Recently Active Questions

\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} ...

\hspace{-16}$For $\mathbf{a\;,b>0}$. Evaluate the Integral\\\\ $\mathbf{\int_{0}^{\infty}\frac{e^{ax}-e^{bx}}{x.(e^{ax}+1).(e^{bx}+1)}dx}$ ...

\hspace{-16}$The Solution of the Inequality\\\\ $\mathbf{(\cot ^{-1}x).(\tan^{-1}x)+\left(2-\frac{\pi}{2}\right).\cot^{-1}x-3\tan^{-1}x-3.\left(2-\frac{\pi}{2}\right)>0}$ ...

*Image* *Image* ...

q) 105 mL of pure water (4°C) is saturated with NH3 gas, producing a solution of density 0.9 g/mL. If this solution contains 30% NH3 by weightt , calculate its volume. (Ans. 166.67 mL) ...

\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}$In $\mathbf{\left(0,\frac{\pi}{2}\right)},$ one Solution of $\mathbf{\frac{\sqrt{3}-1}{\sin x}+\frac{\sqrt{3}+1}{\cos x}=4\sqrt{2}}$\\\\\\ is $\frac{\pi}{12}$ and other solution is $\mathbf{\frac{\lambda.\pi}{36} ...

\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}$Let $\mathbf{P(x)}$ is a Quadratic in $\mathbf{x}$ Satisfying \\\\ $\mathbf{P(0)=\cos^3(40^0)\;, P(1)=\cos (40^0).\sin^2(40^0)\;,P(2)=0}$\\\\ Then $\mathbf{P(3)=}$ ...

\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}$Evaluate $\mathbf{\sum_{r=0}^{n-2}2^r.\tan \left(\frac{\pi}{2^{n-r}}\right)}\forall \mathbf{n\in \mathbb{Z}\geq 2}$ ...

\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 \\\\ $\mathbf{\frac{x}{\sqrt{2+\sqrt{3}}}+\frac{y}{\sqrt{4+\sqrt{15}}}=\frac{2}{\sqrt{3+\sqrt{5}}}}$ ...

*Image* *Image* ...

\hspace{-16}\mathbf{\int\frac{1}{(x^2+a^2).(x^2+b^2).(x^2+c^2)}dx} ...

\hspace{-16}\mathbf{\int_{-\frac{1}{2}}^{\frac{1}{2}}\frac{\sqrt{3-4x-4x^2}}{4x^2+4x+5}dx} ...

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. ...

*Image* A force F acts on a block of mass m placed on a horizontal smooth surface at an angle Θ with horizontal. Then (A) If F sinΘ < mg then a = F + mg/m (B) Acceleration = FCosΘ/m when F > mg cosecΘ (C) Accelerati ...

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= ...

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= ...

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= ...

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= ...

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= ...