are u sure the question is correct? in which book did u find it?

Series combination - whenever 2 plates of a capacitor are joined to each other with no circuit element in between except battery.

Parallel combination - whenever one plate of 2 or more capcitors are joined on one side and other plates of same capacitors on the other side.

You can refer to :

http://www.allaboutcircuits.com/vol_1/chpt_13/4.html

Sania, sry but actually the question is not clear.

Is it 4log₉3 + 9 log₂4 = 10 log_x83 ? If yes, then your answer, i.e. x = (83)^1/2

ok aryan.

Q6. See page 154 and read the article ENERGY IN THE ELECTRIC FIELD IN A DIELECTRIC. From expression you get energy density inversely proportional to r⁴.

Q7. Charge on the plates does not depend upon their area. This is because overall charge on capacitor is always zero and so positive or negative charge cannot be in excess.

Q9. The capacitor C₂ has high potential and thus can store more charge ( Q V ). As it stores more charge, thus it has more capacitance. Thus C₂ > C₁.

ok aryan.

Q6. See page 154 and read the article ENERGY IN THE ELECTRIC FIELD IN A DIELECTRIC. From expression you get energy density inversely proportional to r^-4.

Q7. Charge on the plates does not depend upon their area. This is because overall charge on capacitor is always zero and so positive or negative charge cannot be in excess.

Q9. The capacitor C₂ has high potential and thus can store more charge ( Q V ). As it stores more charge, thus it has more capacitance. Thus C₂ > C₁.

fof(x) = x

or, f [ f (x) ] = x

or, f ( a x / x + 1 ) = x

or, a²x / ax + x + 1 = x

or, a²x  =  ax² + x² + x

or, a² - ax - ( x + 1 ) = 0

So, a = x + ( x² + 4x + 4 )^1/2 / 2 = x + (x + 2) / 2

So, a = x + 1, or a = -1

Yeah, there is a way if u like it. you can apply cramer's rule used widely in determinants but yeah with some modifications. You can refer any maths competition book for it.

sry, i don't know the answers. i have solved 1.(d) and 3.(a). But still i am not been able to solve the sond question. Plz someone reply. By the way,bhavesh how u solved these questions. plz post the proper solutions. thnx anyways.

dude, read that full sentence.

It may be remembered that first member of alkene series is: CH₂ (replacing n by 1 in C_nH_2n) known as methene but has a very short life. Carbon has valency 4 and hydrogen 1. So, this is not stable. So, we start the alkene series form stable member i.e. ethene CH₂=CH₂.

Methylene radical is the bivalent radical CH₂ derived from methane.

dude, read that full sentence.

It may be remembered that first member of alkene series is: CH₂ (replacing n by 1 in C_nH_2n) known as methene but has a very short life. Carbon has valency 4 and hydrogen 1. So, this is not stable. So, we start the alkene series form stable member i.e. ethene CH₂=CH₂.

Methylene radical is the bivalent radical CH₂ derived from methane.

log (21 + 21i) = log | 21 + 21i | + i arg (21 + 21i)

                         = log 21(2)^1/2 + i (/4)

α = log₂18 / log₂12 = 1 + 2log₂3 / 2 + log₂3

β = log₂54 / log₂24 = 1 + 3log₂3 / 3 + log₂3

You can now just assume that log₂3 = t,

So, αβ + 5(α-β) = (1 + 2t / 2 + t) + (1 + 3t) / (3 + t) + 5 [ (1 + 2t / 2 + t) - (1 + 3t / 3 + t) = 1

Hence, Proved.

sry rachit i didn't read that repetition is not allowed. the answer is 179 then as in the second answer post.

399 numbers. Apply permutation and combinations or just see even if u don't know dat

b/w 1-100 there r 4 numbers divisible by 25, same in 100-200 and so on. So, till 10,000 it becomes 4 X 100 = 400. But numbers r to be less than 10,000. so 10,000 is excluded and we r left wid 399 numbers.

Use cosa + cosb + cosc = 1 + 4 cos( a + b / 2 ) cos( b + c / 2 ) cos( a + c / 2 )

Now, ur answer would cum out to be

1 + 4 sin(a/2) sin (b/2) sin(c/2) as a + b + c = 180^o

Use conditional identities!

There is something missing in the question and that is the order of determinant. I might be 3 i suppose. then use

| Adj A | = | A | ^n-1 where n is the order of determinant.

Here | Adj A | is the determinant formed by cofactors.  Remember | A^T | = | A |

a = log₂18 / log₂12 = 1 + 2log₂3 / 2 + log₂3

b = log₂54 / log₂24 = 1 + 3log₂3 / 3 + log₂3

You can now just assume that log₂3 = t,

So, ab + 5(a-b) = (1 + 2t / 2 + t) + (1 + 3t) / (3 + t) + 5 [ (1 + 2t / 2 + t) - (1 + 3t / 3 + t) = 1

1. If w = z / [ 1 - (1/3)i ] and |w| = 1, then z lies on:
(a) circle (b) ellipse (c) parabola (d) straight line

2. sin^-1{(z-1)/i}, where z is non-real, can be the angle of a triangle if
(a) Re(z) = 1, Im(z) = 2
(b) Re(z) = 1, -1 < Im(z) < 1
(c) Re(z) + Im(z) = 0
(d) None of these

3. If A + iB = C tan (x + iy), then tan2x =

(a) 2CA / C² - A² - B²   (b) 2CA / C² + A² + B²   (c) 2CA / C + A + B   (d) none of these

Hey Hemant, i would give u an advice, ok? go and say the same words to ur mom. and see wat she would have to say to you. u'll get my reply.