Recently Active Questions

Do vacancies remain in jadavpur and shibpur after 1st phase wbjee counselling. ? I mean, do some students dont report for admission? ...

Two of the squares of a 7X7 checkboard are painted yellow. and the rest are painted green..two color schemes are said to be equivalent if one can be obtained from the other by a rotation of the board...how many inequivalent s ...

*Image* ...

1. A coil with inductance L=0.70H and active resistance r=20Ω is connected in series with an inductance-free resistance R. An alternating voltage with effective value V=220V and frequency ω=314 rad/s is applied across the t ...

The other day i was solving a logical reasoning problem. One of the statement of the problem read as follows: "Consider a two digit INTEEGER x such that the sum of digits is 3" Confusion: We can have x of ±AB form where A an ...

$\textbf{Solve for $\mathbf{x::}$}$\\\\ \mathbf{\sqrt{x+2.\sqrt{x-1}}+\sqrt{x-2.\sqrt{x-1}}=2}$ ...

In a mathematical competition 6 problems were posed to the contestants. Each pair of problems was solved by more than 2 5 of the contestants. Nobody solved all 6 problems. Show that there were at least 2 contestants who each ...

If difference of cubes of two consecutive natural numbers is equal to n2 (n is a positive integer). Prove that 2n-1 is a perfect square. this is not very difficult ...

a circular hole of radius r/2 is cut from a solid sphere of radius r. if the mass of the remaining plate is M ten what is the moment of inertia about an axis through the centre of original sphere, parallel to the hole? ...

A projectile is projected at an angle 60 degrees with the horizontal with velocity 10m/sec from the bottom of the inclined plane.Find the angle of inclination of plane(alpa) such that direction of motion for the particle is a ...

i have options b/w cse and ece....which stream shall i choose? i hav interests in doing mtech in robotix/artificial intelligence from abroad.....please reply............. ...

In how many ways can one go from A to B ,if movement is allowed only the edges, and travelling the shortest distance possible in each case? *Image* ...

shudn't it be 20 %? *Image* thankx ...

Help me frnds. I am struck.the answer requires integral value.but i am gettimg ans in log function. Q. Find (a logbx) if a= 0.2 , b = √5 and x= (1/4 + 1/8 + 1/16+......∞ terms) the options are (A)1 (B)1/2 (C) 2 (D) 4 ...

if 1/6,instead of1/12,mass of carbon atom is taken as relative atomic mass unit then the mass of 1 mole of an atom will:......REMAIN UNCHANGED could someone prove it? ...

we know that the centroid of an isocelous triangle is also the centre of the circle circumscribing it. So if it is so then we can't draw two different isocelous triangles inside a circle with different centroids. ...

*Image* ' find the compressional force on the ring of radius r carrying current i ,in a magnetic field as shown. Ans given is mew0*r*i ...

for 2 circles to intersect in 2 distinct points prove that |r1 - r2| < c1c2 .. ...

find the minimum of (sin2x+3sinxcosx+5cos2x) ...

maths musing is a section in mathematics today(mtg magazine) which has some good iit related mathematics question i have created a pdf of this section and uploaded here ... http://www.scribd.com/doc/56405508/Math-Musing ...

Q. Determine horizontal velocity with which a stone must be projected horizontally from a point P, so that it may hit the inclined plane perpendicularly. The inclination of the plane is θ and point P is at height 'h' above t ...

\hspace{-15}$\textbf{Find Integer solution for}\\\\ $\mathbf{x(x+1)(x+2)(x+3)(x+4)(x+5)=y^2-1}$ ...

$If $\mathbf{\color{red}f(x)=\frac{(x-a).(x-b)}{(c-a)(c-b)}+\frac{(x-b).(x-c)}{(a-b)(a-c)}+\frac{(x-c).(x-a)}{(b-c)(b-a)}}$\\\\\\ Then find $\mathbf{\color{green}\frac{d}{dx}\left(f(x)\right)=}$ ...

\hspace{-16}\bold{(Q)::}\; $Find all Complex no. $\mathbf{z_{1}}$ and $\mathbf{z_{2}}$ in \\\\\\ $\mathbf{z^2_{1}-3z_{2}+5=0}$\\\\ $\mathbf{z^2_{2}-3z_{1}+5=0}$ ...

\hspace{-16}\bold{(Q):(1):}\; \mathbf{\lim_{x\rightarrow 0}\left(\frac{b^{x+1}-a^{x+1}}{b-a}\right)^{\frac{1}{x}}=}$\\\\\\ $\bold{(Q):(2):}\;$If $\mathbf{f(x)=}$\begin{cases} \mathbf{\displaystyle \frac{x^2-1}{x^3-1}}\;\;, & ...

\hspace{-16}(1):\; \mathbf{\int x\sqrt{1+\sin x}dx}\\\\\\ (2):\; \mathbf{\int_{0}^{\pi}\frac{2+2(x+1)\sin x-(x^2+1)\cos^2 x}{\sin x-x\cos x+1}dx}\\\\\\ (3):\;\mathbf{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos^2 x}{(e^x+1 ...

x+iy=(1-i*root3)^100.........x=?y=? ...

In the following figure, the space b/w the glass lenses is filled with water. We have to find the focal length of the system (radii of curvature, refractive indices given) *Image* Now to calculate the focal length of the wate ...

Try this, it's really appealing.... a,b,c>0 Prove the following inequality: ab(a+b)+bc(b+c)+ca(c+a)\ge \sum_{cyc}ab\sqrt{\frac{a}{b}\left(b+c \right)\left(c+a \right)} ...

\hspace{-15}$(1)\;\;::\;If $\mathbf{f:\mathbb{Z}\rightarrow \mathbb{Z}\;,}$ and $\mathbf{f(x)-f(x-1)=x^3}$ and $\mathbf{f(2)=-1}$\\\\ Then $\mathbf{f(x)=}$\\\\ $\mathbf{Ans:\Leftrightarrow f(x)=\left(\frac{n.(n+1)}{2}\right)^ ...