Explore topic-wise InterviewSolutions in Current Affairs.

∵ (dy/dx) + y cot x = 2 cos x

Here (dy/dx) + Py = ϕ is integral equation of linear

∴ P = cot x and ϕ = 2 cos x

I.F = e^∫Pdx = e^{∫cot x dx}

= e^{log(sin x)} = sin x 

Now solution of differential equation is

y x I.F. = ∫ϕ x I.F dx + c

y sin x = ∫2 cos x . sin x + c

y sin x = ∫sin 2x + c

y sin x = - (cos 2x/2) + c

Because plane passing through (1,2,3)

∴ x = 1, y = 2, z = 3

3x + 4y - 5z = 0

Again plane is parallel to the equation

∴ a = 3, b = 4 , c = -5

∴ required plane equation

a(x - x') + b(y - y') + c(z - z') = 0

3(x - 1) + 4(y - 2) - 5(z - 3) = 0

3x - 3 + 4y - 8 - 5z + 15 = 0 

3x + 4y - 5z + 4 = 0

We know that co-ordinate of origin is (0, 0, 0)

Given points -(a, b, c) 

Now Distance formula

√((a - 0)² + (b - 0)² + (c - 0)²)

= √(a² + b² + c²)

For A, P(A) = 75/100 = 3/4

P(A') = 1 - (3/4) = 1/4

For B, P(B) = 80/100 = 4/5

P(B') = 1 - (4/5) = 1/5

P(A ∩ B') + P(A' ∩ B) = P(A) x P(B') + P(A') x P(B)

= (3/4) x (1/5) + (1/4) x (4/5)

= (3/20) + (4/20)

= (7/20) x 100 

= 35%

वाक्य शब्द से मिलकर बनते है।

Given y = tan^-1 x

dy/dx = d(tan^-1 x)/dx 

= 1/(1 + x²) by formula 

घ. क्रिया विशेषण पदबंध​

अब दरवाजा खोला जा सकता है।

उपर्युक्त वाक्यों में काला छपे शब्द 'क्रिया विशेषण पदबंध​' है।

मनुष्य का जीवन मुख्य रूप से दो मनोभावों पर आधारित होता है- दुख और सुख। शेष सभी मनोभाव इन्हीं दोनों मूल भावों के अंतर्गत समाहित होते हैं या कहा जा सकता है कि इन्हीं के विविध रूप होते हैं। मनुष्य के जीवन का सबसे आश्चर्यजनक पहलू यह है कि जब जीवन में सुख आता है, तब वह उसे अपने अच्छे कर्मों का फल मानता है। इसके ठीक विपरीत जब जीवन में दुख, कष्ट, रोग, शोक का आगमन होता है, तब बड़ी सहजता से वह बोल देता है कि भगवान ना जाने क्यों अप्रसन्न हैं, जाने किस बात का दंड दे रहे हैं।

Character sketch of khushvant singh grandmother: 

The author has described his grandmother very beautifully. He compared her to the winter landscape in the mountains and expanse of pure white serenity breathing peace and contentment. He used this simile to describe all whiteness associated with his grandmother. She always wore a spotless white dress. Her silver hair quite matched with her white attire. She was very spiritual and religious. As a result, she exuded purity and serenity like a winter landscape. There were many appreciable qualities in Khushwant Singh's grandmother. She was quite affectionate. She looked after the narrator at the village so caringly that he did not feel the absence of his parents when they went to the city to settle.  She was a strong woman who could adapt herself to any new challenging situation. Maybe she derived that strength from her devotion to God. She was so divinely dedicated to praying to God that she never left her rosary. Her feeding the village dogs and then the sparrows show her love for animals. She found a company in them. And sparrows reciprocated her love and care. They didn't chirp at all; nor did they eat a single crumb at her death. She was really a saintly woman.

Order = 3, Degree = not defined.

f(x) = 2x² - 3x

diff wrt x

f¹(x) = 4x - 3

f¹ (x) = 0 ⇒ 4x - 3 = 0

or 4x = 3

⇒ x = 3/4

∴ Point x = 3/4 divides the real line into two disjoint intervals (- ∞, 3/4) and (3/4, ∞) In the interval (3/4, ∞), f¹(x) = 4x - 3 > 0

∴ f is strictly increasing in (3/4, ∞)

Correct option is A) Not yet.

Correct option is D) Don’t get an English one!

Correct option is A) Not yet

Correct option is D) Never.

Correct option is: (C) P(A ∩ B) = P(A)P(B)

Correct option is D) I’ve got some

CORRECT OPTION - D) I have got some

Correct option is B) What a

b) what A clever women

Correct option is C) waited ten minutes for

c) waited ten minutes for

Correct option is: (A) 0

Correct option is: (B) -5

Let 2 cos^-1\(\frac45=\theta\)

⇒ cos \(\frac{\theta}2=\frac45\) 

\(\therefore\) sin \(\frac{\theta}2=\frac35\) 

Now, sin θ = 2 sin θ/2 cos θ/2 = 2. 3/5. 4/5 = 24/25

θ = sin^-1(24/25)

\(\therefore\) 2 cos^-1 4/5 = sin^-1(24/25)

\(\therefore\) sin (2 cos^-14/5) = sin (sin^-1(24/25)) = 24/25

Slope = m = gradient or inclination of a line with respect to positive x-axis 

i.e., m = tanθ

Human factors essential in deciding the location of an industry are − availability of cheap labour, availability of services such as consultants and financial advice, and resources for maintaining labour.

Industries are responsible for four kinds of pollution-air, water, land and noise pollution. Industrial pollution can be controlled by: 

• Industries should be set up in distant areas away from human settlements. 
• Minimise the use of water processing through reusing and recycling. 
• Treating hot water and effluents before releasing them in rivers and ponds. 
• Particulate matter in the air can be reduced by fitting smoke stacks to factories with electrostatic precipitators. Smoke can be reduced in factories by using gas or oil instead of coal. 
• Machinery can be redesigned to increase energy efficiency and reduce noise.

Production and consumption of steel is regarded as the index of a country’s development because of the following reasons: 

• The production and consumption of iron and steel reflects the level of industrialisation and economic development of a country. 
• All the other industries depend on it for their machinery. It provides raw material for making industrial machinery, electrical machinery, defence equipments, bridges, dams, shops, houses, etc. 
• Vehicles carrying goods from one place to another are also made up of steel. It is because of these vehicles that our goods are transported from one place to another. 
• Steel is required to manufacture a variety of consumer goods, like bicycles, fans, furniture, tractors, etc. 
• It is the basic unit of economy. All buildings and infrastructures are constructed using iron and steel. 

Characteristics of Kandla sea port: 

(i) First port developed soon after India got independence. 

(ii) Reduced the volume of traffic on Mumbai port. 

(iii) Tidal port. 

(iv) Caters exports and imports of highly productive granary and industrialised states. 

(v) Free trade zone.

Functions of political parties : 

(a) Parties contest elections.

(b) They put forward policies and programmes 

(c) Parties play a decisive role in making laws. 

(d) Parties form and run the government. 

(e) Defeated parties in the election play its role of opposition to the parties in power. 

(f) Parties shape public opinion. 

(g) Parties provide people access to government machinery and welfare schemes.

Roadways still have an edge over railways in India because : 

(a) the construction cost of roads is much lower than that of railway lines. 

(b) roads can traverse comparatively more dissected and undulating topography. 

(c) roads can negotiate higher gradients of slopes and as such can traverse mountains such as the Himalayas, 

(d) road transport is economical in transportation of few persons and relatively smaller amount of goods over short distances.

(e) it also provides door-to-door service, thus the cost of loading and unloading is much lower. 

(f) road transport is also used as a feeder to other modes of transport such as they provide a link between railway stations, air and sea ports.

Roadways are the most important means of transport in India. India has one of the largest networks of roadways in the world, aggregating about 2.3 million km. Road transport has preceded railways and still have an edge over it in view of the ease with which in can be built and maintained. Other means of transport like pipelines have limited applications and waterways are localized in rivers and waterbodies, while airways are costly and out of reach of the common people. 

Road transport is more useful than railways on account of the following merits. 

(a) Construction and maintenance of roads is much lower than the railways. 

(b) Roads can traverse comparatively more dissected and undulating topography. 

(c) They can negotiate higher gradient of slope and can traverse mountainous regions such as the Himalayas. They can reach remote villages and hilly regions where railway tracts cannot be laid. 

(d) Roads provide door-to-door service. Thus the cost of loading and unloading is much lower. 

(e) Road transport is also used as a feeder to other modes of transportation. For example, they provide a link between railway stations, airports and sea ports. 

(f) They link the villages, towns and cities with the railways. They provide linkage between ports and markets and trading centres.

Politics is the way that people living in groups make decisions. Politics is about making agreements between people so that they can live together in groups such as tribes, cities, or countries. Politicians, and sometimes other people, may get together to form a government.

Airways are the fastest, most comfortable and prestigious mode of transport in recent times. They can easily cross over geographical boundaries and vast stretches of seas and oceans. Airways can negotiate difficult terrain like high mountains, dissected terrain, dreary deserts and dense forests with great ease, within short period of time. Fast international travel between countries of the world has been possible because of the development of airways. Airways play a vital role during natural and man-made calamities like floods, famines, earthquakes, epidemics and war. They help in rescue operations and provide relief to the people in affected area within a short time. 

Two merits of airways are: 

(a) It is the fastest mode of transportation. Thousands of kilometres are covered within a few hours. 

(b) It is the most comfortable mode of transportation. One demerit of airways is the costliness of transportation because of which it is out of the reach of common people.

The following are the feature of Indian economy. 

(a) Underutilization of resources: India is endowed with rich natural resources and huge manpower but due to lack of capital and knowledge technology, the resources have not been utilized. 

(b) Agriculture—main occupation: The majority of population depends on agriculture due to underdeveloped manufacturing sector and service sector. 

(c) Low rate of capital formation: Capital formation in the form of roads, dams, bridges, machinery, tools and equipment depends upon the savings of the country. But savings depend upon the national income, which is very low. 

(d) Population pressure: Due to rapidly growing population, the comparative national product is very low. This restricts the economic development by creating problems of unemployment and underemployment. 

(e) Technological backwardness: Due to lack in technology, production is carried out using intensive labour. Less of capital, like machinery, tools and equipment, is used as compared to labour, which hampers productive capacity of the country. 

(f) Unfavourable social and religious conditions: In India, there are social and cultural institutions like caste system, joint family system, laws of inheritance and succession, and child marriage. These institutions are a serious hindrance to our economic growth. These institutions kill initiative, check mobility of labour and encourage the birth rate.

(a) If politics brings casteism and caste identity into the political arena, it can divert attention from pressing issue like poverty, development, and corruption. Thus, in any case this is not very healthy in a democracy. 

(b) Values learnt are– 

(i) Sense of equality (ii) Human dignity and freedom (iii) Promotion of healthy politics

In a democratic set-up, political parties are required because without political parties: 

(a) every candidate in the elections will be independent. No promises could be made and the utility of the government formed will remain uncertain. 

(b) no one will be responsible for running the country. Elected representatives will only be accountable to their constituency. 

(c) there will be no agency to gather and present different views on various issues to the government. 

(d) no one will be responsible for bringing various representatives together so as to form a responsible government. 

(e) there will be no mechanism to support the government, make policies and justify or oppose them.

(A) it covers those enterprises where the terms of employment are regular.

Different caste is not correct about why do different persons have different development goals.

Sum of production in three sectors is Gross Domestic product of a country.

The development goal for a girl from a rich family is to get as much freedom as her brother gets.

Tertiary sector sectors is also called service sector.

Kerala has low infant mortality rate because it has adequate provision of basic health and educational facilities.

'Challenge' is a call or summon to engage in any contest, as of skill, strength, etc.

Problem-solving is the process of thinking, through which entrepreneurs can come up with many solutions to improve their business. An entrepreneur may face many problems or challenges. It is their ability to solve them that makes them so special.