Recently Active Algebra Questions

\hspace{-16}$Show that $\mathbf{\begin{vmatrix} a^2+b^2+c^2 &bc+ca+ab &bc+ca+ab \\\\ bc+ca+ab &a^2+b^2+c^2 &bc+ca+ab \\\\ bc+ca+ab &bc+ca+ab & a^2+b^2+c^2 \end{vmatrix}}$\\\\\\ is always Positive \;, Where $\mathbf{a\;,b\;,c} ...

*Image* ...

\hspace{-16}$Prove that::\\\\\\ $\mathbf{\binom{n}{0}\binom{n}{k}+\binom{n}{1}\binom{n-1}{k-1}+...........+\binom{n}{k}\binom{n-k}{0}=2^k.\binom{n}{k}}$\\\\\\ Where $\mathbf{n\;,k\in\mathbb{N}\;,0\leq k\leq n}$ ...

\hspace{-16}$Calculate value of $\mathbf{x}$ in $\mathbf{\log_{3}(1+2x)=3^x-x-1}$\\\\ ...

Find the remainder when 599 is divided by 13? ...

Find the value of i + -i ? ...

Let ' c ' be a fixed real number. Show that a root of the equation (below) can have a multiplicity atmost 2 and Determine the number of such values of ' c '. x(x+1)(x+2).....(x+2009) = c Source: ISI (B.Math Admission Test 200 ...

\hspace{-16}$If\; $\mathbf{\frac{\alpha+\beta}{2\alpha+\gamma}=\frac{\beta+\gamma}{2\beta+\alpha}=\frac{\gamma+\alpha}{2\gamma+\beta}}$\\\\\\ Then $\mathbf{\frac{2\alpha+3\beta+5\gamma}{7\alpha+11\beta+13\gamma}=}$ ...

\hspace{-16}$Find all Real Value of $\mathbf{m}$ for Which the Given Equation\\\\ $x^2-\mid x \mid+m=0 $ has Real solution ...

Help please! \sum_{1\leq i\leq j\leq n}^{}{}\sum{\frac{9}{(2-\alpha _{i})(2-\alpha_{j})}} Where αi , αj are the roots of unity. ...

What is the probability that if a fair coin is tossed n times we will get at least two heads? ...

Q. Find largest possible integer ' n ' such that the following holds : n\left\{\frac{abc}{ab+bc+ca} \right\}\leq (a+b)^{2}+(a+b+4c)^{2} , a,b,c\in R ...

The coefficient of the term independent of x in the expansion of ( x+1/x 2/3 - x 1/3 +1 - x-1/x- x 1/2 )10 remember 10 is in the power..... ...

*Image* is equal to (A) 3pi/10 (B) 7pi/10 (C) 4pi/5 (D) 3pi/5 (B) is the right answer as per my package but i feel its (A) ...

$\textbf{If $\mathbf{5x^2+y^2+1=4xy+2x}$.\;Then Calculate $\mathbf{x+y=}$} ...

A polynomial f(x) has integer coefficients such that f(0) and f(1) are both odd numbers. Prove that f(x) = 0 has no integer solutions. ...

if b is a real number satisfying b^4 + (1/b)^4 = 6 find the value of (b+ i/b )^16 where i is iota or √(-1). ...

1) If m is a root of the eqn. 4x2 + 2x - 1 = 0, then its other root is given by (a) 4m3 - 3m (b) 4m3 + 3m (c) m - (1/2) (d) -m-(1/2) 2) if a,b,c,p,q,r are six complex numbers, such that p/a + q/b + r/c = 1 + i and a/p + b/q + ...

if we have 18(3t - t3) = 26(1 - 3t2) Then how to factorize it? ...

\hspace{-16}$If $\mathbf{a_{1}\;,a_{2}\;,a_{3},.......,a_{n}}$ are non negative real no., Then find $\mathbf{a_{10}}$ in system of\\\\ equations\\\\ $\mathbf{\begin{Vmatrix} a_{1}+a_{2}+a_{3}+.........+a_{10}=104 \\\\ a_{1}+2 ...

Find the value of- \left( 2+\sqrt{1+\sqrt{2+\sqrt{1+\sqrt{2+...}}}}\right)-\left(1+\sqrt{2+\sqrt{1+\sqrt{2+\sqrt{1+...}}}} \right) ...

prove that for all odd k (1k + 2k + 3k + ... + nk) is divisible by n(n+1)/2. you may use principal of mathematical induction. ...

\hspace{-16}$If $\mathbf{a+b+c=1}$ and $\mathbf{a^2+b^2+c^2=2}\;$\\\\ Then Range of $\mathbf{a^4+b^4+c^4}$ ...

if x+y+z = 1 and 2xy - z^2 = 1 solve for x, y ,z. here x, y, z are real numbers... ...

Show that (x-2) (x-3) (x-4) (x-5)+2 is always positive ...

Q1. The locus of extremities of the latus rectum of the family of Ellipse b^{2}x^{2}+y^{2} =a^{2}b^{2} . Q2. Total no. of divisors of m=3^{5}5^{7}7^{9} that are of the form (4k+1) is equal to 2.P!. Then P is. Q3. Consider a l ...

i have a doubt in finding Min. value of point MA+MB where M(x,0) and A(3/2,1) and A(3/2,1) my Confusion is that why We can not take MA+MB>=AB and answer given is take Image of A at A(3/2,-1). Then find MA'+MB>=AB and pl ...

\hspace{-16}$Find Complex no. $\mathbf{z}$ which satisfy\\\\ $\mathbf{\mid z \mid+\mid z-25 \mid+\mid z-18-24i \mid+\mid z+7-24i \mid=70}$ Ans:: z=9+12i ...

If a + b + c = 0 then find the value of 7(a2 + b2 + c2)2 (a3 + b3 + c3)/a7 + b7 + c7 ...

\hspace{-16}$Solve for $\mathbf{x}$\\\\ $\mathbf{x+\sqrt{11+\sqrt{x}}=11}$ ...