Recently Active Algebra Questions

\hspace{-16}$The Value of $\mathbf{m}$ for Which the equations\\\\ $\mathbf{(5m-m^2)^2.\sin^2 x-10.\sin x.(5m-m^2)+24=0}$\\\\ Has exactly $\mathbf{\underline{\bold{Three}}}$ Solution in $\mathbf{[0,2\pi].}$ ...

\hspace{-16}(1)\;\; $Total no. of Selecting $\mathbf{10}$ Balls from an Unlimited no. of Identical\\\\ Red, Green and Yellow Balls is =$\\\\\\ (2)\;\; $There are $\mathbf{15}$ Matching pairs of Shocks in Drawer.\\\\ $\mathbb{ ...

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\hspace{-16}$Find Real value of $\mathbf{m}$ .If Given equation have Real solution\\\\\\ $\mathbf{\sqrt{x + 6 \sqrt{x - 9}} + \sqrt{x - 6 \sqrt{x-9}} = \dfrac{x+m}{6}}$ ...

\hspace{-16}$If $\mathbf{x,y\in\mathbb{R^{*}}}$ and $\mathbf{xy\leq 1}$ and $\mathbf{\left(x+\sqrt{x^2+1}\right).\left(y+\sqrt{y^2+1}\right)=1}$\\\\\\ Then $\mathbf{\sqrt{\frac{x}{y}+\frac{y}{x}+6}=}$ ...

\hspace{-16}$If $\mathbf{[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+.......+[\sqrt{x^2-1}]=y}$\\\\ Then $\mathbf{(x,y)=}$ ...

If the probability that there are exactly 4 persons between A and B while seating 15 persons around a round table is p/q (where p and q are in their lowest form), then find p+q? ...

\hspace{-16}$Find no. of Integer Solution $\mathbf{(x,y,z)}$ of the equation\\\\ $\mathbf{x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2=24}$ No solution. ...

\hspace{-16}$Let $\mathbf{(x,y)}$ be Real variables Satisfying $\mathbf{x^2+y^2+8x-10y-40=0}$\\\\ If $\mathbf{a=Max\{(x+2)^2+(y-3)^2\}}$ and $\mathbf{b=Min\{(x+2)^2+(y-3)^2\}}$\\\\ Then find\\\\ (i)\;\; $\mathbf{a+b=}$\\\\ (i ...

\hspace{-16}$The no. of Integral values of $\mathbf{a}$ so that $\mathbf{x^2-(a+1)x+(a-1)=0}$\\\\ has Integral Roots. ...

If the equation x2+ax+6a=0 has integer roots,then the no of values of a is ? i got 4...just verifying if its correct... ...

Q) prove that the img. roots of a quadratic eqn. 'ax2 + bx + c = 0' always occur in conjugate pairs. where a,b,c E R ...

What to do and what not to do in the last month before IIT-JEE http://www.youtube.com/watch?v=Z5-AfiJxjOc&context=C4acfebbADvjVQa1PpcFMQX-FKsRHXxJDA7RTt_k4sN1NL6Iapsuo= ...

\hspace{-16}$Find all Integer pairs $\mathbf{(n,r)}$ for which $\mathbf{\binom{n}{r}=120}$ ...

\hspace{-16}(1)\;\; $If $\mathbf{19!=1216451\underline{a}0408832000}$. Then $\mathbf{a=}$\\\\ (2)\;\; If $\mathbf{34!=95232799\underline{c}\;\underline{d}96041408476186096435\underline{a}\;\underline{b}000000}$\\\\ Then $\mat ...

They say for a quadratic eqn. 'ax2 + bx + c = 0' to have integer roots 'a' must equal 1 and the roots must be rational. Prove that when this happens the roots will have be integers...!! ...

\hspace{-16}$(1)\;\; $\mathbf{4}\;$ married Couple are to be seated on a Round Table\\\\ The No. of ways in which husband and wife are Diagonally Opposite is\\\\\\ $(2)\;\; $The no. of No.,s greater then $\mathbf{50,000}$ tha ...

\hspace{-16}$Solve The equation $\mathbf{[x]^5+\{x\}^5=x^5}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function\\\\ And $\mathbf{\{x\}=}$ Fractional part function. ...

\hspace{-16}$The Complex no. Corrosponding to the point of Intersection of\\\\ Tangents at $\mathbf{(4-\sqrt{5}.i)}$ and $\mathbf{(-\sqrt{5}.i)}$ on the Circle $\mathbf{\mid z-2\mid = 3}$ is ...

\hspace{-16}$The Principle $\mathbf{\arg{(z_{0})}}$ satisfying $\mathbf{\mid z-3\mid \leq \sqrt{2}}$\\\\ and $\mathbf{\arg(z-5i)=-\frac{\pi}{4}}$ Simultaneously is $\mathbf{\theta}$.\\\\ Then value of $\mathbf{\mid z_{0}\mid} ...

\hspace{-16}$Calculate all Real $\mathbf{x}$ in $\mathbf{[x]+[\sqrt{x}]=2x-2}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function. ...

\hspace{-16}$If $\mathbf{\mid z+1-i\mid=\mid \bar{z}+2-3i\mid}.$ Then Find Complex no. $\mathbf{z}$\\\\ with Min. Modulus. and also find Min. Value. ...

\hspace{-16}\mathbf{\sum_{k=0}^{n}\left\{\sum_{r=0}^{k}(-1)^r.\frac{n!.2^{k-r}}{(n-k)!.(k-r)!.r!}\right\}=} ...

\hspace{-16}$Solve for $\mathbf{x}$ in \\\\ $\mathbf{2^x+3^x+4^x+5^x+1=2e^x+3.7^x}$ x=0 ...

\hspace{-16}$Let $\mathbf{a,b,c,d}$ are the Roots of the Quadratic equation \\\\ $\mathbf{x^4+px^2+qx+r=0}$. Then find the equation whose\\\\ Roots are $\mathbf{\frac{ab-cd}{a+b-c-d}\;,\frac{ac-bd}{a+c-b-d}\;,\frac{ad-bc}{a+d ...

\hspace{-16}$Determine The Integer $\mathbf{(x,y)}$ such that \\\\ $\mathbf{\frac{x}{\sqrt{2+\sqrt{3}}}+\frac{y}{\sqrt{4+\sqrt{15}}}=\frac{2}{\sqrt{3+\sqrt{5}}}}$ ...

Prove that \bf{\sum_{r=1}^{m-1} \frac{2r^2-r(m-2)+1}{(m-r) \binom {m}{r}} = m-\frac 1m } . I'm not able to arrange it in any useful form. Kindly help. ...

What is the remainder when 256+3.911+14 is divided by 41? ...

\hspace{-16}$Solve The System of equations\\\\ $\mathbf{x^2+y^2+x+y=18}$\\\\ $\mathbf{\log_{2}x.\log_{3}y=1}$ x=2,y=3 ...

Find the no. of real solutions of 2x4+1402-y4 =0 ...