Messages posted by iitkgp_bipin

K C Sinha is best for algebra for any exam as it has wide variety of problems.

If the space between the charges is filled with a non conducting medium or an insulator called dielectric, the dielectric reduces the electrostatic force as compared to free space by a factor called dielectric constant.

Expression for velocity of electron : v = (Z/n) x 2.2 x 10⁶ where Z=atomic number and n = orbit number

Here we have to find electron velocity in 2nd orbit, so Z=2 and n=2.

v = (2/2) x 2.2 x 10⁶ = 2.2 x 10⁶ m/s

Pauling Value = (0.34)(Mulliken Value) - 0.2

Boeing's factory in Everett, Washington, United States is presently the largest building in the world by volume, while the Abraj Al-Bait Towers is the largest building in terms of total floor area.

For ideal gas adiabatic bulk modulus is given by

$K_s=\gamma P\; \; (where \; \gamma\; is\; adiabatic\; constant\; and\; P\; is\; pressure )$

The lone pair of electrons on nitrogen makes amines basic and nucleophilic.Secondary amine is more basic than primary amine because there is more electron density on N of secondary amine due to (+I) effect but on the other hand, tertiary amine is less basic than primary amine due to the steric hindrance on N of tertiary amine.

Carbolic acid is nothing but phenol. It is also known as phenic acid whose molecular formula is C6H5OH.

Because of the higher electro-negativity of oxygen, the carbonyl group is polar, and aldehydes and ketones have larger molecular dipole moments than do alkenes. Therefore, that aldehydes and ketones will have higher boiling points than similar sized alkenes.

We have a formula when the angles of sin are in AP

$sinx+sin(x+y)+sin(x+2y)+...sin(x+(n-1)y)=\frac{sin(ny/2)}{sin(y/2)}\sin\left (x+\frac{n-1}{2}y \right )$

Put y=2x :

$sinx+sin3x+sin5x+...sin(2n-1)x=\frac{sin^2nx}{sin\; x}$

$I=\int \frac{sin^29x}{sin\; x}dx$

$=\int (sinx+sin3x+sin5x+...sin17x)dx$

$=-cosx-\frac{1}{3}cos3x-\frac{1}{5}cos5x......-\frac{1}{17}cos17x+c$

1. Stick to good books (which have already been discussed a lot here). But the more important part is that you study them thoroughly. Donot ignore NCERTs. They are very good at clearing concepts

2. Make a proper plan of your syllabus. Divide it among parts. Layout weekly tasks rather than daily ones. Give time to revision as well.

3. While studying at home, do a question time-bound. This will increase your speed. But remember if you are not able to do it in that time, dont give up by looking at the answer, try again. Even after giving it a good time you are not able to solve you may refer solution or may ask your teahcer or here tiself.

4. Make yourself comprehensive notes and small skecthes. (make them attractive)

5. Dont worry about board exams. The syllabus is not very different and can be managed easily. By studying NCERT you are automatically preparing for them.

6. Be up to date. Periodic revision is must.

7. Regularly solve model papers and keep checking the time. This enhance confidence and shows the pros and cons of ur studies

The system m+2m and other block m are connected by same string and also in the system m+2m m is stationary with respect to 2m implies acceleration of all the blocks are same.

Let the accelaration of m be 'a' downwards and that of m+2m be 'a' rightwards.

Writing force equation for m : mg - T = ma.....(1)

Writing force equation for m+2m : T = (m+2m)a........(2)

From (1) and (2) : a = g/4

Now consider system m+2m : block m moves with accelaration g/4 but friction with block 2m is keeping it stationary with respect to 2m and the magnitude of frictional force = ma = mg/4

Let us consider our frame of reference to be that of flowing water

Since raft is moving with flow it is still with respect to river.

The time taken by boat when travelling downstream and travelling upstream to meet raft will be same as velocity is constant with respect to river (if it had been with respect to ground velocities would have been v+u and v-u). So total time taken = 60+60 = 120 min = 2 hr. This is also the time taken by the raft to travel 6 km.

Velocity of raft = 6km / 2hr = 3 km/hr which will be the velocity of flowing water

You must be thorough with general organic chemistry. If you have doubts don't move to next chapter until and unless you are well with this topic. Organic can be very easy if ur reaction mechanism part is very strong.. Write all the name reaction separately and try to revise them again and again.. Read NCERT book along with this use any reference book like pradeep to clear particular concepts.. Try to solve as many as mcqs u can with reason 4 each question

log(a+b+c) = loga + logb + logc is possible when a+b+c=abc

Examples : (2 , 4 , 6/7) ; (3 , 4 , 7/11)

Generalization : (x , y , (x+y)/(xy-1))....for above expression to be valid you can pick any x & y keeping in mind all numbers in triplet are positive.

2²⁰⁰ - (2¹⁹²)(31) + 2ⁿ

= 2¹⁹² (2⁸ - 31 + 2^n-192)

= 2¹⁹² (225 + 2^n-192)

= 2¹⁹² (15² + 2^n-192)

Here we have to find power which added with 15² gives a perfect square. The simplest pythagorean triplet which we can think of is 15² + 8² = 17²

Given expression becomes 2¹⁹² 17² when 2^n-192 = 8²

=> 2^n-192 = 2⁶

=> n = 198

In maths I prefer R D Sharma for basics but r.b. tripathi is also good if it is supplemented with other books like M L Khanna for competition. Pradeep in physics and chemistry are sufficient for basics.

Among these I would prefer JSS.

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