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To the moderator: sorry, it wont happen again. Anyway, i thoguhy it was ok to ask the 2 since they both wont take more than 10secs each.

nunoxic, you are corrrect.but one doubt, is B correct for the second question? isnt OH^- the conjugate base of H2O? I mean, they are a conjugate acid - base pair, but in the opposite order. thanks! can u explain the first question?

1. yes i understood it A and B have a common ion so they can be eliminated. But how do I know whether C is correct or D?

2. thanks

3. Oh, so they will neutralise each other. ok that makes sense. thanks! can u explain question 1 a bit more clearly?

Hi,

1. Which of the following form conjugate acid - base pairs in the right order?
(A) NaCl + NaOH
(B) Borax + Boric Acid
(C) NaH₂PO₄
(D) NH₄Cl + NH₄OH

2. Which of the following form conjugate acid-base pairs in the right order?
(A) NH₃, NH₂
(B) OH^-, H₂O
(C) HCO₃^-, CO₂^-
(D) H₂S , HS^-

Can you please the answer to both the questions? I always thought that a conjugate acid-base differ by a H, but the answers indicate otherwise.

thanks

Hi,

Can you please help me out with these questions?

1. Lead Iodide will have maximum solubility in
(A) 0.1 Pb(NO_3/)₂ (B) 0.2 M NaI (C) 0.2 Na(NO_3/)₂ (D) 0.1 Ba₃(PO_4/)₂

I thoguht that it wont be (A) or (B) PBI2 wont dissasociate as much in these due to common ion effect. But how do I know whether it is (C) or (D)?

2. Which ion cannot be precipitated by HCl and H₂S?
(A) Pb²⁺ (B) Ag⁺ (C) Cu²⁺ (D) Zn²⁺

3. The pair of compounds which cannot exist together in solutions:
(A) NaHCO₃ and NaOH
(B) Na₂CO₃ and NaHCO₃
(C) Na₂CO₃ and NaOH
(D) NaHCO₃ and NaCl

thanks for your time.

Hi,

I have a few doubts regarding the role of friction when considering rotating body.

1) If the body is purely rotating on a surface, does friction do any work?

2) While writing the equation of motion (linear, i.e Fnet = ma) should I include the frictional force?

3) I know friction produces the torque required for rotating the object, so the torque due to the frictional force needs to be taken into consideration while writing the torque equation right?

sorry for late reply.

n is 4..

hint : C(n+r-1,r) is the number combinations of 'n' objects taken 'r' at a time when each may occur once, twice, or thrice.. or 'r' times in any combination.

well this is the coefficient method if I got u right..

C(n+r-1,r) gives the number of solutions only when

AND

...

Thus the number of solutions is equal to the coefficient of

in the expansion of

= C(4+2m-1,2m)

got it? the maximum value of each of the terms must also equal the value of 'n' to use that formula.

(by the way my name is abhijith too!)

Let

represent the marks scored in each of the exams.

where

Thus, the number of ways the person can obtain '2m' marks is equal to the coefficient of

in the expansion of

i.e, coefficient of

in

= coefficient of

in

= coefficient of

in

(In the expansion of the first term, the higher powers are greater than 2m and hence, you dont need to consider them)

=

Simply and you get,

=

Do ask if any step above is not very clear.

Hi,

If the expression

is multiplied all together and the terms of the profuct thuis obtained are arranged in increasing powers of 'x' in the form

, prove that the co-efficients of the terms in the product equidistant from the beginning and end are equal.

Please help me out with this problem. thanks.

The terms of the H.P are given by :

Consider any two terms:

. So

.

Hence your sum will be:

edit: replace all the x's with a's.. i didnt notice it previously.

Is it 511? I will explain the solution if it is correct. There is a general method to do this type of problem.

The sum-of-factorials function is defined by

where

is the exponential integral.

is the En Function,

is the real part of

, and i is the imaginary number. The first few values are 1, 3, 9, 33, 153, 873, 5913, 46233, 409113, ...

but why do you need this? I am sure no problem of IIT level would require you to remember the above formula.

sorry sir, I made a mistake while calculating. The condition is invalid. sorry,once again.

Thus, x = 1/5.

Aakriti is correct, a and n can have any value.

edit: corrections as pointed out by sudeep.kumar sir.

if the bulbs are identical, only 1 way.

if they are distinct 10! ways