Recently Active Algebra Questions

(1) Find The Remainder when (32) (32)^(32) is divided by 7 (using no. Theory). ...

If n is an even integer and a,b,c are distinct numbers,then find the number of distinct terms in the expansion of (a+b+c)^n + (a+b-c)^n My approach>>>> It should b (n+1)+(n-1)+(n-3)+........+1 So ans should b ((n+ ...

If 7^103 is divided by 25,Then find the remainder? ...

Prove that no of ways in which n identical objects can be dived in r different groups is: n+r-1 C r-1 (I did'nt get the prove of this in any of the books.) ...

Find the number of divisors of N=22335375 of the form 4n+2 Ans=95 ...

Find the largest two digit prime factor of 200C100 ...

Find the number of ordered pairs of positive integers (m,n) satisfying m≤ 2n ≤60 ,n ≤2m≤ 60 ...

Number of Proper factors of 75600 are ? ...

Nine hundred distinct N digit natural numbers are to be formed using digits 6,8,9 only.Find smallest value of N possible. ...

Find the number of integers between 1 and 1000 having their sum of digits equal to 12 ? ...

If x,y,z R such that x2+y2+z2=1 and α=x2+2y2+3z2,then find minimum and maximum value of α ...

There are k different books and l copies of each in a college library.The number of ways in which a student can make selection of one or more books is ? ...

Find the number of n digit numbers ,which have no two consecutive digits being same ans=9n ...

Find the number of divisors of 3630 which leave remainder 1 when divided by 4 ? ans=6 ...

Find the number of permutations of letters a,b,c,d,e,f,g such that neither the pattern 'beg' nor 'cad' appears Ans:4806 ...

Find number of ordered triplets of positive integers which are solutions to the equation x+y+z=100 ans:4851 ...

For c≥1,find all the complex number z satisfying z+c lz+1l+i=0 ...

Prove that {{cosθ+sinφ)+i(sinθ-cosφ)}n+{(cosθ+sinφ)-i(sinθ-cosφ)}n =2n+1cosn(π/4 +θ-φ/2) cos[n(π/4 -θ+φ/2)] ...

Find real part of tan(α+iβ) ...

If ω≠1 is cube root of unity satisfying 1/a+ω +1/b+ω +1/c+ω =2ω2 and 1/a+ω2 +1/b+ω2 +1/c+ω2 =2ω Find value of 1/a+1 +1/b+1 +1/c+1 ...

Find the number of selections of n things from three piles,one consisting of n identical things of one type,second consisting of n identical things of second type and third consisting of n different things . ...

There are 10 greeting cards each of different color and 10 different envelopes of the same colors.Find the number of ways in which cards can go to the envelopes such that 6 cards can go into envelopes of corresponding color ...

First look when i saw this question, I got bowled.. Then the feeling of solving this one was good.. [1] .. I thought THis is a nice question that you guys should try F(x) is a polynomial of degree n such that f(k)=1/k for k=1 ...

Find the no.of triangles that can be formed with the vertices of a polygon of 10 sides as their vertices if 1) the triangle cannot have more than one side in common. 2)the triangle cannot have any side in common with the poly ...

Show that there exists a complex Number Z satisfying |z-a| + |z+a|= 2 |c| if and only if |a| ≤ |c|. If this condition is satisfied what are the smallest and largest values of |z| ?????? ...

Questions from various materials n books : PERMUTATIONS & COMBINATIONS { I would continue adding qs in this forum everyday . } 3) There are 2 women participating in a chess tournment. Every participant played 2 games with the ...

Let m,n ε N ,n>m,then \sum_{k=m}^{n}{u_k(v_{k+1}-v_k)}\equiv \left|u_kv_k \right|_{m} ^{n+1} -\sum_{k=m}^{n}{v_{k+1}(u_{k+1}-u_k)} This is called Summation by parts My question is ...is this of any use for JEE ???? if yes ...

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Find all Complex no. Z which satisfy the following expression (1)Z(bar) = i(Z2) without using Z=x+iy (2) question Z2+|Z|=0 ...

This question is not for the advanced students.. but for those who fear the name Functional equations and have not tried too many.... SOlve this one to get some hold on the topic.. Determine f(x) such that... x^2f(x)+f(1-x)=2 ...