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Let no. of moles of ethanol be x and no. of moles of water be y. therefore, (x)/(x+y) = 1/4. on solving this, we get, 3x=y. One mole of ethanol = 46 gm. One mole of water = 18 gm. If we take one mole of ethanol we must take 3 moles of water from the above equation i.e., 18 * 3= 54 gms of water. hence, % conc. of ethanol by weight will be, [46/(46+54)]*100 = 46%. So, answer is c) 46%.

U can substitute 0 for x nad y turn by turn and find relations. Also u can apply differentiations. All these methods varies from problem to problem. U can also use integration in some kind of problems. It will be better if u give some problem.

PV=nRT-ideal gas equation. When for any two gases P,V,T are constants, ‘n’ will be same for both of the gases. So, if no. of moles are same, no of molecules of that gas will be same.

We do not consider friction when an object is ompletely at rest with respect to the body with which it is in contact. But we consider friction when the object has a tendency of motion with respect to the body with which it is in contact. While drawing the free body diagram, generally, we consider the whole mass of the body to be concentrated at the centre whatever be the area of the object where its mass is distributed. Friction will be more on rough surfaces since it obstructs the tendency of motion. The value of co-efft of friction is never greater than one.

Its the second law of motion where force is defined. But as Ankit said newton’s first and third law could be derived from second law.

Cumene is 2-phenyl propane. It exists only in one form.

No it’s not the correct answer. substitute x= a+h. As x tends to a ‘negative’, h tends to 0. hence, lim as h tends to 0 ( -(a-h)^{3/a – [1 – h/a]}3) = -a^{2-1. so, ans is -a}2-1.

Conservative force is that force which is independent of the path followed.When the final and the initial point are same, u can say that net force is zero. When an object moves from one point to another, conservative force changes the potential energy by an amount independent of the path taken by it. In other words, u can say that this types of forces conserves mechanical energy of the body. Eg:- Gravitational force, spring force, etc., while forces such as frictional force are non-conservative forces.

Indicate whether the wire is charged. Also indicate whether the wire forms a circular loop, semi-circular, straight, finite or infinite.

I agree with Sureshbala Sir.

The slope of the line parellel to x-axis is considered to be 0. The slope of the line parellel to y-axis is not defined or infinity. Their product is not obviously ‘-1’. That’s it!

You have to specify the alkyl groups also, to check about the, inductive, hyperconjugation and other related effects. It will be better if you move on with a specific example bcoz there is no hard and fast rules for determining the stability. There are several effects to be considered while deciding stability. Also, stability is a relative term.

a<0, x is tending to ‘a’ negative, There is a greatest integer function in the question, then how did u get ‘0’ as the answer? Pls explain.

In this Integration, since the limits are 1/2 and 2, i.e, reiprocal of each other & also, 1/x & x are coming, we substitute x=1/t. Let the question be ‘I’. After substituting x=1/t and simplifying (take care of the limits, it will change from 2 to 1/2, & dx= 1/t^2 dt),we get I = -I, hence, 2I=0. so, I=0.

integrn 0 to x; f(x)sintdt = Const., i.e, f(x)* integrn 0 to x;sintdt = const., i.e, f(x)(1-cos x) = const., hence, subst ‘pi’ in above eqn, we get, f(pi)2 = const., but f(pi) = 2, so, const = 4., subst ‘pi/2’ in old eqn once again, we get, f(pi/2)*1 = const = 4., so, f(pi/2) = 4.

When u talk about mono substituted or disubstituted, u can only analyse the stability only if u know the nature of the substituted groups i.e whether they exert + or – inductive effect, hyperconjugation and many such effects. so pls specify the prblm with an example. there is no general rule for the stability of mono or di substituted alkene until and unless the substituted groups are known.

It just burns out. The remains float in the outer atmosphere.Many such remains is a cause for new type of pollution which is the space pollution. It also causes disturbance in launching of new satellites.

Annie Besant, she led the Indian National Congress. But was she an Indian?

Annulenes are cyclic organic compounds which have alternate single and double bonds. The no. attached in the naming of these annulene is the no of carbon atoms present in the ring. for eg., benzene is a annulene having 6 carbon atoms in the ring. Hence, it is known as 6-annulene. Annulenes may be aromatic, non-aromatic or anti-aromatic. according to Huckel’s rule, aromaticity is shown when there are (4n+2)pi electrons in the ring. In 14 annulene if u see the no. of pi electrons is 14 which satisfies the huckel’s rule. annulene to be ant-aromatic it must satisfy the condition of 4npi electrons in the ring which is not satisfied by 10 annulene. hence, it is non-aromatic.

If F is decreasing odd function then F inverse will be odd and decreasing function. g’(y)=1/f’(x), g(f(x))=x, g(-f(x)) = -x, g(y)= y, g(-y) = -y. Hence odd and decreasing function.