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  • For what value of n are the nth terms of two A.Ps 63 , 56 , 67 , ....... and 3 , 10 , 17 .......equal? =============================================== The diameter of a roller 120cm long is 84cm . If it takes 500 complete revolutions to level a playgroun

For what value of n are the nth terms of two A.Ps 63 , 56 , 67 , ....... and 3 , 10 , 17 .......equal? =============================================== The diameter of a roller 120cm long is 84cm . If it takes 500 complete revolutions to level a playground , determine the cost of levelling it at the rate of 30 paise per square metre.

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1);63,65,67,......\* a=63,;d=2\* a_n=a+(n-1)d\*Rightarrow a_n=63+ (n-1)(2)=61+2n\*3,10,17;....\*a=3,;d=7\*a_n=a+(n-1)d\*Rightarrow a_n=7n-4\* according;to;question;they;are;equal\* Rightarrow 61+2n=7n-4\* Rightarrow 65=5nRightarrow n=13\*So,;for;n=13;a_13;of;both;AP;are;equal\* 2);The;roller;is; a;right;circular;cylinder;of;height,h=120;cm\* and,;radius;of;its;base,r=42;cm\* herefore area;covered;by;the; roller;in;one;revolution=curved;surface;area;of;the;roller\*Rightarrow 2 imes pi imes 42 imes120=31667.25;cm^2\*so,;area; covered;by ;the;roller;is;500;revolution=(31667.25 imes500)cm^2\* Rightarrow frac31667.25 imes 500100 imes 100;m^2=1583.36;m^2\* cost;of;levelling;the;playground=1583.36frac30100=475\* Hence,;cost;of;levelling;the;playground;is;Rs;475

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Deependra Verma

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