Recently Active Algebra Questions

i am not sure wether u can say as to it is in jee syllabus or not but kindly post your thoughts and methods so that we can have a good discussion find all polynomials f satisfying f(x)f(-x)=f(x^{2}) ...

A car is parked among N cars standing in a row, but not at either end. On his return, the owner finds that exactly 'r' of the N places are still occupied. The probability that both the places neighbouring his car are empty is ...

Prove that for any complex number z, |z + 1| ≥1/√2 or |z2 + 1| ≥ 1. ...

x+10+6 3 = 1+ 3 -x find x ...

If the valences 1,1/2,1/3,1/4....occur at frequency 1,2,3,4,5.......,n in a distribution then the mean is : a. 1 b. n c. 1/n 4.NONE ...

Prove that √(7/2) ≤ |1 + z| + |1 − z + z2| ≤ 3√(7/6) for all complex numbers with |z| = 1. ...

d probability dat 2 frnds will b able to meet each other between 'a' hours & 'b' hours not waiting for each other more than 'c' hours is ? if 3 squares are selected at random on a chess board den d probability datdey lie on a ...

let f(x) be a function such that f(x-1) +f(x+1)= 2 f(x) then find the period of f(x). ...

Show that the sum of the (m+n)th and (m-n)th terms of an A.P is equal to twice the mth term. ...

εIf P(n) = 2+ 4 + 6+....+ 2n, n N, then P(k) = k(k+1) + 2 => P(k+1) = (k+1)(k + 2) + 2 for all k belongs to N. So we can conclude that P(n) = n(n+1)+2 for a. all n belonging to N b.n>1 c.n>2 d. nothing can be said A ...

The relation "congruence modulo m" on the set I of all integers is a.An equivalence b.A partial order relation c. reflexive and symmetric d.reflexive and anti symmetric Pls explain the Q and option B ...

this is really a simple one...... just wanted to check my answer. So pls co-operate [1] Using transformations or otherwise , find correct four places of decimals the value \prod_{1}^{5}{} (zi+1)/(2zi-1) where Zi are the roots ...

If α,β are the two roots of the equation λ(x2-x)+5=0 such that, α/β + β/a =5 and λ1,λ2 are any two values of λ Find the value of λ1/λ2 + λ2/λ1 ...

3 numbers are chosen from a set of {1,2,3...4n}...the number of ways of choosing such that the sum of them is divisible by 4..?? ...

the equation x- cosx =0 has a.exactly one root in (0,pi/6 ) b.exactly one root in (pi/6,pi/3) c.exactly one root in (pi/3, pi/2) d. has infinite solution in (0, pi/2) i tried to draw the graphs of y= cosx and y=x on the same ...

If A and B are two matrices such that AB=A and BA=B then B2 equals (a)B (b)A (c)1 (d)0 Plz give soln also. ...

What is rank of a matrix??Please explain with an example. ...

Find xyz... x+\frac{1}{y}=4 , y+\frac{1}{z}=1 , z+\frac{1}{x}=\frac{3}{7} ...

If l,m,n are positive integers greater than 1, lm=21 & mn=39, then which of the following must be true? (n>l>m) or (m>n>l) or (n>m>l)? My method: I have understood how n>l. So, I have given only those opt ...

In how many ways can one fill an n x n matrix with ±1 so that the product of the entries in each row and each column equals 1? ...

if a,b,c are integers not all simultaneously equal then the min value of l a + bω + cω2l is (where ω is cube root of unity). ans. 1. ...

what is the shortest method to find the values of - (a)Co/2-C1/3+C2/4-C3/5...upto (n+1) terms. (b)C1/2+C2/4+C3/6+... ans of (a) 1/(n+1)(n+2) ans of (b) 2n-1/n+1 ...

The interval in which x(>0) must lie so that the greatest term in the expansion of (1+x)2n has the greatest coefficient is (a)(n-1/n,n/n-1) (b)(n/n+1,n+1/n) (c)(n/n+2,n+2/n) (d)None of these. ...

12 - 22 + 32 - 42 + 52 - 62 +... = ? solution : LHS = (1-2)(1+2) + (3-4)(3+4) + (5-6)(5+6) + ... = - (1+2+3+4+5+6+...) = - n(n+1)/2 .... Ans... but for odd values of n, the above expression is not correct .... lyk substitute ...

Q1.The coefficient of X6 in {(1+x)6+(1+x)7+...+(1+x)15} is (a)16C9 (b)16C5-6C5 (c)16C6-1 (d)None of these Q2.260 when divided by 7 leaves the remainder (a)1 (b)6 (c)5 (d)2 Please also explain the respective method used for so ...

If (6√6+14)2n+1=[P]+f,then prove that (6√6-14)2n+1=f. ...

Prove that f(n) = 1−n is the only integer-valued function defined on the integers that satisfies the following conditions. (i) f(f(n)) = n, for all integers n; (ii) f(f(n + 2) + 2) = n for all integers n; (iii) f(0) = 1. ...

What is the probability of three cubes chosen out of a cube of n * n * n order, such that they lie on a diagonal?? This is modification of richa's Q, and this req 3-d view..... ...

Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008 × 2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends whe ...

What is the value of x? *Image* ...