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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] ...

find the result of the sum of the following sin3x+ sin33x2 + .........∞ 32 ...

to all the users who are here this site is running today and it is running only because of its three pillars 1) kaymant alias anant kumar sir 2)nishant sir 3) theprophet alias bhatt sir our sirs have helped in many healthy di ...

1. A small 10W source of ultraviolet light of wavelength 99nm is held at a distance 0.1m from a metal surface. The radius of an atom of the metal is approximately 0.05nm. Find a) the average number of photons striking an atom ...

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 ...

Four snails having velocities different in magnitude and direction move in a plane. Out of six encounters possible,five have already taken place. If it is given that the line paths of any three are non concurrent and they mov ...

\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! ...

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*Image* Two rods of length 'L' are connected as shown in figure.the rods rotate about the two hinges and are connected by a third hinge The angular velocity of the horizontal rod is ω find the angular velocity of the vertica ...

*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} } ...

A hammer weighing 2.5 kg is moving with a speed of 1m/s strikes the head of the nail driving it 10 cm into the wall. The acceleration during impact and the impulse imparted to the wall will be respectively.......... ...

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

The accleration of a particle moving rectiliearly varies with the magnitude of its velocity as a = -√v Find the displacement time equation. i don't hav the answer... so pls provide me with the answer.... ...

Try to get a result of 44 by using the 4 basic operations...addition subtraction multiplication and division. U can use only 6,7,8,9 (ONLY ONCE) and the operations any number of times! Source IIT BUZZWORD. I tried a lot...!! ...

i am thinking to take test series or aits of fiitjee is it good actually i wnt to test my percentile among all which institute friends do you prefer fiitjee or any other ......... ...

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

can anyone provide me the relation of how to find a potential diff at 2 points when no current is provided no velocity is given only resistance and B is provided ? ply do reply ...

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 ...

*Image* what is the steady state charge on the capacitors?? pls describ in details...thanx, ...

A car is travelling at 5m/s. Another car in the parking lot just 11m ahead of the first car starts at an acceleration of 1 m/s2. At what time will both of them meet? ...

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 $(x-1).p(x)+1=x.p(x+1)$ ...