Physics, Chemistry, Mathematics Forums

Q.1]  If AD,BE,CF ARE THE MEDIANS OF THE TRIANGLE ABC THEN

AD² + BE²+ CF²\ AB² +BC²+CA² is equal to (a) 4\3 (b)3\2 (c)3\4 (d) 2\3

Q.2] SinA ,SinB, SinC ARE IN  AP FOR THE TRIANGLE ABC ,THEN

(A) the altitudes are in AP   (B)the altitudes are in HP 

(C) the medians are in GP    (d) THE MEDIANS ARE IN AP.

Two liquids of densities 1 g/cm³ and 3g/cm³ are mixed in equal volumes.  A cube of external dimension 20 cm has an inner cubical portion of side 10 cm whose density is twice that of the outer portion.  if this cube is just floating in the liquid mixture, find the density of the inner portion.  if the density of the inner portion is half of this value, what fraction of the volume of the cube will be submerged?

Calculate the capacitance of a parallel plate capacitor with plate area A and distance between plates d, when filled with a dielectric whose dielectric constant varies as

K[x]=e₀ + beta* x , 0<x<d/2

K[x]= e₀ + beta *[d-x]  , d/2<x<d

For what value of  beta would the capacity of the capacitor  be twice that when it is without any dielectric.

My problem is that how should  I introduce the small change in x i.e. dx .

A circle with centre on the positive x- axis and radius 'r' lies completely in the parabola y² = 2008x and touches the parabola at the vertex. Then, the largest value of 'r' is ________.

Ans: 1004

please give the solution, if possible with steps.

( I hope I am not wasting your time, with the JEE round the corner. Sorry if I am.)

Pleeeeeeeeeeeeeeeease someone answer my previous doubt on conics!!!

Can anyone plz solve this question?

A cylinder of radius R is placed between an axle(cylindrical) of radius R and outer coaxial cylindrical shell of rad. 3R. Inner axle rotates anticlockwise with angular vel. 'w' and outer shell rotates also anticlockwise with angular vel. '3w'. If there is no slipping at any contact, find the angular velocity of the intermediate cylinder.

someone plz give the soln. to this question.

A 0.2 mL sample of a soln. containing 1 x 10^(-7) Ci of ₁H ³  is injected into the blood stream of a laboratory animal. After sufficient time for circulatory equilibrium to be established, 0.1mL blood is found to have activity of 20 dis/min. Then the blood volume of the animal is _________.

Ans: 1 L

[.] denotes greatest integer function. The no. of real solutions 'a' satisfying the equation [a/2] + [a/3] + [a/5] = a is _________.

I still have to get the answer (this was a question in a test), but can anyone explain to me how to solve this?

A hemispherical bowl of radius R is rotated about it's axis of symmetry which is kept vertical.Asmall block is kept in the bowl at a position where the radius makes an angle theta with the vertical.The block rotates with the bowl without slipping .The friction coefficient between the block and the bowl surface is w[muu].Find the range of the angular speed for which the block will not slip.

I do not want the answer .I just want to know the direction of friction in minimum angular speed and maximum angular speed.I think that they should be opposite in direction.What do you say,friends?

A ballon is descending at a constant acceleration a.The mass of the ballon is M.When a mass m is released from the ballon it starts rising with accelearation a.Assuming no change in volume of the ballon ,the value of m is

1. 2aM/a+g
2. (a+g\2a)M
3. 2a\(a+g)M
4. Ma\a+g