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सूखी धरती में पानी लौटने से राजस्थान की पूरी तस्वीर ही बदल गईं। भू-जल स्तर उठने से कुएँ जल से भर गए, हरियाली वापस आ गई, धरती की उर्वरा शक्ति बढ़ गई, फसल चक्र बदल गया, अरावली की पहाड़ियों पर पुनः पेड़-पौधे उगने लगे तथा जो लोग रोजी-रोटी की तलाश में गाँव से पलायन कर गए थे, वे वापस आ गए और अपने खेतों में खेती करने लगे।

इस तकनीक की मदद से उस जगह की पहचान की जाती है जहाँ पर पानी इकट्ठा किया जा सकता है, उस तकनीक को रिमोट सेंसिंग कहते हैं।

महामना मदन मोहन मालवीय जी ने ‘हिन्दोस्थान’, ‘अभ्युदय’, ‘लीडर’, ‘भारत’, ‘मर्यादा’, ‘हिन्दुस्तान टाइम्स’, इण्डियन ओपीनियन’ तथा ‘सनातन धर्म’ नामक समाचार-पत्रों का संपादन किया।

जिस प्रकार जन्म देने वाली माँ हमें अपना दूध पिलाकर ही कुछ सालों तक पालती-पोषती है, उसी प्रकार हम जीवनपर्यंत गाय के दूध का या दूध से बने अन्य उत्पादों का प्रयोग करते हैं। इसी संदर्भ में भारतीय संस्कृति में गाय को माता का दर्जा दिया गया। मेरे विचार से ये उचित ही है क्योंकि दूध पिलाकर पालन-पोषण तो माँ ही करती है। इस कारण गाय हमारी सही मायने में माता है जिसका दूध शुदध, मीठा, स्वास्थ्यवर्धक, पौष्टिक और अनेक रोगों को मिटाने वाला होता है।

जिस समय देश में सबके लिए शिक्षा की व्यवस्था नहीं थी, उस समय देश के अधिकांश लोग खासकर गरीब तबके के लोग शिक्षा से वंचित रह जाते थे। महिलाओं को शिक्षा नहीं मिल पाती थी, वे भी अनपढ़ रह जाती थीं। गरीब समाज के लोगों को शिक्षा पाने के लिए अत्यंत संघर्ष करना पड़ता था, विद्यालय बहुत दूर-दूर होते जहाँ रोज समय पर पहुँचना ही एक चुनौती थी। साथ ही उस समय यातायात के साधन भी इतने विकसित नहीं थे फलतः लोगों को शिक्षा लेने में अनेक कठिनाइयाँ झेलनी पड़ती थीं।

महामना मदनमोहन मालवीय का जन्म 25 दिसम्बर, 1861 को प्रयाग में हुआ था। इनके पिता पंडित ब्रजनाथ चतुर्वेदी और माता का नाम श्रीमती मूना देवी था।

(A) Degree 

Degree is the largest unit in Sexagesimal system

(D) \((\frac{1}{60})^{th}\) 

\((\frac{1}{60})^{th}\) part of one degree is called one minute.

Either the vehicle is at rest or it is moving with constant velocity.

Scalar: Surface tension, Temperature

Vector: Force, Torque, Momentum.

Given number = 0.00356

How to find out the characteristic of a number.

A common logarithm is simply on exponent of base 10.

Characteristic is the power of 10 when a number is written in scientific notation i. e., putting decimal point after one digit.

For example if x = 2.567 × 10ⁿ.

Then characteristic of x will be n.

Now the given number = 0.00356 = 3.56 × 10^-3

Hence, the characteristic of given number = \(\bar 3\)

The vector having unit magnitude is known as unit vector.

The vectors which have equal magnitude and same direction.

The vector product of two parallel vectors is Zero.

\(|\vec {A ^2}| or A^2\)

No. because scalar has only magnitude but vector has magnitude and direction both.

Scalar Quantities:

The physical quantities, which have magnitude but no direction are called scalars, accompanied by a unit.
Mass, length, distance covered, time, density, work, temperature, charge, specific heat, energy, power, speed, length, etc. are few examples of scalars,

A scalar quantity can be completely described by a number; representing its magnitude. A scalar may be positive or negative. They can be added, subtracted, multiplied and divided according to the simple rules of Algebra.

Vector Quantities: The Physical quantities which have both magnitude and direction are called vectors.
Displacement, velocity, acceleration, force, momentum, electric field, impulse, gravitational field etc. are few examples of vector quantities.

It may be pointed out that the vectors can not be added, subtracted, multiplied or divided as one may do in case of scalars. It is because, in addition to magnitude, vectors have direction also. Vectors are added, subtracted and multiplied according to the rules of Vector Algebra. The division of a vector by another vector is not a valid operation in Vector Algebra.

Vectors are of two types :

• Polar vectors
• Axial vectors

\(\hat i, \hat j \;and\; \hat k\) are the unit vectors corresponding to X, Y and Z axes respectively.

The vectors can be resolved in following two types.

• In two dimensions
• In three dimensions

The vector which have zero magnitudes and indicates the direction at particular point.

No, Is the vector product obey the commutative law. 

Characteristic of the logarithm of a number = no of digits. -1
Characteristic of no. 83256 = 5 - 1 = 4
Or
The given number = 83256 = 8.3256 × 10⁴
∴ The characteristic of the given number = 4

Yes, if the angle between the two vectors is greater than 90°.

In a direction perpendicular to the plane containing both the vectors and decided by right-hand screw rule.

No, If one of the component of a vector quantity is zero but another component is not zero.

The given number,

x = 8621 = 8.621 × 10³

∴ The characteristic of x = 3

From log table the mantisa of x = 0.9356

Therefore logx = log8621 = 3.9356

Given; U = y² sin y and F = \(-\frac{d U}{d y}\), F = ?
∴ F = \(-\frac{d U}{d y}=-\frac{d}{d y}\left(y^{2} \sin y\right)\)
or F = - (2ysiny + y² cosy)

Microwaves are widely used for point-to-point communications because their small wavelength allows conveniently-sized antennas to direct them in narrow beams, which can be pointed directly at the receiving antenna. This allows nearby microwave equipment to use the same frequencies without interfering with each other, as lower frequency radio waves do. Another advantage is that the high frequency of microwaves gives the microwave band a very large information-carrying capacity. A disadvantage is that microwaves are limited to line of sight propagation; they cannot pass around hills or mountains as lower frequency radio waves can.

LAN has the following characteristics: 

1. Coverage area is generally a few kilometers. 

2. Using different dedicated transmission medium, you can achieve the transmission rate of 1 Mb/s to 100 Mbit / sec or higher, with the further development of LAN technology is currently being developed toward higher speed (e.g. 155Mbps, 655Mbps and 1000Mbps etc.). 

3. In LAN you can run the multiple devices to share a transmission medium. 

4. You can use the different topology mainly bus and ring in LAN.

Analog communications is based upon continuous time signals. For example, your voice modulates a microphone and the continuous time electrical signal from that microphone is sent to the destination, sometimes by modulating a carrier signal.

A digital communications signal is based upon discrete time where the signal is first sampled and converted into a digital signal. That discrete signal is then transmitted to the destination.

(c) Optical Fiber

(a) Radio Link

Bluetooth is a wireless technology that allows computers, phones and other devices to talk to each other over short distances (up to 100 metres). Bluetooth uses radio waves (in the 2.4 Gigahertz range), and is designed to be a secure and inexpensive way of connecting and exchanging information between devices without wires. Bluetooth is used in mobile phones, handheld computers, laptops, printers, handheld organisers. Uses of Bluetooth include: sending photos from your mobile, exchanging business cards, sending voice from a headset to a mobile phone, and real-time satellite navigation using GPS.

Clad is the name of Glass Core surrounding on Optical Fiber.

MODEM is used to convert Analog signal to Digital signal and Digital signal to Analog signal.

(c) Twisted pair

Coaxial cable is used as a transmission line for radio frequency signals. Its applications include computer network (Internet) connections, digital audio (S/PDIF), and distributing cable television.

The router is connected to at least two networks and decides which way to send each information packet based on its current understanding of the state of the networks it is connected to. A router is located at any gateway, including each pointof-presence on the Internet. A router is often included as a part of a network switch.

A router may create or maintain a table of the available routes and their conditions and use this information along with distance and cost algorithms to determine the best route for a given packet. Typically, a packet may travel through a number of network points with routers before arriving at its destination. Routing is a function associated with the Network layer (layer 3) in the standard model of network programming, the Open Systems Interconnection (OSI) model. A layer-3 switch is a switch that can perform routing functions.

(i) Acyclic or open chain compounds

(ii) Alicyclic or closed chain or ring compounds.

(iii) Aromatic compounds.

B) i – z, ii – x, iii – y

The time t spent by a charged particle, of mass m and carrying a charge q, inside a dee of a cyclotron is independent of the radius of the path and the speed of the particle so long as m is constant. Then, the periodic time of the charged particle in its nearly circular path is T = 2t, and the frequency of revolution, 

f = \(\cfrac 1T\) = \(\cfrac 1{2t}\) = \(\cfrac{qB}{2\pi m}\)

are also independent of the radius and the speed.

The cyclotron frequency depends upon 

1. the magnetic induction and 

2. the specific charge (the ratio charge/mass) of the charged particles.

Limitations of a cyclotron :

1. It cannot be used to accelerate electrons. Because electrons have a very small mass, they quickly achieve relativistic speeds, i.e., speeds at which their mass increases significantly with increase in speed. Then they cannot remain synchronous with the alternating electric field between the dees.

2. For higher energies, with a given magnetic field strength, the exit radius and thus the dees must be large. It is difficult to produce a uniform magnetic field over a large area. 

3. Even protons, deuterons, a-particles, etc., cannot be accelerated to very high energy, say of the order of 500 MeV, using a cyclotron with a fixed cyclotron frequency. 

4. No particle accelerator can accelerate uncharged particles, such as neutrons.

The time spent by a charged particle to describe a semicircular path of radius r inside a dee of a cyclotron is independent of the radius of the path and the speed v so long as the mass m of the particle is constant. This is true for any charged particle of mass m and carrying a charge q, and is the critical characteristic of operation of the cyclotron.

r = \(\cfrac{mv}{qB}\)

So that the time spent in a dee,

t = \(\cfrac{\pi r}v\) = \(\cfrac{\pi }v\) x \(\cfrac{mv}{qB}\) = \(\cfrac{\pi m}{qB}\)

which is independent of r and v.

C) Bohr-Bury

A) Number of electrons in K – shell

D) All the above

The function of the electric field in the gap between the dees of a cyclotron is to accelerate the positively charged particles while that of the magnetic field in the dees is to deflect the particles in semicircular paths so that they return to the gap in a fixed time interval to reuse the alternating electric field.

A CGS unit of magnetic induction of historical interest is the gauss, symbol G. However, since the magnetic flux and the magnetic flux density (magnetic induction, B) are defined by similar equations in the CGS system and the SI, this non-SI unit is accepted for use with SI.

1 G = 10^-4 T

[Note : The unit gauss is named after Karl Friedrich Gauss (1777 -1855), German mathematician, who strongly promoted in 1832 the use of the French decimal or metric system, with the metre and the kilogram and the astronomical second, as a coherent system of units for physical sciences. Gauss was the first to make absolute measurements of the Earth’s magnetic field in terms of a decimal system based on the three mechanical units millimetre, gram and second for, respectively, the quantities length, mass and time.]