Messages posted by iitkgp_bipin

Don has done it perfectly.

Since a + 1/a > 2
Similarly b + 1/b > 2, c + 1/c > 2 , d + 1/d > 2

Hence the expression > (2+1)⁴
i.e. expression > 3⁴

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Its a simple AP problem.
For the 1st tree distance travelled is (10+10) = 20 m
For 2nd tree = (15+15) = 30 m
For 3rd tree = 40 m ....................and so on

For the 50th tree he only travels from well to tree and not back to well.
Hence for 50th tree distance travelled = 10 + 49*5 = 255 m

Hence distance travelled upto 49th tree = sum of AP
= (49/2)(2*20 + (49-1)*10)
= 12740 m

Hence total distance travelled = 12740 + 255 = 12995 m

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Please post the correct expression.

Periods of and |sinx| and |cosx| are same i.e.

Hence period of |sinx| - |cosx| is also

.

Period of |sinx + cosx| is

/2.

Hence period of |sinx| - |cosx|
----------------------- is

.
| sinx + cosx |

Lets take example of |sinx|
Its period is

and is an even function.
Then according to u its period should become

which is wrong.

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[sinx] = 0 0<=x<=

= -1

<x<2

Also the period of this function is 2

.

₀

^2*pie [sinx].dx = ₀

^pie 0.dx + _pie

^2*pie (-1).dx = -

Hence I = _[0]

^[2(n-1)pie] [sinx].dx
= (n-1).₀

^2*pie [sinx].dx (since it repeats itself after intervals of 2

)
= (n-1).(-

)

=> I = (1-n)

We

are instructed to answer one query at a time. So please post your other query on a new page.Hope you understand.

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In some of the neutralization reaction MnO₄^- is used as an indicator and the end point is observed by pink colour due to Mn²⁺.
Also Mn²⁺ has 5 unpaired electrons.

Hence Mn²⁺ is not colourless

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Osmotic pressure = CRT
C is the concentration
T is the temperature(constant in this case)

Since their osmotic pressures are equal their concentrations are also equal.
Molarity of NaOH = Molarity of H₂SO₄
                          = Normality/acidity
                          = 4/2
                          = 2 M

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When like plates are connected
V₁ =

₁ -

₂
When unlike plates are connected
V₂ =

₁ +

₂

Hence

₁ = (V₁+V₂)/2
and

₂ = (V₂ - V₁)/2

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When you apply force and torque equations it gives
2F = (M + I/R²).A_cm
For disk I = MR²/2 (negligible thickness)
Hence it gives
2F = (3M/2).A_cm
=> A_cm = 4F/3M
=> A_cm = 4(at+b)/3M

There may be a printing mistake.You have done correctly.

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It should be Na₂B₄O₇

Names are :
Na₂B₄O₇ : anhydrous borax
NaBO₂ : sodium metaborate
B₂O₃ : boron sesquioxide

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a₁ + a₂cos2x + a₃sin²x = 0

=> a₁ + a₂(1-2sin²x) + a₃sin²x = 0

=> (a₁ + a₂) + (a₃ - 2a₂)sin²x = 0

Since its independent of x then coefficient of sin²x is 0.

i.e. (a₃ - 2a₂) = 0

and (a₁ + a₂) = 0

=> a₁:a₂:a₃ = (-1):1:2

Hence infinite triplets are possible.

The extraction of salt from sea water consists of progressive evaporation of brine in large open ponds using solar heat and wind. As the brine evaporates its concentration rises and the constituent salts crystallise in a set order. During this process, the sodium chloride fraction is separated from the brine over a fixed concentration range in a series of flat rectangular ponds and deposits as a uniform crust.

Initially charges on capacitors are CV₁ and CV₂
Let the charges be q₁and q₂ after connection.
When they are connected their potential drops would become same.
=> q₁/C = q₂/C
=> q₁ = q₂
conserving charges gives   q₁ + q₂ = CV₁ + CV₂
Hence q₁ = q₂ = C(V₁+V₂)/2
Energy loss = initial energy - final energy
                  = CV₁² /2 + CV₂² /2 - [C(V₁+V₂)/2]²/2C - [C(V₁+V₂)/2]²/2C
                  = (1/4C)(V₁-V₂)²

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Kepler's 3rd law implies that T² is proportional to R³

Then (T_saturn/T_earth)² = (R_saturn/R_earth)³
=> 29.5² = (R_saturn/(1.5*10⁸))³
=> R_saturn = (1.5)(10⁸)(29.5^2/3)
= 1.43*10⁹ km

Its IUPAC name is (C₆₀-I_h)[5,6]fullerene.
Its trivial name is [60-Ih]fullerene

For A : n=2 m=0(2nd p orbital or s orbital) s=1/2(1st electron in orbital)
Hence A's atomic no. can be 3 or 7.
Hence A can be lithium or nitrogen.

U must specify l values to know rhe exact element.

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Since Hg will conduct electricity as it is metal hence LED will glow in this case.

If it is ocean water then it is a good electrolyte and LED will glow.
But if we use simply water it will not glow.

Mass of solution is 1 kg i.e. 1000 grams
Let A be x grams and B be 1000-x grams in solution
Moles of A = x/241.1 and moles of B = (1000-x)/198.2
Mole fraction of A = [x/241.1]/[x/241.1 + (1000-x)/198.2]
But as per question it is 0.3713
Hence [x/241.1]/[x/241.1 + (1000-x)/198.2] = 0.3713

gives x = 418.0682 gram
Moles of A = x/241.1 = 1.734
Moles of B = (1000-x)/198.2 = 2.936

Hence volume of A = (1.734)(188.2) = 326.339 cm³
volume of B = (2.936)(176.14) = 517.147 cm³

Hence total volume = 326.339 + 517.147 = 843.486 cm³

Since it lies in low frequency band it implies the existence of carbonyl groups in bridged form.

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p

-p

multiple bonding is the sideways overlapping of p orbitals when p orbital of one atom overlaps with p orbital of another atom.

Catenation is the ability of a chemical element to form covalent bonds with itself, resulting in ring, chain and cage molecules. The element most well known for its catenation is carbon.Carbon has the ability to form both sigma and pi bonds to itself. This is due to an overlap between pi-electron orbitals, allowing electron density to be shared and thus stabilising the bond.Silicon on the other hand has negligible overlap between pi-orbitals, and thus tends to not form pi-bonds by preference. As a result, silicon has a relatively poor capacity for catenation.

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