Recently Active Algebra Questions

Find the greatest integer k for which 1991^k divides 1990^1991^1992 + 1992^1991^1990 ...

\text{Here is an awesome probability question that I solved recently.}\\\text{I know this is quite a popular question so don't just copy-paste it directly from some other site.}\\\text{Try it yourself.It's a really good quest ...

6x+5y=7x+3y+1=2(x+6y-1) AND x+y-8/2 = x+2y-14/3 = 3x+y-12/11 ...

x1, x2, x3 are in GP and y1, y2,y3 are also in GP with same common ratio. then (x1,y1), (x2,y2)&(x3,y3) these are a]vertices of a triangle b]situated on a circle c]collinear d]situated on an ellipse ...

\hspace{-16}\bf{(1)\;\;}$ In how many ways can the letters of the word $"\bf{PERMUTATIONS}"$\\\\ be arranged so that there is always exactly $\bf{4}$ letters between $\bf{P}$ and $\bf{S}$, is\\\\\\ $\bf{(2)\;\;}$ Calculate To ...

\hspace{-16}$ Prove that there exists a power of the number $\bf{2}$ such that the last\\\\ $\bf{1000}$ digits in its decimal representation are all $\bf{1}$ and $\bf{2}$ ...

Ram and Sam are playing a ludo tie-breaker game where the first one who throws a six wins the game.Find the probability of Ram winning the game if :- (a) Ram starts the game (b) Sam starts the game ...

6/5 alog9x+1=22log2x+3 value of X=? ...

\hspace{-16}$(1): The no. of Integer ordered pairs $\bf{(x,y)}$ in $\bf{x^2+y^2 = 2013}$\\\\\\ $(2):$ The no. of Integer ordered pairs $\bf{(x,y,z)}$ in $\bf{\begin{Vmatrix} \bf{x=yz} \\ \bf{y=zx} \\ \bf{z=xy} \end{Vmatrix}}$ ...

\hspace{-16}$Solution of following System of equations is\\\\\\ (1) $\bf{y^3-6x^2+12x-8 = 0}$\\\\ $\bf{z^3-6y^2+12y-8 = 0}$\\\\ $\bf{x^3-6z^2+12z-8 = 0}$\\\\\\ (2) $\bf{2y^3+2x^2+3x+3 = 0}$\\\\ $\bf{2z^3+2y^2+3y+3 = 0}$\\\\ $ ...

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logab=3/2 logcd=5/4 a-c=9 find b-d ...

Find [x]+\sum_{r=1}^{2000} \frac {\{x+r\}}{2000} , where [x] = GIF and {x} = FP. ...

The graph of the function cosx.cos(x+2)-cos^2(x+1) is 1.A straight line passing through (0,-sin^2 1) with slope 2. 2.A straight line passing through (0,0) 3.A parabola with vertex(1,-sin^2 1) 4.A straight line passing through ...

\hspace{-16}$Let $\bf{A = }$ set of $\bf{ 3 \times 3}$ determinat having entries $\bf{1}$ or $\bf{-1,}$\\\\ $\bf{(1)}$ If a determinat $\bf{B}$ is chosen randomly from the set of $\bf{A,}$\\\\ then the probability that the pr ...

\hspace{-16}\bf{(1)}$ The Max. and Min. value of $\bf{3 \times 3}$ Determinant whose element are taken\\\\ from the set $\bf{\left\{-1,1\right\}}$\\\\\\ $\bf{(2)}$ The Max. and Min. value of $\bf{3 \times 3}$ Determinant whos ...

What is the maximum possible value of a positive integer n,such that for any choice of seven distinct elements from {1,2,....n}, there will exist two numbers x and y satisfying 1<x/y≤2? ...

2 , 1/3 ...

which book should i take elementary algebra by hall and knight or higher algebra by hall and knight i am class 11 student ...

How do I solve this: f(x)=cos(logx) find f(x)f(y)-[f(x/y)+f(xy)]/2 ...

The number of real roots of x8-x5+x2-x+1=0 is? a] 2 b] 4 c] 6 d] 0 ...

A four digit number is called doublet if any of its digit is the same as only one neighbor . For example, 1221 is doublet but 1222 is not . Number such doublets are ...

Value of nΣr=1 r nCrxr(1-x)n-r=? a] n b] x c] nx d] none of these ...

If 0<ar<1 for r=1,2,3....k and m be the number of real solns of kΣr=1(ar)x=1 and n be the number of solns of kΣr=1(x-ar)101=0 then a] m=n b] m≤n c] m≥n d] m>n ...

If θi belongs to [0, π/6 ] and z4sinθ1+z3sinθ2+z2sinθ3+zsinθ4+sinθ5=2 then z satisfies a] |z|> 3/4 b] |z|< 1/2 c] 1/2 <|z|< 3/4 ...

If 2 roots of (c-1)(x2+x+1)2-(c+1)(x4+x2+1)=0 are real and distinct and f(x)= 1-x/1+x then f{f(x)}+f{f( 1/x )}= a]-c b]c c]2c d]none of these ...

If x2-4cx+b>0 and a2+b2<ab then the range of x+a/x2+bx+c is a]R- b]R+ c]R d]none of these ...

If f(x)=x3-6x2+(π+1)x+7 and p>q>r then [x-f(p)][x-f(r)]/x-f(q) has no value in a](p,q) b](q,r) c](r,∞) d]none of these ...

probability of solving a particular sum by A,B,C, respectively 1/2 , 1/3 , 1/4 , then what is the probability that the problem can be solved ...

If α be the number of solns of the equation [sin x]=|x|, (where [.] represents greatest integer function) and m be the greatest value of cos(x2+xex-[x]) in the interval [-1,1], then what is the relation between α and m (α ...