is not equal to the right axis. then the options is wrong. Checking option A,B,C,DChecking option (A)-3 make x=-3Using CAS1O fx-991MS calculator[ON] [(-)] [3] [SHIFT] [STO] [X] (x= -3)Note:- Please use the key [AC] during calculations after you press the key [ON] on any question given[AC] [9] [^] [(] [2] [ALPHA] [X] [-] [3] [)] [=] (0.000000002) [3] [^] [(] [ALPHA] [X] [+] [3] [)] [=] (1)Option (A) is wrong go to the next optionChecking option (B) 3 make x=3[AC] [3] [SHIFT] [STO] [X] (x=3)Press [↑] [↑] [=](729) Press [↑] [↑] [=](729)If left axis is equal to Right axis, option (B) is correctChecking option (C) 2 make x= 2[AC] [2] [SHIFT] [STO] [X] (x=2)Press [↑] [↑] [=] (9) Press [↑] [↑] [=] (243)If left axis is not equal to right axis option (C) is wrongChecking option (D) 5 make x=5[ON] [5] [SHIFT] [STO] [X] (x=5)Press [↑] [↑] [=] (4,782,969) Press [↑] [↑] [=] (6,561)If left axis is not equal to right axis, option (D) is wrongThe correct answer is option (B)(3). If 3^y+x = 9^y+x and 2^x–y = 8^x–3 find the values of x and y(A) 4, 5 (B) 4, 3 (C) 3, -3 (D) 9, -9x, y x, y x, y x, ySolution:- Using CASIO fx-991MS calculatorPut x and y in the given option above . Left axis must be equal to right axis, If the left axis is not equal to the right axis the option is wrong3^y+x = 9^y+x…………………………….(1)2^x–y = 8^x–3 …………………………….(2)From equation….(1) left axis is = 3^y+x, right axis is = 9^y+xChecking option(A) 4, 5 put x = 4 and y = 5[ON] [4] [SHIFT] [STO] [X] (x = 4)[AC] [5] [SHIFT] [STO] [Y] (y = 5)Note:-Please use the key [AC] during calculcations after you press the key [ON] on any question given[AC] [3] [^] [(] ALPHA] [Y] [+] [ALPHA] [X] [)] [=] (19,683) [9] [^] [(] [ALPHA] [Y] [+] [ALPHA] [X] [)] [=](387,420,489)From equation 1 if the left axis is not equal to right axis option (A) is wrong. Since option (A) is wrong don’t bother to calculate equation 2 go to the next optionChecking option (B) 4, 3 make x = 4 and y = 3[AC] [4] [SHIFT] [STO] [X] (x = 4)[AC] [3] [SHIFT] [STO] [Y] (y = 3)press [↑] [↑] [↑] [=] (2,187)press [↑] [↑] [↑] [=] (4,782,969)From equation 1 if the left axis is not equal to right axis option (A) is wrong. Since option (A) is wrong don’t bother to calculate equation 2, go to the next optionChecking option(C) 3, -3 make x = 3, and y = -3[AC] [3] [SHIFT] [STO] [X] (x=3)[AC] [(-)] [3] [SHIFT] [STO] [Y] (y=-3)Press [↑] [↑] [↑] [=] (1)Press [↑] [↑] [↑] [=] (1)Since left axis is equation to right axis in equation 1. Equation 1 is correct to conclude go to the next equation by calculating equation 2 using CASIOfx-991MS calculator2^x–y = 8^x–3 ………………………………………(2)Since x = 3 and y = -3[AC] [2] [^] [(] [ALPHA] [X] [-] [ALPHA] [Y] [)] [=] (64) [8] [^] [ALPHA] [X] [-] [3] [)] [=] (1)From equation 2 if the left axis is not equal to right axis option (C) is wrong. Since option(C) is wrong don’t go to the next optionChecking option (D) 9, -9 make x = 9 and y = -9[AC] [9] [SHIFT] [STO] [X] (x = 9)[AC] [(-)] [9] [SHIFT] [STO] [Y] (y = -9)Press [↑] [↑] [↑] [↑] [↑] [=] (1) Press [↑] [↑] [↑] [↑] [↑] [=] (1) Press [↑] [↑] [↑] [↑] [↑] [=] (262,144) Press [↑] [↑] [↑] [↑] [↑] [=] (262,144)The correct answer is option “D”**

**(NB: ^ is raise to power, × is multiplication sign)**

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