Recently Active Algebra Questions

Hey guys , this maths musing problem (of MTG December issue ) is really great , please give it a try ---- NOT FOR THE GREAT SIRS Find the last digit of the sum of the roots of the eqn. ( 1/2 x - 1 )2009 = -1 , and also try th ...

A man invites a party to (m+n) friends to dinner and places m at one round table and n at other.Find the no. of ways of arranging the guests . ...

Question. If a,b,c,d are in H.P. ,then show that ab+bc+cd=3ad ...

Question...How is the sum of all arithmetic means between two given numbers related to the single arithmetic mean between those numbers. Show ur steps. Do not give the FORMULA directly. ...

if the squares of a 8x8 chess board are painted either red or black at random 1)the probability taht not all squares in any column are allternating in color 3)the probability that all the squares in any column are of same col ...

What is the sum of all the factors of factorial 30? ...

. . . . Q1 Suppose 0.27 ,x ,0.72 are in GP.If x is a positive irrational no. and S is the sum of first four terms of such GP.Find S Q2 Let a_n=111....1 .Find no. of primes in sequence a2,a3,a4,a5,a6 n times Q3 Let Let a_n=111 ...

I din know under which way to post this... but this was a brilliant brilliant method to prove that sum of squares first n natural numbers is given by permutation and counting principle.. I am giving the hint here and I hope t ...

Let z_i be in G.P for all i satisfying 1≤i≤n and 1st term is unity. Also z1+z2+z3+....zn=0 Now if z1,z2,z3....znrepresent vertices of a n-sided polygon, find the distance bet circum-centre and incentre of the polygon. P.S ...

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ram has to attempt 4 papers each paper containing maximum 'n' marks in how many ways he can get a total of 2n marks ..... note: if u want to use multinomial theorem then also provide proof of multinomial thoerem :) ...

The no. of ways in which 9 identical balls can be placed in 3 identical boxes is __________________ . Ans : 12 Neways i'm posting a method which if you can understand .... explain to the Dark Knight so that I can confuse the ...

(2) If Roots of the equation 2006x^{6}+100x^{5}+10x^{3}+x-2=0 are in the form of (m+\sqrt{n})/r where m and n are non zreo integer and n , r are relatively prime .find m+n+r ...

Q1 If a1,a2,..a101 is an arrangement of the numbers 1,2,...101 then prove that the product of (1-a1)(2-a2)...(101-a101) is an even integer I wasnt in favour of starting aonther revision thread on P&C beocz already many exist. ...

FInd the sum of inifnite series a1+a2+a3+..... where a_n=(log3)^n\sum_{k=1}^{n} \frac {2k+1}{k!(n-k)!} ALso it is known that a0,a1,a2.... be the coefficients in the expasion of (1+x+x2)n in ascending power of x i have calcula ...

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if p1 and p2 are the probability of speaking the truth of two independent witnesses A and B then find the probabilty that der combined statement is true ...

Find the last three digits of 17256 ...

If a0,a1,a2.... be the coefficients in the expasion of (1+x+x2)n in ascending power of x then prove that 1) (r+1)a_{r+1}=(n-r)a_r+(2n-r+1)a_{r-1};0<r<2n 2) (a_0+a_3+a_6+...)=(a_1+a_4+a_7+...)=(a_2+a_5+a_8+...)=3^{n-1} i ...

If there are 'm' non concurrent and non parallel lines, then what is the maximum number of points which are equidistant from all the 'm' lines? from another IIT JEE forum ;) ...

(1)there are 24 balls of 6 different sizes in a bag, there being 4 balls of each size in four different colours .in how many ways 4 balls can be selected so that they are of differnt colours?????? (2) how many 5 digit nos. of ...

Q1 Find the no. of rational and irrational roots of x^3+1=2(2x-1)^{1/3} Q2 Let P(x) be a polynomial such that P(x^2+2)=x^{17}-3x^5+x^3-3 then find roots of P(x) Q3 Let a,b,c ε R and a≠0 be such that (a+c)2<b2 the nfind ...

(1) Prove that \left C(2n,n \right)/(n+1)=Integer where n\ \epsilon Integer ...

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Well ,let's make mincemeats of these --- :) 1 > Do try to find the remainder when 21990 is divided by 1990 . I have found a way without using binomial but , still it would good to see the other ways too ---- maybe an easie ...

If x is real, the maximum value of - y = 2\left(a-x\right) \{ x+ \sqrt{x^2 + b^2} \} is ________ ? ...

Ques1) Let f(n) = 10 n + 3.4 n+2 + 5 , where n belongs to N. The greatest value of the integer which divides f(n) for all n is (a) 27 (b) 9 (c)3 (d) none Ques2) If m and n are any two odd positive integers with n < m , the ...

Q1 Find the real values of a,b,p,q for which (2x-1)^{20}-(ax+b)^{20}=(x^2+px+q)^{20} Q2 Find Sum of series S=C_1-(1+ 1/2)C_2 +(1+ 1/2 +1/3)C_3+...+(-1)^{n-1}(1+ 1/2+....+1/n)C_n Q3 Sum of series S=\sum_{r=0}^{n}\frac{3^{r+4}. ...

6 apples and 6 oranges are to be distributed among 10 boys. Find the number of ways in which this can be done . Ans : (10+6-1 C6 )2 How can this be possible ?????????? ...

S[n]= 3/4 +15/16 +63/64+...... find S[n] a) n - 1/3*4^(n) -1/3 b) n + 1/3*4^(-n) -1/3 c) n + 1/3*4^(n)- 1/3 d) n-1/3*4^(-n) +1/3 ...