Recently Active Algebra Questions

Q:=> \texttt{Prove that for all z with |z|=1, the relation given is true}} \sqrt{2} \leq |1-z|+|1+z^{2}| \leq 4 ...

Please solve this questions....!! I'll be grateful for your this act of kindness.....!! and one more thing.... please do show the steps... :) 1. The number of pairs of reals (x,y) such that x = x2 + y2 and y = 2xy is (A) 4 (B ...

can we say that if |z1|= |z2|= |z3| and z1 + z2 + z3 = 0 one of z1 ,z2,z3 is real? is it obvious that z1, z2,z3 are the roots of x3= |z1|3 they ll be the vertices of an equilateral triangle but are above things always true? p ...

1)find number of real roots of \sum_{r=0}^{r=2n}{}x^r/r! =0 ,(n\epsilon N) 2)Find the number of cubic polynomial p(x) with integral coefficients such that for three distinct integers a,b and c, p(a)=b,p(b)=c and p(c)=a source ...

Let aN be defined as a1 = 0 and aN =(1-(1/N^2))aN-1 -(1/N^2) N is natural no find a2010 ...

1. \left(x-1 \right)\sqrt{x^{2}-x-2}\geq 0 ...

The expressions 1 + x, 1+x+x^2, 1+ x+ x^2 +x^3, .............. 1 + x + x^2 +........+ x^n are multiplied together and the terms of the product thus obtained are arranged in increasing powers of x in the form of a0 + a1X + a2^ ...

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Show that nC0 nC0 - n+1C1 nC1 + n+2C2 nC2 - .......................... = (-1)n ...

I am confused in the approach to two similar questions. So I am posting both- 1) A team of 8 couples (husband and wife) attend a lucky draw in which 4 persons are picked up for a prize. The probability that there is atleast o ...

$If $mn=1$, Then find Least value of $m^2+2mn-4n^2=$ ...

Find the numbers of 4x4 array whose entries are from the set {0,1,2,3} and which are such that the sum of the numbers in each of the four rows and four columns is divisible by 4. ...

Let alpha = e ^ i8pi / 11 , then find Re ( alpha + alpha ^2 + alpha ^3 + alpha ^4 + alpha ^5). ...

$Determine all Polynomial $p(x)$ with real coefficients such that $p(2)=12$\\\\ and $p(x^2)=x^2(x^2+1)p(x),\forall x\in R.$ ...

$(1) Solve the equation $6^x+27^{x-1} = 8^x-1.$ $(2) Solve the equation $5.2^x+4.3^x = 3.4^x+2.5^x$ $(3) Solve the equation $3^{x+1}-9^x+3.5^x-25^x=15^x+3$ ...

From where can i download free a dasgupta iit maths solutions? ...

$(1) Solve the equation $x^3-x^2+9\lambda x-\lambda=0$. if It is known to have only\\\\ positive roots. and also find value of $\lambda$\\\\ (2) Determine The no. of local extreme of \\\\$f(x)=(x-1).(x-2)^2.(x-3)^3.(x-4)^4... ...

If a , b ,c r distinct +ve integers such that ab + bc + ca is greater than equal to 107 , then find the minimum value of 1/6 ( a^3 + b^3 + c^3 - 3abc ) ...

Find solution/s to : (x)[x]=1. here ( ) is Least Integer Function. [ ]=Greatest Integer Function ...

if a,b,c,d are in Harmonic progression prove ab+bc+cd=3ad ...

*Image* correction: independent of lamda ...

$Q:$\Rightarrow$ There are 4 machines & it is known that exactly 2 of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified . Then the probability that only 2 tests are n ...

if a denotes the number of permutations of (x+2) things taken all at a time,b the number of permutations of x things taken 11 at a time and c the number of permutations of (x-11) things taken all at a time such that a=182bc, ...

Q1) How many real solutions of the following equation are possible:6x2+77[x]+147=0 where [x] is Greatest Integer Function of x . ...

consider a m*n matrix what do we mean when we say m and n have same parity? ...

consider a m*n matrix what do we mean when we say m and n have same parity? ...

prove *Image* ...

let z , w be complex nos. such that z + i ( conjugate of w ) = 0 and zw = pi . Then find arg z.. ...

find minimum value of f(X)=(X+A)(X+B)/(X+C) SUCH THAT X>-C,A>C,B>C ...

$(1) Find \underline{\underline{Least value}} in each cases:\\\\ (i) $3\sqrt{x^2+y^2}+4\sqrt{(x-3)^2+(y-4)^2}$\\\\ (ii) $\sqrt{x^2+y^2}+\sqrt{(x-1)^2+y^2}+\sqrt{x^2+(y-1)^2}+\sqrt{(x-3)^2+(y-4)^2}$\\\\ (iii) $\sqrt{(x-1)^2+(y ...