Recently Active Mathematics 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}$Let $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ be a Continuous function and $\mathbf{f(x)=f(2x)\forall x\in \mathbb{R}}.$\\\\ If $\mathbf{f(1)=3}$.Then the value of $\mathbf{\int_{-1}^{1}f(f(x))dx=}$ ...

\hspace{-16}$Min. distance b/w $\mathbf{y^2=4x}$ and $\mathbf{x^2+y^2-12x+31=0}$ is ...

\hspace{-16}$The Curve $\mathbf{y=(\mid x \mid-1)sgn(x-1)}$ Divides $\mathbf{\frac{9x^2}{64}+\frac{4y^2}{25}=\frac{1}{\pi}}$\\\\\\ in Two parts having Area $\mathbf{A_{1}}$ and $\mathbf{A_{2}},$ Where $\mathbf{(A_{1}>A_{2} ...

\hspace{-16}\mathbf{\int_{0}^{5}\left[\{\sin^2 x+\cos(\ln (x))+e^{3x}\}\right]dx=}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function\\\\ and $\mathbf{\{x\}=}$ Fractional part function. ...

\hspace{-16}\mathbf{\int_{1}^{2}\frac{1}{\left(\sqrt{2x-x^2}+2\right)^2}dx} ...

\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 $\mathbf{\cos ^n(x)-\sin^{n}(x)=1}$ have $\mathbf{11}$ Roots in $\mathbf{\left[0,\frac{23\pi}{2}\right)}$. Then $\mathbf{n}$ can be ...

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

\hspace{-16}$Min. Area of Circle Which touches the Parabolas $\mathbf{y=x^2+1}$ and $\mathbf{x=y^2+1}$ ...

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}$If $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ and $\mathbf{f(x)=\ln(x+\sqrt{x^2+1})}$\\\\ Then no. of solution of the equation $\mathbf{\mid f^{-1}(x)\mid = e^{-\mid x \mid}}$ is ...

\hspace{-16}$Period of the function $\mathbf{f(x)},$ Where \\\\ $\mathbf{f(x) = \cos^7 (x)+cos^{7}\left(x+\frac{2\pi}{3}\right)+cos^{7}\left(x+\frac{4\pi}{3}\right)}$ ...

\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}$If $\mathbf{I_{1}=\int_{0}^{1}(1-x^4)^7dx}$ and $\mathbf{I_{2}=\int_{0}^{1}(1-x^4)^6dx}$\\\\\\ Then $\mathbf{\frac{29}{4}.\left(\frac{I_{1}}{I_{2}}\right)=}$ ...

\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} ...