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Linear regression is one of the most common techniques of regression analysis. It is also called a simple linear regression. It establishes the relationship between two variables using a straight line. Linear regression attempts to draw a line that comes closest to the data by finding the slope and intercept that define the line and minimize regression errors.

Multiple regression is a broader class of regressions that encompasses linear and nonlinear regressions with multiple explanatory variables.

It is rare that a dependent variable is explained by only one variable. In this case, an analyst uses multiple regression, which attempts to explain dependent variable using more than one independent variable. Multiple regressions can be linear and nonlinear.

There are two broad categories of POS systems: 

• The hardware and software combination 
• The target business segment of the POS system

Given:

The given number = 195112

Concept:

Calculation skills trick

Calculation:

Step(1):

First, we will take the digit at the unit’s place.

At the unit place, we have 2.

Step(2):

Now consider the cube table, the cube of which number has 2 as at the unit digit place.

We see, 8 x 8 x 8 = 512.

Step(3):

That means the cube root of 195112 will have 8 at the unit place.

Step(4):

Now ignore the last 3 digits of 195112, i.e. 112

Step(5):

Taking 195 as a reference number, we can see from the cubes table 195 lies between cubes of 5 and 6.

Step(6): Here, we choose the lower number i.e. 5

∴ We get the two digit of the answer

∴ Cube root of 195112 = 58

Given:

Reduction price = 25%

C.P. = 100

Formula used:

C.P. : M.P. = (100 - discount) : (100 + Profit)

Calculations:

Here, discount = 25%

⇒ Profit = 20%

According to formula

⇒ C.P./M.P. = (100 - 25)/(100 + 20)

⇒ Here, if 75 = 750

⇒ Then, 120 = 1200

∴ M.P. is Rs. 1200

Given:

Successive discounts = 23% and 46%

Formula used:

When two successive discounts a and b are given, then single discount is calculated as follows ∶

Single discount = [a + b – (ab/100)]%

Calculation:

Single discount = [a + b – (ab/100)]%

⇒ [23 + 46 – (23 × 46/100)]%

⇒ [69 – 10.58]%

⇒ 58.42%

∴ The single equivalent discount is 58.42%.

Given 

Marked price of toy = Rs 770 

Discount percent = 10% 

Formula used 

Marked price : cost price = 100 + profit% : 100 - discount% 

Calculation 

⇒ Marked price : Cost price = 110 : 90 = 11 : 9 

⇒ Marked price = Rs 770 

⇒ 11x = 770 

⇒ x = 70 

⇒ Cost price of toy = 9x = 9 × 70 = Rs 630 

∴ the cost price of a toy is Rs 630 

Objectives of Accounting 

The following are the main objectives of accounting: 

1. To maintain the records of a business as Book-keeping. 

2. To ascertain Profit or Loss 

3. To ascertain Financial Position 

4. To communicate financial information

Benefits of using Telemarketing 

• The main benefit of using telemarketing to promote the business is that it allows you to immediately gauge your customer's level of interest in your product or service. 
• Provide a more interactive and personal sale service. 
• Create an immediate rapport with your customers. 
• Explain technical issues more clearly. 
• Generate leads and appointments. 
• Sell from a distance to increase your sales territory 
• Reach more customers than with in-person sales calls. 
• Sell to both existing and new customers. 
• Achieve results that are measurable

Correct answer is: (C) Both (A) and (R) are incorrect.

Correct answer is: (A) Both (A) and (R) are correct and (R) is the correct reason of (A).

It is an accounting information system that processes the financial transaction and events as per GAAP.

The types of computer are: 

1. Super Computer 

2. Main Frame Computer 

3. Mini Computer 

4. Micro Computer.

Correct answer is: (D) All three (a), (b), (c)

The accounting cycle is a collective process of identifying, analyzing, and recording the accounting events of a company. It is a standard 8-step process that begins when a transaction occurs and ends with its inclusion in the financial statements.

Under single entry system adjusted capital means, closing capital adjusted with drawings and additional capital called adjusted capital [Closing capital + Drawings – Additional Capital = Adjusted Capital].

Correct answer is: (A) ₹1,20,000.

A bill which is accepted by a party and for which he has to pay money called bills payable. Bills payable is a liability.

Trial balance is the list of all debit and credit balances of accounts taken out from the ledger at a given period.

A single transaction entering both the side of two or three column cash book called contra entries.

The three types of accounts under English system are: 

• Personal account 
• Real account 
• Nominal account 
• Revaluation or valuation account

An assets acquired by a concern is recorded in the books of accounts at cost called cost concept.

However, the Rent payable is appearing in credit side of Trial balance.

The value of tan 105° is -2 - √3 or -3.7321 (approx).

Electrowinning is a widely used technology in modern metal recovery, mining, refining, and wastewater treatment applications.

Given straight lines are

x - 2y + 3 = 0

⇒ 2y = x+3

⇒ y = x/2 + 3/2 .......(1)

And 6x+3y+8 = 0

⇒ 3y = -6x - 8

⇒ y = -2x - 8/3 ........(2)

The slope of line (1) is m₁ = 1/2 (By comparing equation y = mx + c)

And slope of line (2) is m₂ = -2

We obsened that m₁ m₂ = 1/2 x -2 = -1

which is condition that both lines are pependicular.

Hence, given lines are pependicular to each other.

In acidic medium the number of electrons involved are 5.

Mno₄ + 8H+ + 5e– → Mn²⁺ + 4H₂O

Eq. mass of KMnO₄ = 158/ 5 =31.6

In basic medium the number of electrons involved are 3.

Mno₄ + 2H₂O+ + 3e– → MnO₂ + 4OH-

Eq. mass of KMnO₄ = 158/ 3 = 52.7

Equivalent mass of KMnO₄ in acidic and alkaline medium is 31.6 and 52.7 respectively.

Let the slope of the required line is m₁

Given line is x - 3y - z = 0

⇒ 3y = x - z

⇒ y = 1/3 (x-2) = 1/3 x - 2/3

Hence, the slope of given line is m₂ = 1/3

Given that angle betwen both lines is 135.

Therefore, tan 135° = \(\frac{m_1-m_2}{1+m_1m_2}\)

⇒ m₁ - m₂ = (-1) (1+m₁m₂)  (∵ tan 135° = tan (90°+45°) = -cot 45° = -1)

⇒ m₁ - 1/3 = -1 (1 + 1/3 m₁)  (∵ m₂ = 1/3)

⇒ m₁ + 1/3 m₁ = -1 + 1/3

⇒ 4/3 m₁ = -2/3

⇒ m₁ = -2/4 = -1/2

Thus, the slope of required line is m₁ = -1/2.

Since, given that line is passing through point (2, -1)

Therefore, equation of line is y - (-1) = m₁ (x-2)

⇒ y+1 = -1/2 (x-2)  (∵ m₁ = -1/2)

⇒ 2y+2 = -x+2

⇒ x+2y = 0

Hence, the equation of required line is x + 2y = 0

Immunoglobulin G, or IgG, antibodies are produced 7 to 14 days after infection.

A={1,2,3,......n}  B={a,b}

A has n elements B has 2 elements

number of surjection is 2ⁿ−2

So, option (b) is correct

Note: The number of surjections from set A having n elements to set B having 2 elements is 2ⁿ−2

Answer:

A contains 5 elements

B contains 6 elements

Since number of elements in B is more than A there cannot be any one-one and onto mapping from A to B

So, the correct answer is (c) i.e 0

Solution:

We have given that point let A(1,2) and point B(3,4) and

the equation is 3x-4y+a = 0

putting both values of A and B in LHS of equation, we get

3*1-4*2+a = 0 --------(1)

a = 5

3*3-4*4+a = 0 ------------(2)

a = 7

From both equation we get the values of a

a =5 and a= 7

So the correct answer is (b)

If a pair of linear equations in two variables is inconsistent then they have no solution.

x³ −6x+11x−6=0 

Put X=1 

1−6+11−6=0 

1 is root of equation, so (x−1) is factor of x³ −6x² +11x−6 

x² −5x+6=0 

(x−3)(x−2)=0 

x=2,3 

root of cubic equation =1,2,3

Given LHS = sin^-1 (2x - √ (1 – x²))

Let x = sin θ

= sin^-1 (2sin θ √ (1 – sin² θ))

We know that 1 – sin² θ = cos² θ

= sin^-1 (2 sin θ cos θ)

= sin^-1 (sin² θ)

= 2θ

= 2 sin^-1 x

= RHS

∴ sin^-1 (2x - √ (1 – x²)) = 2 sin^-1 x

1+ tan 60° + tan 30° x tan 60° +  tan 30°

= (1 + tan 30°) (1 + tan 60°)

= (1 + tan 30°) (1 + cot 30°) .....(1)

(∵ tan (90 - θ) = cot θ)

If you are asking for values the put

tan 30° = \(\frac{1}{\sqrt 3}\) & cot 30° = \(\sqrt{3}\)

∴ 1+ tan 60° + tan 30° x tan 60° +  tan 30°

= (1 + \(\frac{1}{\sqrt 3}\)) (1 + \(\sqrt{3}\)) (From (1))

= \(\frac{(\sqrt3+1)^2}{\sqrt3}\) 

= \(\frac{3+1+2\sqrt3}{\sqrt3}\)

= \(\frac{4}{\sqrt 3}\) + 2

Objectives of accounting in any business are; systematically record transactions, sort and analyzing them, prepare financial statements, assessing the financial position, and aid in decision making with financial data and information about the business.

1. Two or More Persons 

2. Agreement 

3. Lawful Business 

4. Registration 

5. Profit Sharing 

6. Agency Relationship 

7. Unlimited Liability 

8. Not a Separate Legal Entity 

9. Transfer of Interest

10. Mutual Trust and Confidence 

11. Number of Partners 

12. Profit Sharing 

13. Principal-Agent Relationship 

14. Joint Ownership 

15. Ownership and Control 

16. Registration 

17. Duration 

18. Capital and a Few Others.

The derivative is defined as something which is based on some other thing. In Mathematics, Derivative is an expression that gives the rate of change of a function with respect to an independent variable. Derivatives have various applications in Mathematics, Science, and Engineering. We’ll learn about these application of derivatives in the topics below.  

• Rate of Change of Quantities 
• Approximations 
• Increasing and Decreasing Functions 
• Maxima and Minima 
• Tangents and Normals

Capital Reserve is a reserve that is created out of capital profits i.e. gains or profits arising from other than the normal activities of business operations i.e. activities other than sale or purchase of goods and services. This reserve is utilised to meet future capital losses, if any, and to issue bonus shares. It cannot be distributed as dividend among the shareholders.

Nature of the business/Profit or loss sharing ratio.

False. Receipt and payment account is a summary of all capital receipts and payments.

1. Public company 

2. Private company.