Recently Active Mathematics Questions

List all solutions of the system of equations with positive real numbers: x2+y4=16 x2+z2=4+xz y2+z2=4+yz√3 Please give a legitimate solution. ...

\hspace{-16}$Evaluate $\mathbf{\cos (a).\cos (2a).\cos(3a).........\cos(999a)=}$\\\\ Where $\mathbf{a=\frac{2\pi}{1999}}$ ...

$Solve The equation $\mathbf{\sin^{10}x+\cos^{10}x=\frac{29}{16}\cos^4(2x)}$ ...

Given two straight lines. Can you show a bijective mapping of one onto the other? ...

y = x2 + ax + 1 is a parabola. its tangent @ the point of intersection at the y axis also touches the circle x2 + y2 = r2 . given tht no point of the parabola is below the y axis. find maximum value of 'r' ...

1. Show that x^2>(1+x)[ln(1+x)]^2 \text{ } \forall\text{ } x>0 2. Let a+b=4, where a<2 and let g(x) be a differentiable function. If dg/dx >0 for all x, prove that \int_{0}^{a}{g(x)dx}+\int_{0}^{b}{g(x)dx} increas ...

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$Solve Diff. equations $\frac{dy}{dx}=\frac{3x+x^2y}{y+x^2y} ...

\dpi{120} \hspace{-16}(1)::\; $Find acute Angle b/w 2 -Curves $\mathbf{C_{1}:x^2+y^2=8}$ and $\mathbf{C_{2}:x^2+y^2=4x}$.\\\\ (2)::\;Find Least distance b/w the curves $\mathbf{xy=9}$ and $\mathbf{x^2+y^2=1}$. ...

Find \lim_{n\rightarrow \infty}\int_{0}^{1}{}x^{2}e^{-(\frac{x^2}{n^2})}dx ...

\hspace{-16}(1)::\;$Solve for $\mathbf{x\in\mathbb{R}$ in $\mathbf{\mid x^3-1\mid +\mid 2-x^3\mid = 1}} ...

how to find shortest distance between 2 parabolas, 2y2 = 2x-1 and 2x2=2y-1 .. i kind of know how to do this but having some problem in solving it.. can some1 pls solve it completely for me.. my approach: we have to find 2 lin ...

\large \dpi{120} \mathbf{\lim_{n\rightarrow \infty} \frac{\binom{n}{2}}{\binom{7n}{8}}.n^6=} ...

\dpi{120} \hspace{-16}(1)::\; \mathbf{\lim_{n\rightarrow \infty}\frac{\sqrt{n}-\sqrt{n-1}+\sqrt{n-2}-...........+(-1)^n.\sqrt{1}}{\sqrt{n}}} ...

\hspace{-16}(1)::\mathbf{\int e^{\sin x}\left(\frac{x.\cos^3 x-\sin x}{\cos^2 x}\right)dx}\\\\\\ (2)::\mathbf{\int\frac{\sin x.\cos x}{\sin x+\cos x}dx}$ ...

*Image* In the given figure, a chord AB of a circle of 10cm radius subtends a rt. angle at the centre O.Find the area of the sector OABC & of the major segment.(pie=3.14) ...

\large \dpi{100} $\mathbf{Solve for $x\in \mathbb{R}$ in x = 6\left[\sqrt{x}\;\right]+1}$\\\\ $Where $[\;.\;]=$ Greatest Integer function. ...

1) If c be a positive constant and | f(y) - f(x)| ≤ c(y-x)2, then for all real x and y,then a)f(x)=0 for all x b)f(x)=x for all x c)f '(x)=0 for all x d)f '(x)=c for all x 2) If P(x) = x(x+1)(x+2)........(x+2004),then for p ...

This is a good prob from my Xth mathematika... and so i thought of sharing it with u all... *Image* ABCD is a square with each sides equal to 10 cm and in which ABC and BCD are the quadrants where arcs BD and AC intersect at ...

\hspace{-16}(1)\;\;\int\frac{\sin x+\cos x}{\sin^2 x+\cos ^4 x}dx\\\\\\ (2)\;\; \int\frac{\cos x+x.\sin x}{x^2+\cos^2 x}dx asked in goiit ...

the largest value of a for which the circle x2+y2 = a2 lies completely inside the parabola y2 = 4(x+4) ...

Prove this : \lim _{n\rightarrow \infty } \frac{|\sin \theta|+|\sin 2\theta|+...|\sin n\theta|}{n}>0 I must admit that I've its soln. and I'd not have been able to solve it by myself otherwise. But I liked the sum, so flic ...

If 6n tickets numbered 0,1,2,...,6n-1 are placed in a bag, and three are drawn out , show that the chance that the sum of the numbers on them is equal to 6n is \frac{3n}{(6n-1)(6n-2)} Looking for simpler and better ways ...

Let a , b , c possitive real numbers : Show that : a/(b+c)2 + b/(c+a)2 + c/(a+b)2 ≤ 9/4(a+b+c) ...

find the number of non-similar isosceles triangles such that tanA + tanB + tanC = 300. answer is an integer ...

A lighthouse, facing north, sends out a fan-shaped beam of light extending fron north-east to north-west. An observer on a steamer, sailing due west, first sees the light when he is 5 km awayfrom the lighthouse, and continues ...

given, x + xy + y = 2 + 3√2 and, x2 + y2 = 6 Then find the value of |x + y + 1| options are : 1) 1 + √3 2) 2 - √3 3) 2 + √3 4) 3 - √2 5) 3 + √2 This is a good question no doubt...!! ...

*Image* which theorems we hav to use here? ...

Prove that for all real numbers x,y , |cos(x)|+ |cos(y)| + |cos(x+y)|\geq 1 ...