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QUES.1 A metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of eual mass and radius 4a . The cente of the shell falls on the surface of the inner sphere .find the gravitational field at the po ...

Given x0>0 and a>0, show that there exists one and only one sequence {x0, x1, x2,...) such that x_n = \sum_{j=n+1}^{\infty} x_j^a ...

1) If (1-x)n = C0 - C1x + C2x2 -..... + (-1)nCnxn, then the value of C0 - C1 + C2 - .... + C100 is, where n>102 a) 0 b) nC101 c) n-1C101 d) 2nC100 ...

Find all continuous functions f, g, h : R → R for all real values of x and y satisfying the functional equation f(x + y) = g(x)+h(y) . ...

A reversible heat engine takes heat from two sources of 600k and 900k, does work equal to 150 joules and rejects 120 joules of heat into sink at temperature of 300k, find the heat supplied by individual sources? ...

If f be a periodic function as well as an odd function with period p and and x belongs to [ -p/2, p/2] Prove that ∫f(t)dt (lower and upper limits are a and x resp.) is periodic with period p. In the solution, there is a ste ...

1) Find the domain of f(x) = cos^{-1}\sqrt{log_{[x]}(\left|x \right|/x)} ...

*Image* we need to find the equivalent resistance b/w A and B. ...

1. \int \frac{dx}{tanx+secx+sinx+cosx+cotx+cosecx} 2. U_{n}=\int_{0}^{1}{x^{n}\left(2-x \right)^{n}dx}, V_{n}=\int_{0}^{1}{x^{n}\left(1-x \right)^{n}dx} ; prove\ \right| that\ \right| U_{n}=2^{2n}V_{n} ...

If x,y,z are the roots of 7x3-x-2=0, then the value of Σ(x/y+ y/z) is _____________. (ans= -3) ...

1) prove \lim_{x\rightarrow 0} sin x / x =1 by squeeze theorem. 2)prove that all roots of e^x [ d^n/d x^n(x^n/e^x)] are positive 3) prove that e is irrational. ...

what is 100 + 110 ? cant we say its 210 ? 110 also has 2 s.f right ? the rule is that ans should be having same s.f as min. s.f num .. this is the result given by wiki --- http://en.wikipedia.org/wiki/Significance_arithmetic ...

1) if A(1,-1,3) B(2,1,-2) C(-5,2,-6) are the vertices of a triangle ABC , then the length of internal angular bisctor of angle A is?? 2)the median AD of triangle ABC is bisected at E and BE meets AC at F then AF:FC ??? 3)if x ...

*Image* from arihant ,circles ...

Draw the graph of f(x)=x+1/x ...

\int\frac{cos7x-cos8x}{1+2cos^2x}dx ...

\frac{2}{log_{4}(2000)^{6}}+\frac{3}{log_{5}(2000)^{6}} ...

Find the square of the sum of the roots of the eqn log_{3}x .log_{4}x.log_{5}x=log_{3}x.log_{4}x+log_{4}x.log_{5}x+log_{3}xlog_{5}x ...

Find x satisfying the eqn log 4 +(1+\frac{1}{2x})log3 = log(\sqrt[x]{3}+27) ...

Prove that \int_{0}^{n\Pi}{\left|\frac{sinx}{x} \right|}dx < \frac{2}{\Pi}\left(1 + \frac{1}{2} + \frac{1}{3} + ......\frac{1}{n} \right) ...

\int_{0}^{\frac{\Pi }{2}}\frac{dx}{1+cos^{2}x} In arihant, he divides Nr and Dr by cos2x which is absurd as it would be like dividing by 0 as cos2(90) =0 (90 is in the domain of x) Secondly, after this step, the integrand is ...

Hello friends...i filled the bits form today...i have a doubt...do we have to send anything else other than APPLICATION FORM and PHOTO ?? Any marksheet ?? ...

Basic Graph (for beginners) Draw the graph of x4, x3, x2 and x on the same sheet of paper. ...

Evaluate \int_{-1}^{0}\frac{dx}{x^{4}-x^{2}+1} ...

You attach a weight to a vertical fixed spring and release it from rest. When the weight reaches its lowest point, its velocity is zero. So a=dv/dt = 0 But if you apply equation of S.H.M. i.e. a = -Ñ¡2x, x (displacement from ...

this is an easy but nice question... Suppose a car starts from a point A and reaches a point B after time t .The car has definite velocity (which may be variable or constant but it is defined) all through the journey. Let V b ...

Σ(n=2 to n→∞) ((n^4+3n^2+10n+10))/((2^n)(n^4+4)) ...

$Calculate $\int_{\frac{1}{2}}^{2}\frac{1}{(x^2-3x).(x^{2010}+1)}dx$ ...

1. two integers x and y ar drawn (without replacement) out of set (0,1,2,3,---,10) find the probability that -5<x-y<5? 2. Two natural numbers ( x and y) ar choosen at random. What is the probability that x^2 + y^2 is di ...

*Image* *Image* A cylindrical vessel of area of cross section A and filled with liquid to a height of h1 has a capillary tube of length l and radius r protruding horizontally at its bottom.If the viscosity of liquid is \eta a ...