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A surface, real or imaginary, that is the locus of all adjacent points at which the phase of oscillation is the same.

Difference from a ray:

(i) The ray, at each point of a wavefront, is normal to the wavefront at that point.

(ii) The ray indicates the direction of propagation
of wave while the wavefront is the surface of constant phase.

The correct option is (a) 3.

Graph of given polynomial cuts the x-axis at 3 distinct points. 

No. of zeroes is 3.

PAN(Personal Area Network)

(i) A datasheet is a document, printed or electronic that provides details about a product, like a computer, computer component, or software program. The datasheet includes information that can help in making a buying decision about a product by providing technical specifications about the product.

(ii) A form may refer to any of the following:

1. Generally speaking, form is a term used to describe a shape of an object.  

2. Not to be confused with a forum, a e-form or form is a web page or paper that contains a listing of questions or fields that ask for user input.

(iii) The most common filter is a software filter or a filter in a program that reads data in and manipulates the data to fit another output pattern or removes data that may not be needed. For example, spam filters help filter unwanted e-mail from reaching your Inbox.

(iv) In general, the term query is commonly used to describe a question or request that is made by a user or another computer or device. For example, when you use a search engine such as Google, the text you enter is considered the search query.

(v) Used in a variety of fields from business to science, a report is a concise summary distilled from a larger set of data intended for a specific audience. For example, reports are used to detail the findings of an experiment or inquiry.

import matplotlib.pyplot as plt

import numpy as np

model=(‘i20’,’Grandi10’,’Creta’,’Eon’,’Verna’,’Tucson’,’Elantra’) 

y_pos=np.arange(len(model))

sale=[12369,12174,9390,4663,4077,3712,200,150] 

plt.bar(y_pos,sale,align=’center’,alpha=0.5) 

plt.xticks(y_pos,model) 

plt.xlabel(‘Month-June’)

plt.ylabel(‘Sale done’)

plt.title(‘Sales Bar Graph’)

plt.show()

a) Hypermetropia 

b) Two causes: 

(i) The focal length of the eye lens is too long 

(ii) The eye ball has become too small

Environmental Cue – 

• In some animals, the temperature at which fertilized eggs are kept determines whether the developing animal in egg is male or female 
• In some animals like snail, individual can change sex. 

Genetical Cue – 

A child who inherits an x chromosome from her father will be a girl and one who inherits a y chromosome from the father will be a boy.

Reproduction : It is a (biological) process by which new individuals of the same species are produced by the existing organisms. 
(i) Populations of organisms live in well defined place called niches in the ecosystem and divide using their ability to reproduce. 
(ii) Reproduction involves DNA copying which is the source of information for making proteins thereby controlling body design. 
(iii) These body designs allow the organism to use a particular niche for the stability of the population of a species. 
(iv) (Minor) variations may also lead to the stability of the species.

Differences between Acquired Trait and Inherited Trait :

Alloys are used rather than pure metals in electrical heating devices since they have low electrical conductivity and low melting point. Alloys also have higher resistivity than metals.

Metal particles are held together by strong metallic bonds, and they have high melting and boiling points. The free electrons in metals can move through the metal, allowing metals to conduct electricity. Whereas glass does not have free electrons to conduct free electrons resulting as bad conductors of electricity.

Metals are good conductor of electricity – as they have low resistivity / have free electrons

Glass is a bad conductor of electricity – as it has high resistivity / have no free electrons

(i) In sexual reproduction two opposite sexes are involved where as in asexual reproduction only one individual is involved.

(ii) In sexual reproduction male and female gamete formation takes place where as in asexual no gamete formation occurs.

• Sexually reproducing organisms have better chances of survival

• Because more variations are generated.

Factors on which resistance of a conductor depends:

(i) Length of conductor [or R ∝ l]

(ii) Area of cross-section of the conductor [or R ∝ 1/A]

Neutron will continue to move in same direction because no force will act on it since it carries no charge.

Distinction between Census and Sample Survey Method :

Functions of Statistics are

(a) Statistics is helpful in formulating the policies.

(b) It presents the facts in a definite and precise form.

(c) Statistics is helpful in predicting the future trends or forecasting.

i. Class Limit. 

ii. Percentiles. 

iii. Direct taxes

iv. 2. 

v. India

 Correct option (a) Gross Domestic Product 

• Programmes introduced by State and Central Govt.
• Indirect employment generation in private sector.
• By creating basic facilities.
• Creation of economic, social and community assets.
•  Micro credit programmes.

Detailed Answer : 

The employment is generated through direct and indirect efforts of the government. The direct efforts include employment of people in various departments for administrative posts. These people run government enterprises which increase production of goods and services. With an increase in production, there is requirement for more people. 

The private enterprises are also linked with government enterprises. With an increase in output in government enterprises, there is a proportionate increase in goods and services of these private enterprises also. As a result, government generates employment opportunities indirectly also. Government also organises various micro credit programmes for the employment of youth in entrepreneurial activities.

Simple bar diagrams are those diagrams which are based on a single set of numerical data, whereas Multiple bar diagrams are used when we have to present two or more attributes with relation to time and space.

Meaning of liberalisation :

Major sector reforms :

(a) Deregulation of Industrial sector.

(b) financial sector reforms.

(c) Tax reforms.

(d) Reforms in Trade and Investment - Explain each sector.

Detailed Answer : 

Liberalization is the loosening of government regulations in a country, so that, private sector companies are allowed to operate business transactions with lesser restrictions. Major reforms under liberalization are categorized as : 

(a) Industrial sector reforms which include 

(i) Contraction of public sector industries. 

(ii) Abolition of industrial licensing. 

(iii) Dereservation of production areas for all scales of business. 

(b) Fiscal reforms which include 

(i) Reduction in rate of indirect taxes. 

(ii) Simplification of income tax structure. 

(iii) Moderation of overall tax regime. 

(c) Financial sector reforms which include 

(i) Reserve Bank of India’s role changed from regulator to facilitator. 

(ii) Opening of Banking sector for private sector. 

(d) Trade reforms which include 

(i) Abolition of import quota. 

(ii) Abolition import licensing. 

(iii) Withdrawal of export duty. 

(iv) Reduction in tariff rates. 

(e) Foreign Exchange reforms which include. 

(i) Devaluation of rupee. 

(ii) Determination of foreign exchange rate by market forces of demand and supply.

(a) 33

(b) 25

Meaning of Education  

Importance : 

(a) Gain of knowledge. 

(b) Shill development. 

(c) Removal of ignorance. 

(d) Moral development. 

(e) Individual evaluation. 

(f) Econonomic development - with explanation.

Detailed Answer :

The reasons for this are :

(a) Increase in knowledge and skill. 

(b) Development of rationality.

(c) Adoption of modern technology. 

(d) Development of intellect.

(e) Inculcation of moral values and ethics. 

(f) Increase in rate of participation.

(g) Encouragement for innovation. 

(h) Human capital development.

(i) Economic development. 

(j) Reduction in income inequality.

(k) Improvement in living standard.

Meaning of organised sector 

Reasons for fall in employment :

(a) Use of modern Technology.

(b) Sick organised industries.

(c) Lack of proper management.

(d) Neglect of government-with explanation.

Detailed Answer :

Organised sector refers to the sum total of all public sector enterprises and those private sector enterprises which employ ten or more workers. The workers working in the organised sector are referred to as organised sector workers.

The reasons for fall in employment in organised sector are :

(a) Use of modern technology. 

(b) Sickness of organised sector industries.

(c) Lack of proper management. 

(d) Neglect of government.

(e) Strict labour laws. 

(f) Political biasness of trade unions.

(g) Overdependence on social security benefits.

Some measures that I can suggest to tackle the problem of poverty are as follows : 

(a) Spending on human capital formation especially in the form of education and health. 

(b) Making people aware of the various government programmes that are in operation. 

(c) Providing easy loans for starting self-employment. 

(d) Keeping a control on population growth.

Classification is the process of arranging data into sequences and group according to their common characteristics of separating them into different but selected parts.

Causes for land degradation in India are :

(i) Deforestation.

(ii) Indiscriminate and over exploitation of forest products for fuelwood and overgrazing.

(iii) Conversion of forest land into agricultural land.

(iv) Faulty methods of activation.

(v) Excessive application of pesticides and insecticides.

(vi) Improper planning and management of irrigation systems.

(vii) Excess extraction of ground water.

(viii) No proper introduction of crop pattern and organic farming.

(xi) Illiteracy and ignorance of people.

Primary Data

Secondary Data

Detailed Answer :

Primary Data : Data originally collected by an investigator for the first time for any statistical investigation. 

Secondary Data : Data already collected and processed by some other person and subsequently used by another investigator.

Discrete Variable.

Continuous Variable.

Detailed Answer :

Discrete Variable : Variable that can only take integral values.

Continuous Variable : Variable that can take integral as well as fractional value in an interval.

M.D.= ∑|d|/2

Detailed Answer :

Mean Deviation is the sum of absolute deviations from an average divided by the number of times.

Mean deviation = ∑|D|/n

• To know the change in the purchasing power of money.
• To know the change in the general price level.
• To know the value of variables which change daily.
• To know the change in value of a particular.
• To know the change in value of a particular set to items, production, etc.

• Frequency polygon.
• Correlation.
• Standard deviation.

Detailed Answer :

•  Frequency polygon.  
• Correlation.
• Standard deviation. 
• Histogram

Use of natural pesticides such as neem extracts and mixed cropping, instead of chemicals pesticides and insecticides and insecticides to safeguard against pests and disease is called bio pest control.

Sample survey provides better results than census :

(a) Reasonably reliable.

(b) Samples are smaller.

(c) Needs smaller team of enumerators (explain briefly).

(a) Statistics helps to simplify complex data.

(b) Helps in formulating policies.

(c) Helps in forecasting.

(d) Helps in comparing different set of figures (explain briefly).

The feasible region is the set of all points whose coordinates satisfy the constraints of a problem.

If R is unbounded ,where R is the feasible region ,then a maximum or a minimum value of the objective function may not exist.

Step 1: If the feasible region for a LPP is unbounded, then the objective function Z = ax+b may or may not exist. 

Step 2: Unbounded means that the feasible region does extend indefinitely in any direction.

For equal roots, b² -4ac=0 

Here, a= k, b= -k and c=1 

 k² - 4(k)(1)=0

i.e. k(k- 4)=0 

i.e. k=0 or k= 4 

rejecting k=0, we get k= 4.

Perimeter of ∆ABC= AB BC CA 

 = AB+[ BP+CP]+CA

= AB+BQ+CR+CA (Tangents from an external point are equal) 

= AQ+AR

= AR+AR (Tangents from an external point are equal) 

=2AR 

Point R divides PQ in ratio 2:3. 

Co-ordinates of point R are given by 

 x = (2 x - 3 + 3 x 2)/5=0 

y = (2 x 4 + 3 x -1)/5=1

So, the required point R is (0,1)

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