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If in an AP,the sum of m terms is equal to sum of next n terms as well as sum of next p terms,then prove: (m+n){(1/m) -(1/p)}=(m+p){(1/m)-(1/n)} My attempt: from given information we can say that 2m{2a+(m-1)d}=(m+n){2a+(m+n-1 ...

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$\textbf{If $\mathbf{S=(sin\;x+sin\;2x+sin\;4x)^5 -(-sin\;x+sin\;2x+sin\;4x)^5-(sin\;x-sin\;2x+sin\;4x)^5-(sin\;x+sin\;2x-sin\;4x)^5$}}$\\\\ $\textbf{Then Calculate value of $\mathbf{S}$ at $\mathbf{x=20^0}$}. ...

$\textbf{Find Max. and Min. value of the expression}\\\\ $\mathbf{f(x)=\sum_{k=0}^{27}\left\{^{27}C_{k}.\left(\frac{x}{100}\right)^k}.\left(\frac{100-x}{100}\right)^{27-k}.\left(80k-23x\right)\right\}$.\textbf{Where} $\mathbf ...

The mass density per unit area of each circle is " σ " , and all the surfaces are frictionless . It is also given that the radius of each circle is " R " . Find the force required to keep the two bottommost circles together ...

Q: An interstellar explorer discovers a remarkable planet made entirely of an uniform incompressible liquid of density " ρ ". The radius of the planet is " R " and Accn. due to gravity at surface is " g ". What is the pressu ...

There are n children on a merry-go-round. They' decide to change places so that somebody else is in front of each one. In how many ways can they achieve this? ...

A spherical tank of 1.2m radius is half filled with oil of relative density 0.8. If the tank is given a horizontal acceleration of 10 m/s2. Calculate the maximum pressure on the tank. ...

Consider an arbitrary function f:X→Y. It includes two important set mappings. If A is a subset of X, then its image f(A) is the subset of Y defined by f(A)={f(x) : x ε A}. Similarly, if B is a subset of Y, then its inverse ...

Q: A cone made of insulating material has a charge Q spread uniformly over it's sloping surface. Calculate the work done in bringing a small positive test charge ' q ' from infinity to the apex of the cone. The cone has a slo ...

If tan A=ntanB , sinA=msin B prove that cos2A= m2-1/n2-1 ...

x+y+z=pi (angles of a triangle) show that sin x + sin y + sin z >= 3 3 /2 Solution \frac{\sin x+\sin y+\sin z}{3}\ge(sin x\times\sin y\times\sin z)^{1/3} (AM GM Inequality) Equality holds when all terms are equal.... So si ...

(From Brahmagupta, 7th century A.D.) A girl was carrying a basket of eggs, and a man driving a horse hit the basket and broke all the eggs. Wishing to pay for the damage, he asked the girl how many eggs there were. The girl s ...

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Some beginner will also be able to answer I guess.. So anyone with the answer please help: What will be the difference if I write: #include <iostream> using namespace std; int main() Or, #include <iostream> int ma ...

Is civil engg a boring and laborious branch? ...

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why dont the experts like kaymant help the students here nowadays? ...

what is its significance?how is it useful? ...

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A particle moves along the curve y=x2/2. Here x varies with time as x=t2/2.Where x and y are measured in metres and t in second. At t=2s the velocity of the particle is: (a)2 i - 4 j b) 2i + 4 j c) 4i +2j d) 4i - 2j ...

qwerty had asked for the unofficial iit jee 2011 results here is the link http://captnemo.in/projects/iitjee/2011.html ...

This is a standard question which appears everywhere.... (almost) sin x = 1 + x + x^2 Find the number of solutions.... PS: Am trying to give sometime here daily just by posting the QOD. A promise that I have often failed to d ...

Can anyone and every one post some JEE level problems on BINOMIAL theorom. Thnks! ...

doubt-1: *Image* doubt-2: *Image* in this second doubt i can't understand how we came up with the condition to be satisfied for one root to be sqaure of other? ...

Do we need to memorize all the results of the expansions...mainly in the topic binomial coefficients...??? Which book is better for MATH arihant or TMH??? ...

Suppose we construct a plane such that it only contains points whose ordinates as well the abscissae are integers . Each point of this plane is labeled by a positive integer . Each of these numbers is - 1 > The arithmetic ...

i thought my mouse was not working and clicked on "Add post" several times !!! Extremely sorry....!!! how to delete a post ????? ...