Recently Active Mathematics Questions

f(x)=ax3+bx2+cx+dsin x. Findthe condition that f(x) is always injective function. 2. Let f: X→Y be a function defined by f(x)= a sin(x+pi/4)+b cos x+c.If f(x) is bijective,find X. ...

\hspace{-16}$If $\mathbf{f:\mathbb{N}\rightarrow \mathbb{R}}$ be a function such that $\mathbf{f(1)=\frac{2007}{6}}$ and \\\\\\ $\mathbf{\frac{f(1)}{1}+\frac{f(2)}{2}+\frac{f(3)}{3}+.........+\frac{f(n)}{n}=\frac{n+1}{2}.f(n) ...

\hspace{-16}$Determine all Positive Integer that satisfy $\mathbf{\frac{1}{x}+\frac{2}{y}+\frac{3}{z}=1!}$\\\\ ...

If the function f:R→A given by f(x)= ex-e-|x|/ex+e|x| is surjectoon then find A. ...

f\left(x \right)=\cos \left(\frac{\Pi }{x} \right) then prove that f(x) is increasing in the interval \left(\frac{1}{2n+1} ,\frac{1}{2n}\right) n\epsilon N ...

Here are the problems of RMO 2011 *Image* Source: Mathlinks. ro ...

how to use latex? ...

\hspace{-16}$The no. of solution of the equation $\mathbf{ae^x=1+x+\frac{x^2}{2}}$\\\\ Where $a>0$ ...

\hspace{-16}$If $\mathbf{n}$ be a Positive Integer Then Prove that\\\\\\ $\mathbf{\frac{1}{\binom{2009}{1}}+\frac{1}{\binom{2009}{2}}+\frac{1}{\binom{2009}{3}}+..............+\frac{1}{\binom{2009}{n+1}}<\frac{1}{2007}}$ th ...

\hspace{-16}$Find all positive Integer $\mathbf{x\;,y\;,z}$ such that \\\\ $\mathbf{x!=4y!+10z!}$ ...

\hspace{-16}$find minimum value of $f(\theta)=a\sec\theta+b\csc\theta$\\\\ $0 <\theta<\frac{\pi}{2}$ ...

Evaluate the following integral: ∫ √cos2x/sinx dx Plz show me the steps also. ...

Prove that for $$a,b,c>0$$ $$\frac{1}{2a^{2}+bc}+\frac{1}{2b^{2}+ca}+\frac{1}{2c^{2}+ab}\leq \left( \frac{a+b+c}{ab+bc+ca}\right) ^{2}.$$ ...

C1,C2 and C3 are 3 tangent circles, these circle tangent to a line too. If the radius of C1 is 9 and radius of C2 is 4. Find the raduis of c3. ...

Find range: f(x)= sin2x+sinx-1/sin2x-sinx+2 ...

Let x,y be two nonzero real numbers with a,b real show that : a2| x/y |+b2| y/x |≥2ab ...

If x,y>0 show that : 1/x+y < 1/x + 1/y ...

1) Find the total no.of +ve integral solutions of the inequality 3x+y+z<= 30.. Can a student not knowing multinomial theorem solve this Problem?? ...

For which of the following, y can be a function of x? 1. x4=y2 2.y=(log x)2 ...

Q.1. In a Triangle ABC, the bisector of angle A meets the opposite side at D. Using vectors Prove that BD : DC = c : b. Q.2. The vector (-1,1,1) bisects the angle between the vectors C(x,y,z) and (3,4,0). determine a unit vec ...

How many times does the Number 5 appear in front of you when you start writing numbers from 1 to 105 in a row..???? ...

if you have infinite no of Rs.10,20 nd 50 notes....in how many ways can u give a person Rs.1000? i tried dis... getting to find the no of integral solutions to a+2b+5c =100 how to proceed after this? ...

1) Find the value of limit |x|[cosx] where x tends to 0.. [.] is the Greatest integer function.. 2) Find the value of limit (xy-yx)/(xx-yy) where x tends to y. 3) Find the solution of 2x+2|x|>= 2√2. Please provide the pr ...

If \vec{a},\vec{b},\vec{c} are non-co-planar unit vectors such that \vec{a} x ( \vec{b} x \vec{c} ) = (\vec{b}+\vec{c})/(\sqrt{2}) , \vec{b} and \vec{c} are non parallel, then find the angle between \vec{a} and \vec{b} . ...

Q.1 Four dice are rolled once. Find the number of ways in which one die shows at least 3. Q.2 A die is rolled 10 times. Find the number of ways so that the outcomes always contain 1,2,3. ...

Q1:f(x)=(-1)[x] is even or odd?[.] is GINT. Q2: If f:[-20,20]→R given by f(x)=[ x2/a ]sin x+cos x is an even function.then find a.[.] is GINT. ...

There are exactly two linear functions,which map[-1,1] onto [0,3].Then find the point of their intersection. ...

Determine whether the following function is even or odd f(x+y)+f(x-y)=2f(x)f(y). f(0)≠0.x,y are reals. ...

Find the range of the following Q1: [sin2x]-[cos2x] .[.] is GINT functiion. Q2:sin-1[x2+0.5]+cos-1[x2-0.5] .[.] is GINT. ...

f(x)= sinx-cosx+√2/x1.5 for pi/4 ≤x≤ 5pi/4 . if M is maximum value of f(x) and m is minimum value of f(x) , find [ 2M/5m ] , where [ ] is box function. ...