The Students Helpers For IIT, NEET and KVPY |

2021-05-05 08:24:00 It's just hilarious too see how the website is gaining traffic thr day I stopped sharing new content

It all started when this group was made on 14th August 2020 and with a few ups and downs and several shutdowns we reached to 1K family. But then we decided to stop sharing new materials wef 5th January 2021.

In the meantime I made some new friends and I guess many of them have left the group already. Since when I see the members list except a few all are new names. Many of us are now busy in chasing their dreams including me. This year the exams have got postponed and students of next year are trying their level best to impove just make sure you are giving your best.

If you have read the message till here I want to say you a big thank you

Just a small thought in my mind when we finish our exams ( of whichever field) I want you to stay here. I will be back when I am finsihed achieving my goals. ( most probably by next year)

Stay busy with your goals till you acheive them. Stay Safe Stay Happy ओपन / कमेंट

2021-04-20 20:21:36 Sodium

Sodium is a soft, silvery color, and highly reactive alkali metal.
In the periodic table, Sodium is kept in group 1, as it has single electron in its outer shell.
The symbol of sodium is ‘Na,’ which has been actually taken from Latin word ‘natrium.’
In terms of abundance, sodium is the sixth element found in the Earth's crust.
Sodium exists in various minerals including feldspars, sodalite, and rock salt (NaCl).
In 1807, Humphry Davy first isolated sodium by the electrolysis of sodium hydroxide.
By the time, 20 isotopes of sodium are known, but among all, only 23Na is stable.


Salient Features of Sodium
Sodium metal a soft element that be can be easily cut with a knife.
Sodium is a good conductor of heat and electricity.
Because of having low atomic mass and large atomic radius, sodium is one of the least dense elements (third least dense element – first two are lithium and potassium).
Sodium can float on water.
Sodium along its compounds glow yellow (see image below).
Sodium compounds have very high commercial importance and have high demand in the industries of glass, paper, soap, and textiles.


Occurrence of Sodium
The crust of Earth contains about 2.27% sodium.
Sodium is the 5th most abundant metal; other four are aluminum, iron, calcium, and magnesium.
In the oceanic water, about 1.08 × 104 milligrams sodium found in per liter.
Sodium does not found as a pure element, as it is highly reactive.


Uses of Sodium
Sodium chloride is highly useful for anti-icing and de-icing as well as a preservative.
In cooking, sodium bicarbonate is used.
Sodium and some of its compounds are used in medicines.
In comparison to potassium (which is a better ion), sodium is more frequently used because of its lower price and atomic weight.
In organic chemistry, sodium hydride is used as various reactions.
Metallic sodium is principally used for the production of sodium borohydride, sodium triphenylphosphine, azide, indigo, etc.
In some fast reactors, liquid sodium is used as a heat transfer fluid because of having the property of good heat conductivity.
Sodium is also an essential mineral for the human health, as it regulates blood pressure, blood volume, osmotic equilibrium, and pH value.
The minimum amount of 500 milligrams sodium is required every day for a healthy human body. ओपन / कमेंट

2021-04-20 20:13:27 Doubt Discussion Group for Class 12 2022 batch ( especially for Lakshya Jee students )
Group is for serious students only!!
https://t.me/joinchat/Fh4FZ9Pq0LIzNzM1 ओपन / कमेंट

2021-04-19 12:09:15 1. Formulas related to force:
F = ma
F = kx
F = m(vf² - vi²/2S)
F = mv/t
F = md/t²
F = m(vf - vi) /t
F = Area × density × velocity²
F = 1/2 mv²/d
F = 1/2 Pv/d
F = Power/velocity
Fc = mv²/r
Fc = mrw²
Fc/2 = mv²/2r
Fc = 2K.E/r
F = Area × Stress
F = pir² × stress
F = YA × Strain
F = YAl/L
F = pressure × area
F = change in momentum × time interval
F = - 2mVx × Vx/2l
F2 = F1/A1 × A2
F = qE
F = kQ/r²
F = ILB sintheta
F = q (v × B)
F = qE + q(v × B)

2. Formulas related to energy and work
Fd = k.e
mgh = 1/2 mv²
E = 1/2 kx²
E = Ve
E = nhf
E = nhc/lambda
E = Pc
K.e = hf - work function = hf - hf° = hf - hc/w° (here w° is cutt off wavelength)
E = 1/2 Pv
mv²/2r= Fc/2
K.E/r = Fc/2
K.E = Fc×r/2
K.e = 1.5 KT
E = VQ
E = Power × time
E = Fvt
% loss in K.e = v1² - v2²/v1² × 100
% loss in P.e = h1² - h²/h1² × 100
Energy lost due to air friction(Fh) = 1/2mv² - mgh (when body is thrown upward)
Energy lost due to air friction(FS) = mgh - 1/2mv² (when body is thrown downward)
E = 1/2 CV² (capacitor)
E = R × hc (R is Rydberg' constant)
J = m-¹ × Js ms-¹
hf kalpha x rays = EL - Ek
hf kbeta x rays = EM - Ek
Binding energy = mass defect × c²
W = Fd Costheta
W = nmgh (when person is climbing stairs)
W = n(m+m) gh (when person is climbing stairs with some load)
W = 0mgh + 1mgh + 2mgh + 3mgh ....... (in case of stacking bricks. For ist brick h=0. For 2nd brick h=1. For 3rd brick h=2 and so on)
W = Fd = PA × change in V
W = Q - change in U
Q = mc × change in T
T/273.16 = Q/Q3 (Thermodynamic scale)
W = I²Rt
W = emf×charge
W = VQ
W = 1/2 lF
W = YAl²/2L
W = StressAl²/2Strain
W = PressureAl²/2Strain
W = Fl²/2Strain

3. Formulas related to Power
P = Fv
P = E/t
P = n(mgh/t)
P = Fd/t
P = mv²/2t

4. Formulas related to distance, displacement, velocity and accelration
d = vt
d = at²
d = (vf + vi/2) ×t
d = 5t² (for distance in 'n' seconds)
d = 5(2tn - 1) (for distance in 'nth' second)
d = 1/2 mv²/F
d = vit + 5t²
d = v × underroot 2H/g
d = vt = x°wt = x°2pi/T × t = x°2pift
x = x° Sin wt
x = x° Sin (underroot k/m) t
vf = vi + at
2as = vf² - vi²
2as = (vi + at)² - vi²
2as = vf² - (vf - at) ²
v = underroot Vfx² + Vfy²
v = Power/Force
v = 2×K.E/momentum (k.e = 1/2 Pv)
v² = 2×Power×time/mass (P = mv²/2t)
v = underroot 2as
v = underroot gr (speed at highest point in a verticle circle)
v = underroot 5gr (speed at lowest point in a verticle circle)
v² = 2FS/m
v² = 2E/m
v² = 2Ve/m
v = eBr/m (velocity of particle under action of magnetic force along circular path)
v² = Force/Area.Density
v = w underroot x°² - x²
v = underroot k/m × underroot x°² - x²
v = x°w (at mean position where x=0)
v = x° underoot k/m
v = v° underroot 1 - x²/x°² (for determining ratio b/w inst. Velocity and maxi. Velocity)
v= x°2pif = x°2pi/T
a = x°w² = x°w.w = vw = v.2pif
Common velocity = m1v1/m1+m2
vi² = Rg/Sin2theta
v = underoot Tension×length/mass
V = 2pi ke²/nh (speed of e- in nth orbit)
Vn = V/n
v = nh/2pimr (lambda = 2pir and lambda=h/p)
ma = kx
a = kx/m (SHM)
a = - gx/l (Simple pendulum)
ac = v²/r

5. Formulas related to wavelength 'w'
w = v/f
w = 1/wave number
w1 = 2l (when pipe is opened at both ends)
w1 = 4l (when pipe is opened at one end)
Delta w = Us/f (doppler shift)
Wavelength for obs. = w - delta w = v/f - Us/f
w = hc/Ve
w = hc/E
w = h/mv
w = h/P as P = underroot 2mE so
w = h/underroot 2mE (de Broglie wavelength)
w = underroot 150/V A° (short method for de Broglie wavelength. This formula is applicable only for e-)
1/w = RH (1/p²-1/n²)
Wmaxi/Wmini = n²/n²-p² (for determining ratio b/w maxi. Wavelength to mini. Wavelength for series of atomic spectrum)
w = 2pir/n (n is no. of loops in a circle)
h/mv = 2pir ओपन / कमेंट

2021-04-18 08:53:10 ओपन / कमेंट

2021-04-17 09:47:28 For those students who are giving jee 2022 can join @lakshya_doubt ओपन / कमेंट

2021-04-14 16:02:23 ओपन / कमेंट

2021-04-08 13:13:45 Revision Notes on Arithmetic Progression

If ‘a’ is the first term and ‘d’ is the common difference of the arithmetic progression, then its nth term is given by an = a+(n-1)d

The sum, Sn of the first ‘n’ terms of the A.P. is given by Sn = n/2 [2a + (n-1)d]

If Sn is the sum of n terms of an A.P. whose first term is ‘a’ and last term is ‘l’,Sn = (n/2)(a + l)

If common difference is d, number of terms n and the last term l, then Sn = (n/2)[2l-(n -1)d]

If a fixed number is added or subtracted from each term of an A.P., then the resulting sequence is also an A.P. and it has the same common difference as that of the original A.P.

If each term of A.P is multiplied by some constant or divided by a non-zero fixed constant, the resulting sequence is an A.P. again.

If a1, a2, a3, …, an andb1, b2, b3, …, bn, are in A.P. then a1+b1, a2+b2, a3+b3, ……, an+bn and a1–b1, a2–b2, a3–b3, ……, an–bn will also be in A.P.

Suppose a1, a2, a3, ……,an are in A.P. then an, an–1, ……, a3, a2, a1 will also be in A.P.

If nth term of a series is tn = An + B, then the series is in A.P.

If a1, a2, a3, ……, an are in A.P., then a1 + an = a2 + an–1 = a3 + an–2 = …… and so on.

In order to assume three terms in A.P. whose sum is given, they should be assumed as a-d, a, a+d.

Four terms of the A.P. whose sum is given should be assumed as a-3d, a-d, a+d, a+3d

Five convenient numbers in A.P. a–2b, a–b, a, a+b, a+2 b.

In general, we take a – rd, a – (r – 1)d, …., a – d, a, a + rd in case we have to take (2r + 1) terms in an A.P.

Likewise, any 2r terms of an A.P. should be assumed as: a – (2r-1)d, a – (2r – 3)d, …., a – d, a, a + d, ………….. , a+(2r-3)d, a + (2r-1)d.

The arithmetic mean of two numbers ‘a’ and ‘b’ is (a+b)/2.

The terms A1, A2, ….. , An are said to be arithmetic means between a and b if a, A1, A2, ….. , An, bis an A.P.

Clearly, ‘a’ is the first term, ‘b’ is the (n+2)th term and ‘d’ is the common difference. Then, we have b = a+(n+2-1)d = a+(n+1)d

Hence, this gives ‘d’ = (b-a)/(n+1) ओपन / कमेंट

2021-04-07 15:14:48 Physics Handwritten Notes based on Prayas Batch and Lakshya JEE 2022
For more join @lakshyajeedoubt ओपन / कमेंट