Recently Active Algebra Questions

find the smallest number that can be represented by a sum of 9,10 and 11 consecutive integers.....? ...

\hspace{-16}$Determine $\mathbf{\mathbb{R}}$eal value of $\mathbf{x}$ in $\mathbf{1+[x]=[nx]}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function and $\mathbf{n\in\mathbb{N}}$ ...

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Find the coefficient of x^{\frac{n(n+1)}{2}-7} in the expansion of (x-1)(x^2-2)(x^3-3) \; \cdots \;(x^n-n) \quad; n\ge8. Help Please! ...

There is a rectangle with m vertical lines and n horizontal lines (taking the edges too). Find the no.of ways in which a pencil can travel from the North-West to the South-East corner going through the shortest possible dista ...

Sn = x + x2 +x4 + ..... +x2n i remeber man111 posting a question some time ago related to this i think when |x|<1 and n→∞ , this sum should be converging which is why i am interested to find the result. plz try this pr ...

In how many ways can a dice be coloured with 6 different colours? Means all the 6 faces should have 6 different colours. there are no other conditions.. ...

Not my Doubt, Just a share : Normals are drawn from Point P with slopes mi (i=1,2,3) to the parabola y2 = 4x. If the locus of P with m1 . m2 = α is a part of parabola itself, then α C1 + α3 C3 + α5 C 5 + ..... equals? ...

Q: If z3+(3+2i)z+(ai-1) = 0 has a real root, then ' a ' lies in the interval (a ε R) : My Ans: (-1,0) , Given answer (-2,3) ...

\hspace{-16}$Find Minimum value of $\mathbf{xy}\;,$ Given that\\\\ \begin{Bmatrix} \bold{x^2+y^2+z^2=7} \\\\ \bold{xy+yz+zx=4} \end{Bmatrix}\\\\\\ Where $\mathbf{x,y,z\in\mathbb{R}}$ ...

If (z+1)^7+z^7=0 , then find \sum_{k=0}^{k=6} \text{Re}(z_k) , where zk are roots of the the given equation. ...

find the remainder when 21990 is divided by 1990? ...

1) Find the sum of [(1/3√4) +(1/3√5) +(1/3√6).............(1/3√1000000)] [.] stans for G.I.F. 3√n denotes the cube root of n. ...

Q) In how many ways can you colour the faces of a cube with six di erent colours, if all the faces are to have a di erent colour ? i am getting 30 . guys, plz try and tell me your answers. ...

6x + 8y = 48 intersects the coordinate axis at A and B respectively. a line L bisects the area and the perimeter of the triangle AOB. where O is the origin. the number of such lines possible is - (a) 1 (b) 2 (c) 3 (d) more th ...

\sum_{0\le i}\sum_{<j\le n} \left(\frac{i}{\binom {n}{i}} + \frac{j}{\binom {n}{j}} \right) = \frac{n^2}{2} \cdot \sum_{r=0}^{n}\frac{1}{\binom{n}{r}} ...

1 + 2w +3w2 +..... nwn-1 find the sum where,w = nth root of unity ...

1.pls explain these a)[-2x/pi]+1/2 = -([2x/pi]+1/2) b)-3≤|[x]|≤2 implies -2≤x<3 2. What is the formula to find number surjections from A to B? 3.If f"(x) = -f(x) and g(x) = f'(x) and F(x) = (f(x/2))2+(g(x/2))2 and gi ...

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1+(2+3)+(3+4+5)+,,,,,,,,,, ...

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Find the remainder when 2202 is divided by 101 . ...

1)If x2-y2-84y=2012,x,y belonging to N,find x-3y? 2)Let S={20,21,22,23,.....210).Consider all positive differences of elements of S.If M is the sum of all these differences,find the sum of the digits of M? ...

prove that [√(4n+1)]=[√n+√(n+1)] for n belonging to positive integers. [.]→ G.I.F ...

1) [x2+2x] = [x]2+2[x] ....Find the real solution set of x. [.] Stands for G.I.F. (INMO 2009) ...

find the least value of x2cot9+y2cot27+z2cot63+w2cot81 if x+y+z+w=5 ...

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Find the value of \sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-....\propto }}}} ? my method... let \sqrt{7+\sqrt{7-\sqrt{7+\sqrt{7-....\propto }}}} =x and {\sqrt{7-\sqrt{7+\sqrt{7-....\propto }}}} =y now, x2=7+y and y2=7-x subtracting the ...

0<x,y<1 , Prove that x^{y}+y^{x} > 1 . ...

\hspace{-16}$Find real values of $\mathbf{x}$ in $\mathbf{x^2-(1+[x]).x+2011=0}$\\\\ Where $\mathbf{[\;.\;]=}$ Greatest Integer function. ...