Recently Active Mathematics Questions

\cot^{-1} \frac{y}{\sqrt{1-x^{2}-y^{2}}}=2\tan^{-1} \sqrt{\frac{3}{4x^{2}}-1}-\tan^{-1} \sqrt{\frac{3}{x^{2}}-4} &\\\\ \text{Q. Express the above as a rational integral equation between x and y.} My attempt went dirty after a ...

1. All the three roots of equation x3 –- 3x +1 = 0 lie on the interval (A) [–2, 0] (B) [–1, 1] (C) [–2, 2] (D) [–1, 2] 2. If ax2 + bx + c, a, b, c belog to R has no real zeros and if a + b + c < 0 then (A) c > 0 (B ...

please help me proof this one....The area formed by the three intersecting line y=m1x + c1, y=m2x + c2, y=m3x + c3.......is 1/2 Σ[ (c1-c2)2/(m1-m2) ] how to proof this one??? ...

Q. If the roots of the equation ax2+bx+c=0 , are of the form α/α-1 and α+1/α , then the value of (a+b+c)2 is? [ans - b2-4ac] I got the answer by putting any value of alpha but how to solve it in subjective form ...

Let f(x+a) = 1/2 + f(x) - (f(x))2 and 0<=f(x)<=1 Then prove that period of y=f(x) is 2a . ...

Q . Solve: cos-1 x2-1/x2+1 + tan-1 2x/x2-1 = 2 π/3 I'm getting ± 3 but the book says 3 , 2 - 3 ! [7] ...

$\textbf{The equation $\mathbf{x^4+ax^3+bx^2+ax+c=0,a,b,c\in\mathbb{R}$} }$\\\\ $\textbf{has all real roots . Then Prove that $\mathbf{\sqrt{|1-b+c|}\geq 1+\sqrt{|c|}}$} ...

$\textbf{Solve for $\mathbf{x}$: }$\\\\ \mathbf{\sqrt{12-\frac{12}{x^2}}+\sqrt{x^2-\frac{12}{x^2}}=x^2}$ ...

$\textbf{Solve for $\mathbf{x}$: }$\\\\ \mathbf{\left(sin\;x+\sqrt{1+sin^2\;x}\right).\left(cos\;x+\sqrt{1+cos^2\;x}\right)=1}$ ...

\textbf{Solve System of Equations: }$\\\\\left\{\begin{matrix} \mathbf{\sqrt{x^2+y^2}=z+1} \\\\ \mathbf{\sqrt{y^2+z^2}=x+1} \\\\ \mathbf{\sqrt{z^2+x^2}=y+1} \end{matrix}\right;\mathbf{x.y,z\in\mathbb{R}} . ...

Simplify \left({\sqrt{75}-\sqrt{12}}\right)^{-2/3} ...

1.Consider a circle with centre O.2 chords AB and CD extended intersect at a point P outside the circle.If <AOC=43 and <BPD=18,then the value of <BOD is: a.36 b.29 c.7 d.25 ...

f(x)= xn sinx cosx n! sin((npi)/2) cos((npi)/2) a a2 a3 show that dn/dxn[f(x)] at x=0 is 0.... ...

Prove that for any " x , y > 0 " , x x + y y ≥ x y + y x ...

Explain Lagranges Multipliers with some examples (please ;) atleast giv some q on lagranges multipliers (related to inequality of course) ...

1. Solve the inequality sin x + cos 2x > 1 if 0 ≤ x ≤ π/2 2. For a triangle ABC, it is given that : cos A + cos B + cos C = 3/2. Prove that the triangle is equilateral. ...

3 . *Image* " a r , b r and c r" are three sequences of real numbers . ...

\mathbf{\int_{0}^{1}\frac{1}{(1+x^{2011}).\sqrt[2011]{(1+x^{2011})}}dx}$ ...

$\textbf{If $\mathbf{z_{1}}$ and $\mathbf{z_{2}}$ are two distinct Complex no. such that $\mathbf{|z_{1}|=|z_{2}|}$\\\\ and $\mathbf{Re(z_{1})>0}$ and $\mathbf{Im(z_{2})<0}$.Then find value of $\mathbf{\displaystyle \fr ...

$If $x,y,z$ are real no. such that $\left\{\begin{array}{c} x+y+z=2\\ x^2+y^2+z^2=16\\ xyz=1\end{array}\right.$ .\\\\\\ Then Calculate value of $\displaystyle \frac{1}{xy+2z}+\frac{1}{yz+2x}+\frac{1}{zx+2y}=$ ...

$\textbf{Calculate value of $\mathbf{x}$ in }$\\\\ \mathbf{\left[\frac{x}{1!}\right]+\left[\frac{x}{2!}\right]+\left[\frac{x}{3!}\right]+.................+\left[\frac{x}{2007!}\right] = 1005}$\\\\ \textbf{Where $\mathbf{\left ...

[log {(log a)/(log b)} x (log b) / (log a)] / log {(log b)/(log a)} ...

how to integrate cosec ^3 x w.r.t x? ...

summation r=1 to r=101 of, (r)*(101-r)c50 ...

Q. Evaluate: \lim_{n\rightarrow \infty}\frac{[1^{2}x]+[2^{2}x]+[3^{2}x]+ ...+[n^{2}x]}{n^{3}} , [.] \; is \; G.I.F ...

*Image* ...

If in an AP,the sum of m terms is equal to sum of next n terms as well as sum of next p terms,then prove: (m+n){(1/m) -(1/p)}=(m+p){(1/m)-(1/n)} My attempt: from given information we can say that 2m{2a+(m-1)d}=(m+n){2a+(m+n-1 ...

$\textbf{If $\mathbf{S=(sin\;x+sin\;2x+sin\;4x)^5 -(-sin\;x+sin\;2x+sin\;4x)^5-(sin\;x-sin\;2x+sin\;4x)^5-(sin\;x+sin\;2x-sin\;4x)^5$}}$\\\\ $\textbf{Then Calculate value of $\mathbf{S}$ at $\mathbf{x=20^0}$}. ...

$\textbf{Find Max. and Min. value of the expression}\\\\ $\mathbf{f(x)=\sum_{k=0}^{27}\left\{^{27}C_{k}.\left(\frac{x}{100}\right)^k}.\left(\frac{100-x}{100}\right)^{27-k}.\left(80k-23x\right)\right\}$.\textbf{Where} $\mathbf ...

There are n children on a merry-go-round. They' decide to change places so that somebody else is in front of each one. In how many ways can they achieve this? ...