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∠ACD = 180 – (30 + 90) = 60 

∠BCD = 60 – 15 = 45 ∠CBD = 45

∠ABC = 135 [∵ 180 – (30 + 15)]

BD = \(\frac{BC}{\sqrt{2}}=\frac{12}{\sqrt{2}}=6\sqrt{2}\) = 8.48

CD = \(6\sqrt{2}\)

(∵ ∆BCD is an isosceles right angles)

AC = 2 x \(6\sqrt{2}=12\sqrt{2}\)

AD = \(6\sqrt{2}\times\sqrt{3}=6\sqrt{6}=14.69\)

AB = AD - BD = 14.69 - 8.48 = 6.21

The ratio of the sides of the triangle with angles 30°, 15°, 135° are 12 : 6,21 : \(12\sqrt{2}\) 

Q – meter works on the principle of series resonance.

Use the asset for a specified period.

Ownership Capital

Ploughing back of profit

Long Term Sources: 

The amount of funds required by a business for more than five years is called long-term finance. Generally this type of finance is required for the purchase of fixed assets like land and building, plant and machinery furniture, etc. It include sources such as shares and debentures, long-term borrowings and loans from financial institutions. 

Short Term Sources: 

Short-term funds are those which are required for a period not exceeding one year. These sources include Trade credit, loans from commercial banks and commercial papers etc. Short-term finance is used for financing of current assets such as accounts receivable and inventories.

Equity Share Capital

Collects the client’s debt or account receivables.

(a) Owners of the company

generated within the business.

Retained earnings

(a) Owners of the company

Types of Preference Shares: 

a. Cumulative and Non-cumulative Preference Share: In cumulative preference shares, the unpaid dividends are accumulated and carried forward for payment in future years. On the other hand, in non- cumulative preference share, the dividend is not accumulated if it is not paid out of the current year’s profit. 

b. Participating and Non-participating Preference Share: Participating preference shares have a right to share the profit after making payment to the equity shares. The non-participating preference shares do not enjoy such a right. 

c. Convertible and Non-convertible Preference Share: The preference shares which can be converted into equity shares after a specified period of time are known as convertible preference share. Nonconvertible shares cannot be converted into equity shares. 

d. Redeemable and Irredeemable Preference Share: Redeemable preference shares are those where the company undertakes to repay it after a specified period. Where the amount of the preference shares is refunded only at the time of liquidation, are known an irredeemable preference shares. 

Merits: 

1. Preference shares provide reasonably steady income in the form of fixed rate of return and safety of investment. 

2. Preference shares are useful for those investors who want fixed rate of return with comparatively low risk 

Limitations: 

1. Preference shareholders have no voting right. 

2. The dividend paid is not deductible from profit for income tax.

The correct answer is an Excise tax.

• Tax can be divided into two categories.

• First is Direct Tax such as Income tax, wealth tax, and corporation tax.
• The second is Indirect Tax such as Sales tax, Excise duty, and customs duty.
• Indirect tax means that tax that reaches the government indirectly.
• Such tax is completely opposite to direct tax.
• The tax levied by the state on consumption, import, export, and production, etc. is an indirect tax.
• Excise Duty is a type of Indirect Tax which is imposed on all production or manufacturing of goods.

•  The Appointments Committee of the Cabinet (ACC) has appointed Shri J B Mohapatra as Chairman, Central Board of Direct Taxes (CBDT).

Debentures are called creditorship securities.

Ownership Securities

Secured debentures

(i) a business proposal 

(ii) give you five minutes. 

(iii) just three minutes will do.

Convertable debentures

The important differences between ADR and GDR are:

It is Leasing

(c) Participate in the surplus profit

Preference shares.

ADRs are issued in USA

1. Yes, it is possible to add transportation and loading charges to the purchased price of furniture.

2. “Historical cost principle” – This principle requires that all transactions should be recorded at their acquisition cost. The cost of acquisition refers to the cost of purchasing the asset and expenses incurred in bringing the assets to the intended condition and location of use.

Answer is Factoring

1. Leasing 

2. Factoring 

3. Mutual fund

The accountant’s viewpoint is correct because the business is separate from the businessmen as per the ‘‘Accounting Entity Concept”.

Factoring service

Lease Financing: 

A lease is a contractual agreement whereby the owner of an asset (lessor) grants the right to use the asset to the other party (lessee). The lessor charges a periodic payment for renting of an asset for some specified period called lease rent. 

Merits: 

1. It enables the lessee to acquire the asset with a lower investment; 

2. Lease rentals paid by the lessee are deductible for computing taxable profits; 

3. It provides finance without diluting the ownership or control of business 

4. The lease agreement does not affect the debt raising capacity of an enterprise;

5. Simple documentation makes it easier to finance assets. 

Limitations: 

1. A lease arrangement may impose certain restrictions on the use of assets. 

2. The normal business operations may be affected in case the lease is not renewed. 

3. The lessee never becomes the owner of the asset.

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

\(\frac{y-3}{x+1}=\frac{2}{3}\)

3(y - 3) = 2(x + 1)

2x - 3y + 11 = 0

x coordinate of R = 2 + 1 – (–3) = 6

y coordinate of R = 9 + 7 – 2 = 14

(6, 14) is the coordinate of R

\(PR=\sqrt{((6-(-3))^2+((14-2))^2}\)

= \(\sqrt{9^2+12^2}\) = 15 unit

Mid point of the line segment joining the line segment joining the points (3, 0), (–1, 4).

\(=(\frac{3-1}{2},\frac{0+4}{2})=(1,2)\)

A(0, 0), B(10, 0), C (5, 5√3)

AB = 10 unit

BC = \(\sqrt{(10-5)^2+(0-5\sqrt{3})^2}\)

= \(\sqrt{25+75}\) = 10 unit

AC = \(\sqrt{(10-5)^2+(0-5\sqrt{3})^2}\)

= \(\sqrt{25+75}\) = 10 unit

AB = BC = AC

∴ ΔABC is equilateral

∵ Straight line can be formed by joining two points & triangle can be formed by joining three non-collinear points.

(i) Number of ways in which 2 points are selected from 13 points = \(^{13}C_2\).

But given that 6 points are collinear (in straight line).

Therefore these 6 points can form only one line.

So, we have to subtract (\(^6C_2\) - 1) from the ways of selection 2 points from 13 points.

∴ Total straight lines that can be possible 

= \(^{13}C_2\) - (\(^6C_2\) - 1)

= \(\frac{13\times 12}{2}\) - \(\frac{6\times 5}{2}\) + 1

= 13 x 6 - 15 + 1

= 78 - 14

= 64.

(ii) Number of ways in which 3 non-collinear points are selected from 13 points = \(^{13}C_3\).

But given that 6 points are collinear that never be formed any triangle.

So, we have to subtract the selection of 3 non-collinear points from these 6 points.

So, total number of triangle = \(^{13}C_3\) - \(^{6}C_3\)

= \(\frac{13\times 12\times 11}{3\times 2}\) - \(\frac{6\times 5\times 4}{3\times 2}\)

= 286 - 20

= 266.

Given that,

A is on y−axis with ordinate of 5

⇒A is (0,5) and B is (−3,1)

Length of AB = Distance between their co-ordinates

= \(\sqrt{(0-(-3))^2 + (5-1)^2}\) 

= 5 units

Shortest distance from the origin (0, 0) to the plane x- 2y - 2z = 3 is

\(d = \left| \frac{0-2\times 0 - 2\times 0 -3}{\sqrt{1^2 + (-2)^2 + (-2)^2}}\right| = \left|\frac{-3}{\sqrt{1 + 4 + 4}}\right|\)

\(= \frac 3{\sqrt 9} = \frac 33 = 1\) unit

|x| is non-differentiable at x = 0.

Similarly |2x + 3| is non- differentiable at point where 2x + 3 = 0

⇒ \(x = \frac{-3}2\)

Hence, f(x) = |2x + 3| is non-differentiable at \(x = \frac{-3}2\).

\(y = tan^{-1} (cot (\pi/2 - x))\) 

y = tan^-1 (tanx) = x

\(\frac{dy}{dx} = 1\)

Bioreactors are vessels in which raw materials are biologically converted into specific products such as enzymes using microbial, plant, animal or human cells. A bioreactor provides the optimal conditions for achieving the desired product by providing optimum growth conditions like temperature, pH, substrate, salts, vitamins and oxygen