Recently Active Algebra Questions

\hspace{-16}$Find Complex no. $\mathbf{z}$ Which satisfy the equation \\\\ $\mathbf{\left|\frac{z-\bar{z}-i}{z+\bar{z}+2}\right|=\frac{\sqrt{2}}{2}}$ ...

\hspace{-16}$Prove that the equation $\mathbf{2x^{n+2}+1=3x}$ has one real root in $\mathbf{(0,1)}$ ...

\hspace{-16}$If $\mathbf{f(x)=x^{n+8}-10x^{n+6}+2x^{n+4}-10x^{n+2}+x^n+x^3-10x+1}$\\\\ Then Find $\mathbf{f(\sqrt{2}+\sqrt{3})=}\;,$ Where $\mathbf{n\in\mathbb{Z^{+}}}$ ans = 1+ 2 - 3 ...

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Roots of the equations x2+px+q=0 & x2+rx+s=0 are respectively (α,β), (γ,δ). Write down the value of {(α-γ)(α-δ)(β-γ)(β-δ)} in terms of p,q,r,s . And find out the condition of having common roots of those equetions ...

can any1 prove the result that number of digits in xy is [ylogx+1]....where [] denotes G.I.F? ...

find the first non-zero digit in 80!? ...

if 21(x2 + y2 + z2 )=(x + 2y +4z)2 find the relation between x,y,z a)ap b)gp c)hp d)none of them problem form new pattern math-sk goyal ...

1)Two squares are chosen at random from the 64 squares of a chessboard The probability that they have a side in common is ___ Probability that they have just one vertex in common is ____ 2)If P(AUB)=P(A∩B), (a)P(A)=P(B) (b) ...

a 4 digit number(numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is same as the sum of its last 2 digits.If a four-digit number is picked up at random,the probability that it is a lucky number i ...

1)In an AP, Sn = n2p,Sk = k2p ; k,n,p are natural numbers and k≠n Sp = ? can we answer p2p just by seeing the pattern? 2) 1/1x2 + 1/2x3 + 1/3x4 +,,,,,,,,, to n terms 3)Sum of 9 AM's between 2 and 24 is _____ 4)If a,b,c be r ...

\hspace{-16}$Suppose that $\mathbf{\log_{y}x+\log_{x}y=11}$\\\\ Then Evaluate $\mathbf{(\log_{y}x)^k+(\log_{x}y)^k=}$\\\\ For $\mathbf{k=2\;,3\;,4\;,5}$ ...

\hspace{-16}$Let $f(x)=x+x^2+x^4+x^8+x^{16}+x^{32}+...........................$\\\\ Then find Coeff. of $x^{10}$ in $f(f(x))$ ...

Show that the locus formed by z in the equation z^3+iz=1 never crosses the coordinate axes in the argand`s plane.Further show that |z|=√((-Im(z))/(2Re(z)Im(z)+1)) ...

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\bg_green \hspace{-16}$Solve System of equations for real $\mathbf{x\;,y\;,z}$\\\\\\ \begin{Bmatrix} \bold{x^2+y^2=2.(\lfloor z^2 \rfloor +1).(\left\{z^2\right\}+1)} & \\\\ \bold{y^2+z^2=2.(\lfloor x^2 \rfloor +1).(\left\{x^2 ...

\hspace{-16}$(1)\;\; Find all Triplet $x,y,z$ such that \\\\ $\lfloor x \rfloor -y=2\lfloor y \rfloor -z=3\lfloor z \rfloor -x=\frac{2004}{2005}$\\\\\\ (2)\;\; Find all Real no. $x$ such that\\\\ $\frac{x}{x+4}=\frac{5\lfloor ...

domain of √(x12-x9+x4-x+1) is __________ ...

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\hspace{-16}$If $\mathbf{\mid z^2+1 \mid =2\mid z+1\mid }$\\\\ Then find Max. value of \mathbf{z} ...

1)Let a,b,c be roots of the equation x3-3x2+1=0.Find (a-2)(b-2)(c-2)? 2)Suppose f(x)=x3+px2+qx+72 is divisible by both x2+ax+b and x2+bx+a(where p,q,a,b are constants and a≠b).Find the sum of squares of the roots of the cub ...

Prove that \sum_{i=1}^{p}i \binom{p}{i}(n-1)^{p-i} = p n^{p-1} n is real, p is natural number ...

\hspace{-16}$Find the First Digit after the decimal point of $\mathbf{\left(2+\sqrt{5}\right)^{2010}}$\\\\ ...

\hspace{-16}$How many Integer $\mathbf{n}$ are there such that $\mathbf{n+20}$ and $\mathbf{n-20}$ are Perfect Squares\\\\ ...

1)If the range of the function f(x) = x2+ax+b/x2+2x+3 is [-5,4],a,b are natural nos,then find the value of a2 + b2 ? 2)Given,x,y belong to reals and x2 +y2 > 0.If the max and min value of the expression x2 +y2/x2+xy+4y2 ar ...

1)Number of ways 10 persons can take seats in a row of 24 fixed seats so that no two persons take consecutive seats is 2)C02 + C12 + C22 + .... + Cn2 = 3)C1+4.C2 + 7.C3 + ... + (3n-2).Cn = 4)Number of integral terms in the ex ...

The no. of natural Numbers ≤ 2012 which are relatively prime to 2012 is : ...

If cosα + cosβ + cosγ = sinα + sinβ + sinγ, then prove that i) cos2α + cos2β + cos2γ =0 & ii) sin2α + sin2β + sin2γ =0 ...

Find the coeff. of x15 in the expansion of (1 - x)(1 - 2x)(1 - 22x).............(1 - 215x). Please help me its urgent. ...

\hspace{-16}$If $\mathbf{1\leq x<y\leq 100}$ and $\mathbf{x,y\in\mathbb{Z}}$. Then find the Probability that $\mathbf{i^x+i^y\in\mathbb{R}}$\\\\ Where $\mathbf{i=\sqrt{-1}}$ ...