Recently Active Mathematics Questions

\hspace{-16}$If each side of Square $\mathbf{OABC}$ is $\mathbf{4}\;$unit\\\\ and There are $\mathbf{4}$ Quarter Circle Center at Corrosponding Vertex\\\\ Then Find Area of Region denoted by $\mathbf{\bold{\alpha}}$ and $\mat ...

1)f(x) and g(x) are linear functions for all x such that f(g(x)) and g(f(x)) are Identity functions.If f(0)=4 and g(5)=17 find f(2006)? 2)let f(x)=(x+1)(x+2)(x+3)(x+4)+5 where x belongs to [-6,6].If range of f(x) is [a,b] whe ...

\hspace{-16}\mathbf{\int\frac{x.\sin^2 x}{\cos (2x).\cos^2 x}dx} ...

\hspace{-16}\mathbf{(1)\;\; \int\frac{1}{x+\sqrt{x^2+x+1}}dx}$\\\\\\ $\mathbf{(2)\;\; \int\frac{\sqrt{\sqrt{x^4+1}-x^2}}{x^4+1}dx}$ ...

Tangents drawn from the point P(3,8) to the circle x^2+y^2-6x-4y-11=0 touches the circle at the point A and B . Then equation of circumcircle of a Triangle PAB is I have a doubt:: why PO act as a diameter for Circumcenter of ...

P is an interior point of an equilateral \Delta ABC so that *Image* , and BP and CP meet AC and AB at D and E respectively. Suppose that PB : PC = AD : AE. Find \angle BPC . ...

\hspace{-16}$It is known about real $\mathbf{a}$ and $\mathbf{b}$ that the inequality $\mathbf{a\; cosx +b\;cos3x >1}$\\\\ has no real solutions.then Prove that $\mathbf{\mid b\mid \leq 1}. ...

\hspace{-16}(1)\;\;\mathbf{\int \frac{1}{2x\sqrt{1-x}\sqrt{2-x+\sqrt{1-x}}}dx}$\\\\\\ $(2)\;\;\mathbf{\int\frac{1}{(x+1).\sqrt{1+x-x^2}}dx}$ ...

\hspace{-16}$If $\mathbf{\mid z^2+1 \mid =2\mid z+1\mid }$\\\\ Then find Max. value of \mathbf{z} ...

1)Let a,b,c be roots of the equation x3-3x2+1=0.Find (a-2)(b-2)(c-2)? 2)Suppose f(x)=x3+px2+qx+72 is divisible by both x2+ax+b and x2+bx+a(where p,q,a,b are constants and a≠b).Find the sum of squares of the roots of the cub ...

Prove that \sum_{i=1}^{p}i \binom{p}{i}(n-1)^{p-i} = p n^{p-1} n is real, p is natural number ...

\hspace{-16}$Prove that If $\mathbf{n}$ is an positive Integer Then,\\\\ $\mathbf{\sum_{k=1}^{n}\cos^4\left(\frac{k\pi}{2n+1}\right)=\frac{6n-5}{16}}$ thanks guys now i have edited it ...

\hspace{-16}$Find the First Digit after the decimal point of $\mathbf{\left(2+\sqrt{5}\right)^{2010}}$\\\\ ...

\hspace{-16}$How many Integer $\mathbf{n}$ are there such that $\mathbf{n+20}$ and $\mathbf{n-20}$ are Perfect Squares\\\\ ...

1)If the range of the function f(x) = x2+ax+b/x2+2x+3 is [-5,4],a,b are natural nos,then find the value of a2 + b2 ? 2)Given,x,y belong to reals and x2 +y2 > 0.If the max and min value of the expression x2 +y2/x2+xy+4y2 ar ...

1)Number of ways 10 persons can take seats in a row of 24 fixed seats so that no two persons take consecutive seats is 2)C02 + C12 + C22 + .... + Cn2 = 3)C1+4.C2 + 7.C3 + ... + (3n-2).Cn = 4)Number of integral terms in the ex ...

1) Please do this sum without using Complex no.(Actually this sum can be solved by pure trigonometry...) 1: if theta= pi/1999 then find the value of cos(theta) x cos(2theta) x cos(3theta) x ..... cos 999(theta) ...

Evaluate: ∫01 xa-1/ln x dx ...

1)A(2,5),B(-1,3), and C(5,-1) are the vertices of a triangle. The image of the point (1,2) with respect to the median through A is 2)Equation of the circle passing through (0,0),(4,3) and (-3,4) is 3)The points (5,-4,2),(4,-3 ...

The no. of natural Numbers ≤ 2012 which are relatively prime to 2012 is : ...

If cosα + cosβ + cosγ = sinα + sinβ + sinγ, then prove that i) cos2α + cos2β + cos2γ =0 & ii) sin2α + sin2β + sin2γ =0 ...

Find the coeff. of x15 in the expansion of (1 - x)(1 - 2x)(1 - 22x).............(1 - 215x). Please help me its urgent. ...

\hspace{-16}$If $\mathbf{1\leq x<y\leq 100}$ and $\mathbf{x,y\in\mathbb{Z}}$. Then find the Probability that $\mathbf{i^x+i^y\in\mathbb{R}}$\\\\ Where $\mathbf{i=\sqrt{-1}}$ ...

if roots of the equation x2-10cx-11d=0 are a,b and those of x2-10ax-11b=0 are c,d,then find the value of (a+b+c+d)? ...

The number of distinct terms in the expansion of ( 1/xy + 1/zy + 1/xz +x+y+z)2 and ( 1/z + 1/y + 1/x +x+y+z)2 are? ...

Please see this question here. http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=454883&p=2556669#p2556669 ...

\hspace{-16}$If $\mathbf{a,b\in\mathbb{Z^{+}}}.$ Then prove that $\mathbf{\frac{a}{b}<\sqrt{2}<\frac{a+2b}{a+b}}$ ...

*Image* ...

If p + q = 1, then show that *Image* ...

\hspace{-16}$Find all Integer Roots of the equation\\\\ $\mathbf{\cos\left(\frac{\pi}{10}\left(3x-\sqrt{9x^2+80x-40}\right)\right)=1}$ ...