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Homologous series may be defined as a series of similarly constituted compounds in which the members possess similar chemical characteristics and the two consecutive members differ in their molecular formula by – CH₂.

Area, A = l² ⇒dA/dt  = 2l × dl/dt = 2 × 20 × 5 

dA/dt = 200cm²/sec. 

P = 41 ⇒ dP/dt = 4 dl/dt 4 × 5= 20cm/sec

v = 10t + 4 Initial velocity = 0 + 4 = 4 

a = 10

It is an authentication service developed at the Massachusetts Institute of Technology. Kerberos uses encryption to prevent intruders from discovering passwords and gaining unauthorized access to files.

It is an Internet routing protocol that scales well, can route traffic along multiple paths, and uses knowledge of an Internet's topology to make accurate routing decisions.

It is a very simple protocol used for transmission of IP datagrams across a serial line.

It is using a router to answer ARP requests. This will be done when the originating host believes that a destination is local, when in fact is lies beyond router.

The average weather condition of place for a long period like 30- 33 years in known in known as climate. India’s climate is said to be “Tropical Monson”.

The main factors are monsoon winds.

(i) Location: The northern part of India lies in sub-tropical and temperate zone and the part lying to the south of the tropic of cancer come under tropical zone. The tropical zone being nearer to the Equator, experiences high temperature throughout the year, with small daily and annual range. Tropic of Caner 23 1/2° N latitude passes through the centre of the country. So India is situated both in the tropical and temperate region.

(ii) Mountain Ranges: The lofty Himalayan Mountains have prevented the cold winds of central Asia, and keep India warm. They are also greatly responsible for the monsoon rains in the country. 

(iii) Distribution of Land and Water: India is bounded by the Arabian Sea in the west and Bay of Bengal in the east, Indian Ocean in the south. These adjoining seas have influenced the climate of the country considerably. They influence the rainfall of the coastal region. Even the cyclones which originate from these seas regularly affect the weather condition.

(iv) The relief features of India also affect the temperature, air pressure, direction and speed of wind, the amount and distribution of rainfall. The windward side of Western Ghats and north east received high rainfall from June to September. 

(v) Monsoon winds: The climatic conditions of other country are greatly influenced by monsoon winds. The winds blow in a particular direction during one season, but get reversed during the other season.

Following are the advantages of LED— 

(1) Light emitting diods are easily manufactured,

(2) LEDs have low cost,

(3) LED works at low voltage as compared to the incandesent bulb,

(4) No warm up time is taken by them,

(5) They can emit monochromatic light as well as bright light.

The peninsular region of India has the largest forest cover with around 57% of the total forest area. 

According to geo-climatic conditions, forests are classified into:

a. Evergreen Forests: These forests are found in the regions of heavy rainfall and high temperature. Tall umbrella shaped trees with dense assemblage is a prominent feature of this forest. The ever green forest always looks green because various species of trees are found here and they shed leaves in different seasons.

The hardwood trees, rose wood, white cedar, toon, gurjan, chaplash, ebony, Mahogany, canes, bamboo, shisham etc. These are found in North-east India, Western Ghats, Andaman and Nicobar islands, parts of Assam and some areas of Himalayan foot hills.

b. The Deciduous forests: The deciduous forest covers a wide range of rainfall regimes. The trees of these forests seasonally shed their leaves. The Indian deciduous forest is found in a range of landscapes from the plains to the hills. These forests provide shelter to most endangered wild life in the country, such as the Tiger, Asian Elephant, Bison, Gaur etc. The deciduous forest are two types

(i) Moist Deciduous forests: The moist deciduous forests are found in wet regions, receiving annual rainfall between 100cm to 200cam and temperature of 25° C to 30° C. The trees of these forests shed their leaves during spring and early summer. They are found on the eastern slopes of the Western Ghats, Chota Nagpur Plateau, the siwaliksetc. 

(ii) The Dry Deciduous Forests: The dry deciduous forest are found I the areas where annual rainfall is between 50cm to 150 cm and temperature of 25° C to 30° C. Sal is the most significant tree found in this forest. Varieties of acacia and bamboo are also fund here. These forests are found in areas of central Deccan plateau, South-east of Rajasthan, Punjab, Haryana and parts of Uttar Pradesh and Madhya Pradesh.

(iii) The mountain forests: As the name indicates these forests are confined to the Himalayan region, where the temperature is less compared to other parts of the country. The trees in this forest are cone shape with needle like leaves. The important trees are oak, fir, pin e spruce, silver fir, deodhar, devdar, juniper, picea chestnut etc. They provide softwood for making country boats, packing materials and sport articles.

c. The Desert forests: These forests are found in the areas of very low rainfall. Thorny bushes, shrubs, dry grass, acacia, cacti and babul are the important vegetation found in these forests. The Indian wild date known as ‘Khejurs”, is common in the deserts. They have spine leaves, long roots and thick fleshy stems in which they store water to survive during the long drought. These vegetations are found in Rajasthan, Gujarat, Punjab and Haryana. 

d. The Mangrove Forests: These forests occur along the river deltas (Ganga, Mahanadi. Godavari and Krishna) of eastern coast and also concentrated in the coastal areas of Katchch, Kathiawar, and Gulf of Khambar. The mangrove forests in the Ganga delta are called Sunder bans because, they have extensive growth of Sundari trees. The trees in these forests are hard, durable and are used in boat making and as fuel. In the recent years mangrove vegetation is being grown I the coastal areas to control effects of tidal waves and coastal erosion.

The correct option is: (D) 3πr²

Following are the applications of laser technology—

(1) It is used in industry,

(2) It is used in surgery,

(3) It is used in communication,

(4) It is used in making holograms,

(5) It is used in scientific research.

The correct option is:(A) 25 : 49

For obtaining pure spectrum following conditions should be satisfied—

(1) Slit should be narrow,

(2) Rays coming out from convex lens should have parallel incidence,

(3) Prism should be in condition of minimum deviation,

(4) Emerging light rays should be focussed by achromatic lens.

Surface area of the sphere = 4πr²

= 4 × 22 / 7 × 14 × 14 

= 4 × 22 × 2 × 14

= 2464 cm²

Power of Lens—The power of a lens is defined as the reciprocal of its focal length is meters.

P = 1/f(in metre)

The S.I. unit of power of lens is ‘dioptre’ (D).

Significance Of Himalayas

1. Strategic significance. A natural frontier of India with other countries(China, Pakistan, Afghanistan,etc)

2. Climatic significance. Prevent further northward movement of summer monsoon and also prevent cold northern winds from Siberia to enter into India. 

3. Agricultural significance. Formation of Himalayas created a trough to its south which is later filled by. the sediments from the Himalayan rivers which is today known as northern plains- Indogangetic plains – Rich agricultural grounds. 

4. Economic significance – Himalayan rivers have huge hydroelectric power potential. Moreover, Himalyan timber and medicinal plants have economic significance. 

5. Tourist spot – large ecological diversity and hill stations 

In 1875, Forcault observed that when a metal piece is kept in variable magnetic field, current are always induced in the plate which is of whirling nature. They are called eddy currents or Forcault's current. Core of transformer is laminated to prevent the induction of these currents. They are used to made moving coil galvanometer dead beat. The direction of eddy currents is given by Lenz's law.

The Correct Answer:  

y = 0

sinθ = AB / BC

sinθ = 3 / 5

It deals with ‘Earth and its inhabitants’.

The shape of the earth is ‘Oblate spheriod’ or ‘Geoid’.

To draw ∠ ARP = 115^o .

Bisect ∠ ARP.

Uses of cyclotron are as follows—

(1) It is used to produce radioactive material for medical purposes.

(2) It is used to bombard the atomic nuclei with highly accelerated particles to study the nuclear reactions.

(3) It is used to improve the quality of solids by adding ions

Temperature, Rainfall, Wind, Ice.

Two factors on which resisitivity depends are as follows—

(1) It depends on the nature of the material of the conductor.

(2) It depends on the temp. of the conductor.

\(3x+2y+2=0...(1)\)

\(5x- y-27=0...(2)\)

Multiply equation (2) by (1),  we get

\(10x-2y-54=0...(3)\)

By adding equations (1) and (3), we get

\(13x-52=0\)

\(\Rightarrow x =\frac{52}{13}=4\)

put  x = 4 in equation (1) , we get

\(12+2y+2=0\)

\(\Rightarrow 2y=-14\)

\(\Rightarrow y=-7\)

Hence, \(x = 4\) & \(y = -7\) is solutions of a given system of equations

The thin layer of gaseous matter encircling the earth in the form of blanket is known as Atmosphere.

(i) ∠d and ∠e or (ii) ∠c and ∠f

\(\frac{3^{n+3}+3^n}{3^{n+3}-3^{n+1}}\) \(=\frac{3^n(3^3+1)}{3^{n+1}{(3^2-1)}}\)

\(=\frac{1}{3}\times\frac{27+1}{9-1}\) 

\(=\frac{28}{3\times8}\)

\(=\frac{7}{6}\)

Fathamometer. 

Point M is the midpoint of seg AB

AM = 1 / 2 × AB

∴ AM = 1 / 2 × 14 

∴ AM = 7 Unit

(i) The sale of dealer A = 100 / 5 × 5000 = 1,00,000 rupees

(ii) The purchase of dealer B = 100 / 5 × 4000 = 80,000 rupees

(iii)∴ Balance of CGST paid by A = 1000 / 2 = Rs. 500 and SGST = Rs. 500

Answer: (1)  tan1>tan2

\(A=\begin{bmatrix}1&-1&2&-3\\4&1&0&2\\0&3&0&4\\0&1&0&2\end{bmatrix}\)

↔ \(\begin{bmatrix}2&1&-1&-3\\0&4&1&2\\0&0&3&4\\0&0&1&2\end{bmatrix}\)

(Applying C₁ ↔ C₃ Then C₂ ↔ C₃)

↔\(\begin{bmatrix}2&1&-1&-3\\0&4&1&2\\0&0&3&4\\0&0&0&2\end{bmatrix}\) (Applying R₄ → 3R₄ - R₃)

∴ Rank of matrix A is 4.

Given equation is

x³ – 2x² – 5x + 6 = 0

since, 1 is root of the equation, therefore (x + 1) is a factor of it.

⇒ (x – 1)(x² – x – 6) = 0

⇒ (x – 1)(x² – 3x + 2x – 6) = 0

⇒ (x – 1)(x(x – 3) + 2(x – 3)) = 0

⇒ (x – 1)(x + 2)(x – 3) = 0

⇒ x = 1, –2 or 3.

Hence, 1 –2 & 3 are roots of given equation.

Then α & β are –2 & 3.

i.e, either α = –2 & β = 3

or α = 3 & β = –2.

Superposition principle—It states that—“Total force acting on a given point charge due to a number of point charge around it is the vector sum of the individual forces acting that point charge due to all other point charges.”

By using the principle of superposition, we can apply coulomb's law to any collection of point charges.

A = \(\begin{bmatrix}-1&1&1\\1&-1&1\\1&1&-1\end{bmatrix}\)

|A| = -1 + 1 + 1 + 1 + 1 + 1 = 4

Now, 

|2 adj (3adj(4A^-1))| = 2³|adj(3adj (4A^-1))|

(\(\because\) |KA| = Kⁿ|A|)

 = 2³|3adj(4A^-1)|² (\(\because\) |adj A| = |A|^n-1)

 = 2³(3³|adj (4A^-1)|)² (\(\because\) |KA| = Kⁿ|A|)

= 2³.3⁶ |adj(4A^-1)|⁴

= 2³.3⁶(4³. (A^-1))⁴ (\(\because\) |KA| = Kⁿ|A|)

=  2³.3⁶(4³. \(\frac14\)) (\(\because\) |A^-1| = \(\frac1{|A|}=\frac14\))

= 2³.3⁶(4²)⁴

= 2³.3⁶.4⁸

= 2³.3⁶.2¹⁶

= 2¹⁹.3⁶

\(\therefore\) a = 19, b = 6

\(\therefore\) a - 2b = 19 - 12 = 7

Two basic properties of charge are as follows— 

(1) Quantization of electric charge—

It is the property of an electric charge by virtue of which any charged body can have charge which is an integral mulitple of the basic charge ‘e’.

q = ± ne

(2) Conservation of electric charge—

Total charge in an isolated system remains conserved. Charges appear in pair of equal and opposite sign.

1. Noise is an unwanted signal which interference with original message signal and occur disorder in communication process between a speaker.

2. Communication noise refers to influences on effective communication that influence the interpretation of conversations.

(a) Tension at a point at a distance x from the support is the due to the weight of the cable

T = \(\frac{m(L-x)}{L}g\)

\(\mu\) = \(\frac mL\)

The speed of transverse wave

v = \(\sqrt{\frac{T}{\mu}}\)

v = \(\cfrac{\frac{m(L-x)g}{L}}{\frac mL}\)

v = \(\sqrt{g(L-x)}\) 

(b) Time taken to transverse a distance 

dt = \(\frac{dx}{\sqrt{g(L-x)}}\)

total time taken t = \(\int\limits_0^L\frac{dx}{\sqrt{g(L-x)}}\) 

t = 2\(\sqrt{\frac Lg}\)

The correct answer is potential energy .
Reason:- the time period of potential energy and kinetic energy is 1/2 that of the shm

Correct option  (1)

Explanation:

For ohmic resistance V  α I

\(8 + 16 + 24 + \,....+ 8n\)

\(= 8(1 + 2 + 3 + ...+ n)\)

\(= 8\frac {n(n+ 1)}{2}\)     \(\left(\because 1 + 2 + 3 + ....+ n = \frac {n(n + 1)}{2}\right)\) 

\(= 4n(n+ 1)\)

Hence proved.

Two time-out can be availed in one set. The time out is for 30 seconds only.

The team that wins two sets out of the three sets is declared the winner. Five sets take place in national and international games. The team that wins three out of five is declared the winner.

In a volleyball game six players play from each side. Three out of them are in front of the attacking line and three are behind it. The first one takes the service. At the time of service 4, 3, 2 are before the attack line and 5, 6, 1 are behind them.