Recently Active Mathematics Questions

If a1<a2<a3<a4<a5<a6, then equation (x-a1) (x-a3) (x-a5) + 3(x-a2) (x-a4) (x-a6)=0 has: A) three real roots B) a root in (-∞,a1) C) no real root in (a1,a2) D) no real root in (a5,a6) There may be more than on ...

A person has got 15 aquantances of which 10 are relatives. In how many ways he may invite 9 guests so that 7 would be relatives? [I am a beginner so please explain the result] ...

Let H be a finite set of positive integers none of which has a prime factor greater than 3.Show that the sum of the reciprocals of the elements of H is smaller than 3. ...

how many ways can the word VENUS be arranged so that the vowels do not change thein orders?? ...

Solve the equation : cos2x + cos22x + cos23x = 1 for all x ...

\hspace{-16}$If $\alpha,\;\beta,\;\gamma$ be The roots of the equation$ \\\\ \left\{\begin{matrix} \alpha^3+a.\alpha+b=0\\\\ \beta^3+a.\beta+b=0\\\\ \gamma^3+a.\gamma+b=0 \end{matrix}\right.\\\\\\ $Then $a\lpha+\beta+\gamma=$ ...

∫dx 1/sinx + cosx ∫ x2/√1+x3 ∫ sec7x-7/sin2x ∫(1+cot(x+α)cot(x-α)) dx ∫ log(cosx)/cos2x ex-1/(x2-5x+4) please try them! ...

*Image* ...

\mathbf{(1)\;\;\int\frac{1}{\left(\sec x+\csc x+\tan x+\cot x\right)^2}dx} \mathbf{(2)\;\int_{0}^{\pi}\left\{\mid \sin (2010x)\mid}-\mid \sin (2011x)\mid\right\}dx$ ...

If x , y , z are three real numbers not equal to 1 such that xyz=1 show that : x2/(x-1)2 + y2/(y-1)2 + z2/(z-1)2 ≥1 ...

x2+x3≤x+f(x)≤x5-x3 , for value of x near 0, f(x) is: A) -1 B) 0 C) 1 D) none of these ...

$\hspace{-16}\textbf{(1)\;Solve the equation z^4=\bar{z}}:$\\\\ $\textbf{(2)\;If Z\in\mathbb{C}\textbf{\;and $\mid z\mid<\frac{1}{2}.$ Then Show that }}$\\\\ \mathbf{\mid (1+i).z^3+iz\mid<\frac{3}{4} } ...

Let Tn = 1 + 2 + 3 + · · · + n and Pn = T2/T2-1 . T3/T3-1 . T4/T4-1 ....... Tn/Tn-1 Find Pn???? ...

find the integration ......... ∫sin(sin(sin(sin(..........∞........(sinx)))..........)) dx ...

The ends of a rod of length l move on 2 mutually perpendicular lines. Find the locus of the point on the rod, which divides it in the ratio 2:1 ...

find x such that 1+ 1/1+ 1/1+ =x . . 1+ 1/x ...

\hspace{-16}\textbf{Solve the equation for real x}:\\\\ \mathbf{4^x.9^{\frac{1}{x}}+9^x.4^{\frac{1}{x}}=210} ...

\hspace{-16}$Find all Polynomials $p(x)$ such that $(x-1).p(x)+1=x.p(x+1)$ ...

Prove that if n>2,then there exists a prime p satisfying n>p>n! ...

This is a dig from the old threads of TargetIIT which was unsolved. Let f be a continuous function in [a,b]. Prove that there exists c \in \left(a,b \right) such that \int_{a}^{c}{f(x)dx}=\left(b-c \right)f(c) . ...

The least positive integer n for which ( 1+i/1-i )n= 2/π sin-1( 1+x2/2x ) x≥0 ...

A book contains pages numbered from 1 to 50. 4 leaves (i. e., 8 pages) were torn off the book. What is the probability that the sum of the page numbers is 68? ...

find the sum to infinity....1/2.4+1.3/2.4.6+1.3.5/2.4.6.8 ....... ...

\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{1}{\sin^2 x.\sin\left(x+\frac{\pi}{6}\right)}dx=$ ...

prove this... The angle between the two focal radii in a parabola y2 = 4ax is double the angle between the tangents drawn from their end points. ...

1. Let f be defined on [0,1] be a twice differentiable function such that, \left|f''(x) \right|\leq 1 for all x \in \left[0,1 \right] . If f(0)=f(1) , then show that, \left|f'(x)\right|<1 for all x \in \left[0,1 \right] . ...

In mathematics, the Gamma function (represented by the capitalized Greek letter Γ) is an extension of the factorial function to real and complex numbers. For a complex number z with positive real part the Gamma function is d ...

show that the semi-latus rectum of the parabola y2 = 4ax is the harmonic mean between the segments of any focal chord. ...

find greatest integer of the following 1/ 2 +1/ 3 +1/ 4 +.............+1/ 80 ...

if a + 2b + c = 4 then find the max(ab + bc + ac) ...