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I =  ∫ cosec6 x dx

I = ∫ cosec⁴ x cosec² x dx

We know that:

cosec² x =  1 + cot² x

I = ∫ cosec⁴ x (1 + cot² x) dx

I = ∫ cosec⁴ x dx + ∫ cot² x cosec⁴ x dx

I = ∫ cosec² x cosec² x dx + ∫ cot² x (cosec² x cosec² x) dx

I = ∫ cosec² x (1 + cot² x) dx + ∫ cot² x cosec²x (1 + cot² x) dx

I = ∫ cosec² x dx + ∫ cosec² x cot² x dx + ∫ cot² x cosec² x + ∫ cot⁴ x cosec² x dx

I = ∫ cosec2 x dx + 2 ∫ cosec2 x cot2 x dx + ∫ cot4 x cosec2 x dx

Put cot x = z

By differentiating we have,

- cosec² x dx = dz

I = ∫ (- dz) + 2 ∫ z² (- dz) + ∫ z⁴ (- dz)

 \(I~=~-~z~-~\frac{2z^3}{3}~-~\frac{z^5}{5}~+~c\)

Put z = cot x in above equation:

\(I~=~-~cot~x~-~\frac{2cot^3~x}{3}~-~\frac{cot^5~x}{5}~+~c\)

\(I~=~\frac {-1}5 \cot^5x-\frac 2 3 \cot^3 x - \cot x + c\)

CONTRL + S a key command to save a project or session in Neundo/ Cubase.

To open a vsti window in necundo-F-11 

To split a track in neundo – opt+x

1. directly from the transport panel 

2. to press Control + T for opening new window of BPM

G command to zoom out in Neundo / Cubase.

An Input list is a chart of all instruments and microphones which are connected to the audio mixing console .Input list contents information about each channel of audio mixing console which is connected to different instruments by using different microphones. An input list also contain the information about phantom power on/off microphones stands and insert.

Band Name-

Date-

Contact Details-

Following things have to be covered in Input list :-

This input list goes on according to requirements of instruments.

Both A and R are true, but R is not the correct explanation of (A) .

Concept:

1 + cos 2x = 2cos2 x

1 - cos 2x = 2sin2 x

\(\rm \int \cos x\;dx = \sin x + c\)

Calculation:

I = \(\rm \int sin^2 x\;dx\)

= \(\rm \int \frac{1-\cos 2x}{2}\;dx\)

= \(\rm \frac{1}{2}\int (1-\cos 2x)\;dx\)

= \(\rm \frac{1}{2} \left[x-\frac{\sin 2x}{2} \right ] + c\)

= \(\rm \frac{x}{2}-\frac{\sin 2x}{4} + c\)

Concept:

Integral property:

• ∫ xn dx = \(\rm x^{n+1}\over n+1\)+ C ; n ≠ -1
• \(\rm∫ {1\over x} dx = \ln x\) + C
• ∫ ex dx = ex+ C
• ∫ ax dx = (ax/ln a) + C ; a > 0,  a ≠ 1
• ∫ sin x dx = - cos x + C
• ∫ cos x dx = sin x + C

Integration by parts: Integration by parts is a method to find integrals of products. The formula for integrating by parts is given by:

⇒ \(\rm ∫ u vdx=u ∫ vdx- ∫ \left({du\over dx}\times ∫ vdx\right)dx \) + C

where u is the function u(x) and v is the function v(x) 

ILATE rule is Usually, the preference order of this rule is based on some functions such as Inverse, Logarithm, Algebraic, Trigonometric and Exponent.

Calculation:

I = ∫ (x2 cos x) dx

Using integration by parts

⇒ I = x² ∫ cos x dx - ∫ \(\rm \left({dx^2 \over dx}\times ∫ \cos xdx\right)\) dx + C

⇒ I = x² sin x - ∫\(\rm \left(2x\sin x\right)\) dx + C

⇒ I = x2 sin x - 2 ∫ \(\rm x\sin x\) dx + C

⇒ I = x2 sin x - 2[x ∫ sin x dx - ∫ \(\rm \left({dx \over dx}\times ∫ \sin xdx\right)\)dx] + C

⇒ I = x2 sin x - 2x (-cos x) + 2 ∫ - cos x dx + C

⇒ I = x2 sin x + 2x cos x - 2 sin x + C

First We will open Neundo. Then we will go to the file and select new. We will give the name of the project by making a folder and save it in the desired location. 

Fixing BPM Time signature and Pitch- We will fix the BPM according to our requirement. Then we will fix the time signature and Pitch.

Making Rhythm - For making rhythm we will open a MIDI track then select a drum kit according to our song requirement. Then we will record kick, tom, snare, Hi hat and other percussion instruments in a multi/separate tracks.

Making Melody and Chords- Then we have to open instruments track and select a melodic instruments then play and record the melody line. Then we will record chords /bass line suitable to the melody. 

This is a basic structure of a demo song.

Concept:

\(\rm \tan^{-1} x - \tan^{-1} y = \tan^{-1}\left[ \frac{x-y}{1+xy} \right ]\)

\(\rm \frac{d(\tan^{-1} x)}{dx}= \frac{1}{1+x^2}\)

Calculation:

Given: y = \(\rm \tan^{-1}\left[ \frac{2x}{1+15x^2} \right ]\)

\(\rm y=\rm \tan^{-1}\left[ \frac{5x-3x}{1+5x\cdot 3x} \right ]\)

As we know that, \(\rm \tan^{-1} x - \tan^{-1} y = \tan^{-1}\left[ \frac{x-y}{1+xy} \right ]\)

So, \(\rm y=\rm \tan^{-1}\left[ \frac{5x-3x}{1+5x\cdot 3x} \right ]\)= tan-1 5x - tan-1 x

Differentiating with respect to x, we get

\(\rm \frac{dy}{dx}=\frac{d(\tan^{-1} 5x)}{dx}-\frac{d(\tan^{-1} 3x)}{dx}\)

\(= \rm \frac{5}{1+(5x)^2}-\frac{3}{1+(3x)^2}\)

\(=\rm \frac{5}{1+25x^2}-\frac{3}{1+9x^2}\)

Vijay Amritraj

Dadasaheb Phalke

Concept:

Integral property:

• ∫ xn dx = \(\rm x^{n+1}\over n+1\)+ C ; n ≠ -1
• \(\rm∫ {1\over x} dx = \ln x\) + C
• ∫ ex dx = ex+ C
• ∫ ax dx = (ax/ln a) + C ; a > 0,  a ≠ 1
• ∫ sin x dx = - cos x + C
• ∫ cos x dx = sin x + C

Integration by parts: Integration by parts is a method to find integrals of products. The formula for integrating by parts is given by:

⇒ \(\rm ∫ u vdx=u ∫ vdx- ∫ \left({du\over dx}\times \int vdx\right)dx \) + C

where u is the function u(x) and v is the function v(x) 

ILATE rule is Usually, the preference order of this rule is based on some functions such as Inverse, Logarithm, Algebraic, Trigonometric and Exponent.

Calculation:

I = ∫ (x ln x) dx

Using integration by parts

⇒ I = ln x ∫ x dx - ∫ \(\rm \left({d\ln x\over dx}\times \int xdx\right)\) dx + C

⇒ I = \(\rm {x^2\over2}\) ln x - ∫ \(\rm \left({1\over x}\times{x^2\over2}\right)\) dx + C

⇒ I = \(\rm {x^2\over2}\) ln x - ∫ \(\rm {x\over2}\) dx + C

⇒ I = \(\boldsymbol{\rm {x^2\ln x\over2}-}\) \(\boldsymbol{\rm {x^2\over4}}\) + C

Concept:

\(\rm \tan^{-1} x + \tan^{-1} y = \tan^{-1}\left[ \frac{x+y}{1-xy} \right ]\)

\(\rm \frac{d(\tan^{-1} x)}{dx}= \frac{1}{1+x^2}\)

Calculation:

Given: y = \(\rm \tan^{-1}\left[ \frac{8x}{1-15x^2} \right ]\)

\(\rm y=\rm \tan^{-1}\left[ \frac{5x+3x}{1-5x\cdot 3x} \right ]\)

As we know that, \(\rm \tan^{-1} x + \tan^{-1} y = \tan^{-1}\left[ \frac{x+y}{1-xy} \right ]\)

So, \(\rm y=\rm \tan^{-1}\left[ \frac{5x+3x}{1-5x\cdot 3x} \right ]\)= tan-1 5x + tan-1 x

Differentiating with respect to x, we get

\(\rm \frac{dy}{dx}=\frac{d(\tan^{-1} 5x)}{dx}+\frac{d(\tan^{-1} 3x)}{dx}\)

\(= \rm \frac{5}{1+(5x)^2}+\frac{3}{1+(3x)^2}\)

\(=\rm \frac{5}{1+25x^2}+\frac{3}{1+9x^2}\)

Durga Shankar Mukherjee

The molecules must colloid to react with one another. The number of collision is very big but the rate of most of the reactions are still slow, because rate of reactions are depend on the rate of collision as well as orientation of the collision.

correct option is d) All of the Above

In water PbI₂ more soluble as compare to the given other solvents. In water there is no common ions effect while in, Pb(NO₃)₂, NaI and KI solvents, there are common ion effects due to this PbI₂ less soluble in these solvents compare to water.

correct option is d) All of the above

The correct answer is Rajnath Singh:

• Defence Minister Rajnath Singh inaugurated 2nd production line of Hindustan Aeronautics Limited''s Tejas Light Combat Aircraft in Bengaluru on 2 February 2021.
• The delivery of the Tejas LCA to the Indian Air Force under a Rs. 48,000-crore deal will begin from March 2024.
• Around 16 aircraft will be rolled out annually till the completion of the total supply of 83 jets.
• The Cabinet Committee on Security (CCS) chaired by Prime Minister Narendra Modi on January 13, 2021, approved the largest indigenous defence procurement deal worth about Rs. 48,000 crores to buy 83 LCA Tejas Mark1A fighter jets.

correct option is c) IAF’s airstrike during “Operation Vijay” 

correct option is b) Fighter Aircraft 

• Automatic Summarization, 
• Sentiment Analysis, 
• Text classification, 
• Virtual Assistants

correct option is a) India 

A) Bluetooth is a wireless technology standard for exchanging data over short distances (using short-wavelength UHF radio waves in the ISM band from 2.400 to 2.485 GHz from fixed and mobile devices, and building personal area networks (PANs).

B) General Packet Radio Services (GPRS) is a packet based wireless communication service that promises data rates from 56 up to 114 Kbps and continuous connection to the Internet for mobile phone and computer users. The higher data rates allow users to take part in video conferences and interact with multimedia Web sites and similar applications using mobile handheld devices as well as notebook computers. GPRS is based on Global System for Mobile (GSM) communication and complements existing services such circuit-switched cellular phone connections and the Short Message Service (SMS).

C) A subscriber identity module or subscriber identification module (SIM), widely known as a SIM card, is an integrated circuit that is intended to securely store the international mobile subscriber identity (IMSI) number and its related key, which are used to identify and authenticate subscribers on mobile telephony devices (such as mobile phones and computers).

D) UMTS (Universal Mobile Telecommunications Service) is a third generation (3G) broadband, packet-based transmission of text, digitized voice, video, and multimedia at data rates up to 2 megabits per second (Mbps).

E) Infrared radiation (IR), sometimes referred to simply as infrared, is a region of the electromagnetic radiation spectrum where wavelengths range from about 700 nanometers (nm) to 1 millimeter (mm).Infrared waves are longer than those of visible light, but shorter than those of radio waves.

Correct answer is a) 1 -> B; 2 -> A; 3 -> D; 4 -> C 

correct option is d) MiG-27

Automatic Summarization is an example of Applications of Natural Language Processing.

b) You do not need an Internet connection to use your Gmail account. 

Correct answer is b) Internet of Things 

Evaluation is the last stage of the AI project Life cycle. 

correct option is d) All of the Above

Correct answer is c) Ruler 

Correct answer is c) Both Statement1 and Statement 2 are correct 

In Deep Learning, the machine is trained with huge amounts of data which helps it in training itself around the data. 

Correct answer is a) Circles -> elements; arrowed lines -> relationship 

Correct answer is d) Both Statement 1 and Statement 2 are incorrect

1  E) enjoyed themselves by singing and dancing all night.

2  B) a terrible storm at sea

3  A) everyone was feeling happy

Financial market plays an important role in the allocation of scarce resources in an economy by performing the following four important functions.

1. Mobilisation of savings and channelizing them into the most productive uses: A financial market facilitates the transfer of savings from savers to investors. It gives savers the choice of different investments and thus helps to channelize surplus funds into the most productive use. 

2. Facilitating price discovery: In the financial market, the households are suppliers of funds and business firms represent the demand. The interaction between them helps to establish a price for the financial asset which is being traded-in that particular market. 

3. Providing liquidity to financial assets: Financial markets facilitate easy purchase and sale of financial assets. In doing so they provide liquidity to financial assets, so that they can be easily be converted into cash whenever required. 

4. Reducing the cost of transactions: financial markets provide valuable information about securities being traded in the market. It helps to save time, effort and money to both buyers and sellers of a financial asset.

Correct option: a) Surveys and Interviews

Surveys, Observing the therapist’s sessions, Databases available on the internet, Interviews, etc.

Correct option is: (C) Informal organisation

c) Our airlines have a problem that the current boarding system wastes four minutes of time when passengers aboard the plane. An ideal solution would be to board the plane from the sides rather than from the back to the front. 

Correct answer is c) ii) , iii) and iv) 

Factors affecting the requirement of Fixed Capital: 

1. Nature of Business: The type of business has-a bearing upon the fixed capital requirement. A trading concern needs lower investment in fixed assets compared with a manufacturing organization. 

2. Scale of Operations: A larger organization operating at a higher scale needs the bigger plants, more space, etc and therefore, requires higher investment in fixed assets. A smaller organization requires less fixed capital. 

3. Choice of Technique: Some organizations are capital intensive which require higher investment in plant and machinery. Therefore the requirements of such capital intensive business units are more. Labour intensive organizations require less fixed capital comparatively. 

4. Technology Up-gradation: Higher investment in fixed assets requires more fixed capital. The organizations which use assets which are prone to obsolescence require higher fixed capital to purchase such assets repeatedly.

Correct answer is d) Web scraping

Semantic barriers are concerned with problems and obstructions in the process of encoding and decoding of message into words or impressions. 

Some Semantic barriers are as follows: 

1. Badly expressed massage: Badly expressed massages may be on account of inadequate vocabulary, usage of wrong words, omission of needed words, etc., 

2. Symbols with different meanings: A word may have several meanings. Receiver has to perceive the right meaning of the word used by communicator. Wrong perception leads to communication problems. 

3. Faulty translations: Sometimes, the communications originally drafted in one language need to be translated to the language understandable by the receivers. If the translator is not proficient with both the languages, mistakes may creep in causing different meanings to the communication. 

4. Unclarified assumptions: Some communication may have certain assumptions which are subject to different interpretations. These assumptions may lead to wrong understanding between the speakers.

Controlling is a systematic process involving the following steps: 

1. Setting performance standards: The first step in the controlling process is setting up of performance standards. Standards are the criteria against which actual performance would be measured. Standards can be set in both quantitative as well as qualitative terms. 

2. Measurement of Actual Performance: Once performance standards are set, the next step is measurement of actual performance. It is generally believed that measurement should be done after the task is completed. 

3. Comparing actual performance with standards: This step involves comparison of actual performance with the standard. Such comparison will reveal the deviation between actual and desired results. Comparison becomes easier when standards are set in quantitative terms. 

4. Analysing deviations: Some deviation in performance can be expected in all activities. After identifying the deviations that demand managerial attention, these deviations need to be analysed for their causes. These causes may be unrealistic standards, defective process, inadequacy of resources, structural drawbacks, etc. It is necessary to identify the exact cause of deviation, failing which an appropriate corrective action might not be possible. 

5. Taking corrective action: The final step in the controlling process is taking corrective action. No corrective action is required when the deviations are within acceptable limits. When the deviations go beyond the acceptable range, it demands immediate managerial attention. Corrective action might involve training of employees if the production target could not be met.

1. Functional structure: Grouping the jobs of similar nature and organizing these major functions as separate departments create a functional structure. All departments report to a co-coordinating head. It is more useful for large organisation. 

2. Divisional structure: Grouping of activities on the basis of product is known as divisional structure. Under this structure the top-level delegates extensive authorities to the divisional heads. The divisional head is in charge of manufacturing, purchase, sales, engineering and other departments of the division. 

He is also made responsible for the profit or loss of his division. Divisional structure is advantageous for an organisation involved in production of different lines of products.

Given:

Given numbers are 5/6, 11/12 and 8/9

Calculation:

LCM of 6, 12 and 9 is 36

\({5 \over 6} \Rightarrow {{5 \times 6} \over {6 \times 6}} \Rightarrow {30 \over 36}\)

\({11 \over 12} \Rightarrow {{11 \times 3} \over {12 \times 3}} \Rightarrow {33 \over 36}\)

\({8 \over 9} \Rightarrow {{8 \times 4} \over {9 \times 4}} \Rightarrow {32 \over 36}\)

From 30, 33 and 32 arranging them in ascending order get 30 < 32 < 33

∴ The required ascending order is \(\dfrac{5}{6}, \dfrac{8}{9}, \dfrac{11}{12}\)