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### Second derivatives of vector fields and product rules

There are number of rules that we might use while solving problems involving vector differentiation. These are

1.Sum rule

2. Multiplication by a constant

3. Product rule

fig3

4. Quotient rule

fig4

5.

### Semiconductor Physics (Things you should know)

1. Resistance of a pure semiconductor is millions and millions of times greater then that of a good conductor like copper.
2 Charge carriers in semiconductors are electrons(-e) and holes(p having charge equal to +e).
3 Pure semiconductor known as intrinsic semiconductor contains equal number of both holes and electrons.
4 Drift velocity of electrons is greater then that of holes.
5 Taking both charge carriers in semiconductor into account current is given as I=neA(vn+vp) where n is number of holes and electrons, vn is the drift velocity of electrons and vp is drift velocity of holes and A is the cross-sectional area.
6 Electrical resistance of pure semiconducter decreases with increase in temperature.
7 Semiconductors can be doped with a tiny amount of impurity such as one part in a million to form an impure or extrinsic semiconductor.
8 p-type semiconductor is a type of ectrinsic semiconductor formed when pure semiconductor is doped with trivalent element (for ex- indium). It has large majority of holes and small minority of electrons. Thus majority charge carriers in a p-type semiconductor are holes.
9 n-type semiconductor is a type of ectrinsic semiconductor formed when pure semiconductor is doped with pentavalent element (for ex- phosphorus). It has large majority of electrons and small minority of holes. Thus majority charge carriers in a p-type semiconductor are electrons.
10 Junction diode is a simplest kind of semiconductor device. It has a pn junction and consists of a p-type crystal and n-type crystal and is formed by growing n-type semiconductor over p-type semiconductor. Junction diodes are used as rectifiers.
11 Bipolar junction transistor is a three terminal device. There are two type of transistors npn and pnp transistor. Three terminals of the transistor are joined to base, emitter and collector of the transistor.
12 With Common emitter transistor, the base current Ib is the input current and the

### Gravitation questions for IITJEE

1.Which is of the following statement is true
A) Gravitational constant G value does not depend on the medium between the bodies
B) Gravitational constant G depends on the masses of the bodies and the sizes of the bodies
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong

2.If the distance between the earth and sun were half its present value,the number of days in a year would be
a. 64.5
b. 129
c. 182.5
d. 730

3.if both the mass of earth and its radius are decreased by 1%,the value of acceleration of gravity will
a. Decrease by 1%
b Increase by 1%
c. Increase by 2%
d remain unchanged

4. A body weigh W newton of the surface of the earth.Its weight at a height equal to half the radius of the earth will be
a. W/2
b. 2W/3
c. 4W/9
d. W/4

5.when a stone of mass m is falling in th earth of mass M,the acceleration of the earth will be
a zero
b. mg/M
c. Mg/m
d g

6.The weight of the object will be
a. zero at the center of the earth
b.same in all the satellites
c. same at all the points on the surface of the earth
d. none of the above

7.Which is of the following statement is true
A) it is possible to put an artificial satellite in a orbit such a way that it will remain always directly over New Delhi
B) An earth satellite continues to move in the orbit due to centripetal force provided by the burning of the fuel of its engine
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong

8. A mass m is divided into two part ym and (1-y)m .For a given seperation,the value of y for which the gravitattional attraction between the two pieces becomes maximum
a. 1/2
b. 3/5
c. 1
d 2

9.Two bodies of mass M and 2M are at rest at infinte seperation.They move towards each other under the mutual gravitaional attraction.Then at seperation r ,which of the following is false
a. The total energy of the system is not zero
b The force between them is zero
c. The center of the mass of the system is movind
d non of the above

10.Choose the correct statement
a. the gravitational forces between the two bodies are an action and reaction pair
b. G and g are constant everywhere
c.The acceleration due to gravity increase due to rotation of the earth
d. none of the above

Solutions