Find the 28383rd term of the series: 123456789101112....
a) 3 b) 4 c) 9 d) 7
1-9 have 9 digits 10-99-89 digits 100-999-899 digits and so on...just calculate in this way you will get your answer
i'm having problem in one question from Number system: n is number such that 2n has 28 factors and 3n has 30 factors, 6n has a) 35 b)32 c)28 d) None of these plz tell me how to solve...
answer of this question would be option (A) "2n" has "28" factors and 28 can be written as 7*4,14*2,28*1 similarly "3n" has 30 factors it can be written as,6*5,10*3,15*2,30*1 now the diff between case(1) and case(2) is that in (1) we added 2^1 in "N" and in (2) we added 3^1 so a power of 2 will be reduced and a power of 3 will be increased hence on 7*4 and 6*5 satisfy this condition i hope this will help
I dint get that above soln.. plz explain clearly. hey you all people hw is ur prep goin on? We need to discus more probs on nos. anyways.. here are some of my doubts plz share the soln of the following:
Q1)Remainder=? for 10^10+ 10^100+ 10^1000+.....+ 10^10000000000 divided by 7 is a) 0 b) 1 c) 2 d) 5 e) 4
Q2) Remainder=? for 43^101 + 23^101 by 66: a) 2 b) 10 c) 5 d) 0 e) 35
Q3) 10^n -(5+ sq root (17))^n is divisible by 2^(n+2) for wht whole no. value of n? options : 2 ; 3 ; 7 ; 8; none of these
I dint get that above soln.. plz explain clearly. hey you all people hw is ur prep goin on? We need to discus more probs on nos. anyways.. here are some of my doubts plz share the soln of the following:
Q1)Remainder=? for 10^10+ 10^100+ 10^1000+.....+ 10^10000000000 divided by 7 is a) 0 b) 1 c) 2 d) 5 e) 4
Q2) Remainder=? for 43^101 + 23^101 by 66: a) 2 b) 10 c) 5 d) 0 e) 35
Q3) 10^n -(5+ sq root (17))^n is divisible by 2^(n+2) for wht whole no. value of n? options : 2 ; 3 ; 7 ; 8; none of these
Q1) Use Euler method, numerator will reduce to 10^5. 10^5mod7 = 5. Q2) Euler method, Euler number of 66 = 20.. hence numerator will reduce to *43+*23 -> 43+23/66 -> remainder = 0. Q3) Whatever values we put, there will always be a sq rt 17 element, hence none of these.
This is how i see it.. 58! - 38 ! can be written as 38!(58*57*56...39 - 1).. Now 58*57*56...39 is a multiple of 3.. Any multiple of 3 minus 1 is not a multiple of 3... Therefore the power of 3 will solely be determined by 38!.. It will be 12+4+1= 17...
Q1) Use Euler method, numerator will reduce to 10^5. 10^5mod7 = 5. Q2) Euler method, Euler number of 66 = 20.. hence numerator will reduce to [43^(20*5)]*43+[23^(20*5)]*23 -> 43+23/66 -> remainder = 0. Q3) Whatever values we put, there will always be a sq rt 17 element, hence none of these.
Pg 166 Q 26: In a village consisting of p persons, x% can read and write. Of the males alone y% , and of the females alone z% can read and write. Find the number of males in the village in terms of p,x,y and z if z
Pg 166 Q 26: In a village consisting of p persons, x% can read and write. Of the males alone y% , and of the females alone z% can read and write. Find the number of males in the village in terms of p,x,y and z if z
Take the total population be 100 [=p] : 70 males, 30 females.
This is another question from lovely "Arun Sharma's book" I am also uploading the figure. The question is Q)A circle is inscribed in the quadilateral ABCD. Given that AB = 27cm, BC=38m, DC= 25cm and AD is perpendicular to DC. Find the maximum limit of radius and the area of the circle a)10cm,226cm^2 b) 14cm,616cm^2 c)14cm,216cm^2 d)28cm,616cm^2 e) none of these
My approach was since OP=OS (radii) and PD=PS(tangents) and angle D= S=P=90 , hence OPDS is a square , i determined AD by foll. method AD=AP+PD = 27-TB+PD (since AP= AT as both are tangents and AT= 27-TB) = 27-(38-SC)+PD = 27-(38-SC)+(25-SC) (since PD=SD and SD= 25-SC) AD = 14cm and as from fig. AD= AP+PD , PD has to be smaller than 14cm under any condition and PD= OS radius of the circle , therefore the radius of the circle will definately be less than 14cm but Arun Sharma is saying answer as option(d) radius = 28cm which is not possible . At the back the book gives explanation as "WORK THROUGH THE OPTIONS"
PS: Estallar bhai aap kahaan ho ajkal:biggrin: , zara help karo
(Pg-44) Three numbers are such that the second is as much lesser than the third as the first is lesser than the second.If the product of the two smaller numbers is 85 and the product of two larger numbers is 115,find the middle number
(Pg-44) Three numbers are such that the second is as much lesser than the third as the first is lesser than the second.If the product of the two smaller numbers is 85 and the product of two larger numbers is 115,find the middle number
the three numbers are in AP. let the nos. be (a-n), a, (a+n). a^2-n = 85. a^2+n = 115. Solving, a^2 = 100, a = 10.
In Arun Sharma's Number System Chapter,there is a Topic related to Finding the highest power (n) of a number which divides a Factorial number(xy00!) completely. In this topic, i have a major problem in solving the different type of questions.
Ques1.Highest Power of 82 which divides 342! Ans1. 7x3x2x2 . In this case which check only for no. of 7s.
But in Ques2. Highest Power of 175 which divides 344! Ans2. 5x5x7 . But in this case we find no. of 7s as well as 5^2s.
Why so?
Also provide solutions to the below Questions with Explanations:-
Ques1> Highest Power of 12600 which divides 50! Ques2>Highest Power of 720 which divides 77! Ques3> Highest Power of 2520 which divides 50!
P.S. The main point of concern is how we determine which terms need to be counted for finding the answer?
. At the back the book gives explanation as "WORK THROUGH THE OPTIONS" 