Explore topic-wise InterviewSolutions in Current Affairs.

Answer is (a) first

From the equation,

P(E₁) = 1/2, P(E₂) = 1/3, P(E₃) = 1/4

P(bar E₁) = 1/2, P(bar E₂) = 2/3, P(bar E₃) = 3/4

∴ P (not solving the Problem)

= 1/2 x 2/3 x 3/4 = 1/4

P (solving the Problem)

= 1 - (1/4) = 3/4

Salient features of centripetal and centrifugal forces. 

Centripetal Force:

• It is a real force which is exerted on the body by the external agencies like gravitational force, tension in the string, normal force etc. 
• Acts in both inertial and non-inertial frames 
• It acts towards the axis of rotation or center of the circle in circular motion

\(|\vec F_{CP}|\) = mω²r = \(\frac{mv^2}{r}\)

• Real force and has real effects 
• Origin of centripetal force is interaction between two objects. 
• In inertial frames centripetal force has to be included when free body diagrams are drawn.

 Centrifugal Force:

• It is a pseudo force or fictitious force which cannot arise from gravitational force, tension force, normal force etc.
• Acts only in rotating frames (non-inertial frame) 
• It acts outwards from the axis of rotation or radially outwards from the center of the circular motion

 \(|\vec I_{Cf}|\) = mω² r = \(\frac{mv^2}{r}\)

• Pseudo force but has real effects 
• Origin of centrifugal force is inertia. It does not arise from interaction. In an inertial frame the object’s inertial motion appears as centrifugal force in the rotating frame. In inertial frames there is no centrifugal force. 
• In rotating frames, both centripetal and centrifugal force have to be included when free body diagrams are drawn.

D) Both B & C

A non-renewable resource is a finite resource. It cannot renew itself completely, making it a valuable and limited in quantity. An example of a renewable resource is coal. Coal is a fossil fuel which is derived from the remains of plants and animals that lie buried in the earth. It takes billions of years to form naturally, so it is considered to be a non-renewable resource.

1. If the speed is increased the velocity of the motorcycle will increase and if the speed is decreased the velocity of the motorcycle will decrease.

2. As speed is scalar quantity while velocity is vector quantity so by turning velocity will change while speed remains same.

3. Its velocity will change because velocity depends on speed as well as direction and here both speed and direction are changed.

(a) increases

D) net force

Correct option is A) mass

Correct option is A) Newton

Correct option is C) 1 Newton

Correct option is: (a) Both B and C

Correct option is: (a) potential

Correct option is: (d) kinetic

Given tan^-1 {2 sin (2 cos^-1 √3/2)}

= tan^-1 {2 sin (2 cos^-1 cos π/6)}

= tan^-1 {2 sin (2 × π/6)}

= tan^-1 {2 sin (π/3)}

= tan^-1 {2 × √3/2}

= tan^-1 {√3}

= π/3

∴ tan^-1 {2 sin (2 cos^-1 √3/2)} = π/3

Given tan^-1 {2 sin (2 cos^-1 √3/2)} 

= tan^-1 {2 sin (2 cos^-1 cos π/6)} 

= tan^-1 {2 sin (2 × π/6)} 

= tan^-1 {2 sin (π/3)} 

= tan^-1 {2 × √3/2} 

= tan^-1 {√3} 

= π/3 

∴ tan^-1 {2 sin (2 cos^-1 √3/2)} = π/3

Let tan θ = 1/5 

Given tan (2 tan^-1 1/5) = tan 2θ 

We know that \(tan2\theta=\frac{2tan\theta}{1-tan^2\theta}\)

\(=\frac{2\times\frac{1}{5}}{1-\frac{1}{25}}\)

\(=\frac{\frac{2}{5}}{\frac{24}{25}}\)

\(=\therefore tan(2tan^{-1}\frac{1}{5})=\frac{5}{12}\)

\(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\)

\(=-\frac{\pi}3+\frac{\pi}6\)

{Since sin^-1x = An angle in\([-\frac{\pi}2,\frac{\pi}2]\) whose sine is x, Similarly, cos^-1 = An angle in [0, π ] whose cosine is x}

\(=-\frac{\pi}6\)

Hence,

\(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) = \(-\frac{\pi}6\)

\(\therefore\) Principal value of \(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) is \(-\frac{\pi}6\)

Given tan^-1(1) + cos^-1 (-1/2)

We know that cos^-1 (-θ) = π – cos^-1 θ

\(=\frac{\pi}{4}+[\pi-\frac{\pi}{3}]\)

\(=\frac{\pi}{4}+\frac{2\pi}{3}\)

\(=\frac{3\pi+8\pi}{12}\)

\(=\frac{11\pi}{12}\)

\(\therefore tan^{-1}(1)+cos^{-1}(-\frac{1}{2})=\frac{11\pi}{12}\)

[Formula: cos ^-1(-x)=π – cos(x) and sin ^-1(-x)= -sin(x) ]

\(\tan^{-1}1+\left(\pi-\cos^{-1}\left(\frac{1}{2}\right)\right)+\left(-\sin^{-1}\left(\frac{1}{2}\right)\right)\)

Putting the values for each of the inverse trigonometric terms

\(=\frac{\pi}{4}+\left(\pi-\frac{\pi}{3}\right)-\frac{\pi}{6}\)

\(=\frac{\pi}{12}+\frac{2\pi}{3}\)

\(=\frac{9\pi}{12}=\frac{3\pi}{4}\)

Putting the values of the inverse trigonometric terms

\(\frac{\pi}{3}+2\times \frac{\pi}{6}\)

\(=\frac{\pi}{3}+\frac{\pi}{3}\)

\(=\frac{2\pi}{3}\)

Let I = ∫x/(x² + 1)(x + 1) dx

Now, x/(x² + 1)(x + 1) = (1/2)[(x + 1)/(x² + 1) - (1/x + 1)] (partial function)

So, I = (1/2)∫x/(x² + 1) dx + ∫dx/(x² + 1) - ∫dx/(x + 1)

= (1/4) log(x² + 1) + 1/2) tan^-1 x - (1/2) log|x + 1| + k

PI₃ is used to convert ethylene glycol to ethylene.

Oxirane is the product formed when ethylene glycol is heated at 773 K.

(d)  Ethanal

(c) Either (a) or (b)

Ethene is formed when ethan – 1, 2 – diol is treated with PI₃

The correct answer is :  (b) 110 %

(a) Excretory system and Female Reproductive system

(b) 1. Kidney

2. Ureter

3. Fallopian Tube

4.Infundibulum

5. Ovary

6. Uterus

7. Urinary Bladder

8.Cervix

9. Vagina

10. Valva

(c) Function of Fallopian Tube (part 3): The fallopian tubes carry the ovum released from the ovary to the uterus.

Function of Infundibulum (part 4): Infundibulum is the funnel shaped distal end of the ovary which picks up the released ovum and pushes it further on its passage into the fallopian tube.

Function of Ovary (part 5): Ovary produces female gametes i.e. ova. 

Function of Uterus (part 6): Uterus allows the growth and development of the embryo.

(a) Testes.

(b) Ovaries.

(c) Penis.

c. secured loan.

d. commercial banks.

Commercial paper is an unsecured promissory note issued by a firm to raise funds for a short period, varying from 90 days to 364 days. It is issued by one firm to other business firms, insurance companies, pension funds and banks. The amount raised by CP is generally very large. The CP can be issued only by firms having good credit rating as this debt is totally unsecured. Issue of CP is regulated by the Reserve Bank of India.

Merits of Commercial Paper

1. A commercial paper does not contain any restrictive conditions as it is sold on an unsecured basis. 

2. It has high liquidity as it is a freely transferable instrument. 

3. It provides more funds compared to other source. 

4. The cost of CP to the issuing firm is generally lower than the cost of commercial bank lo Answer:

5. A commercial paper provides a continuous source of fund because their maturity can be tailored to suit the requirements of the issuing firm. 

6. Companies can invest their excess funds in commercial paper and can earn good return on them.

Limitations of Commercial Paper

1. Only firms which are financially sound and have high credit ratings can raise money through commercial papers. New and moderately rated firms are not in a position to raise funds by this method as these are unsecured. 

2. The amount of money that can be raised through commercial paper is limited. 

3. Commercial paper is an impersonal method of financing and if a firm is not in a position to redeem its paper due to financial difficulties, extending the maturity of a CP is not possible.

b. a budget.

b. funds raised by borrowing that must be repaid.

d. all of the above.

Correct Answer is: d. A&C.

(a) Add sodium hydrogen carbonate. Ethanol will not react. Ethanoic acid will give brisk effervescence due to carbon dioxide. 

(b) Pure ethanoic acid exist as solid like glaciers at 291 K, therefore, called glacial acetic acid.

Debentures:

• A debenture is a certificate issued by a company to public in order to obtain public money as loan.
• The way a company invites public to buy shares it can ask public to buy debentures.
• The basic difference between a share and a debenture is that a share-holder becomes the part owner of the company whereas a debenture holder becomes creditor of the company from whom the company has taken the money as loan.
• Debentures are issued when company is in need of additional capital but does not want to issue shares. The total capital needed is divided into small parts i.e. debentures and then public is invited to subscribe for them.
• Debenture is a liability to the company. Buyers of debentures become creditors of the company. The company needs to pay them interest at pre-decided rates and period. At the end of the pre-decided time frame the company as per conditions returns the entire money to the debenture holders or convert the money equal to the share value and gives shares to the debenture holders.
• Issuing debentures is a good medium-term as well as long-term nnance option for the company.
• When a company issues debentures it appoints trustees who work for protecting the interests of debenture holders as per the Trust Deed.

Debentures:

• A debenture is a certificate issued by a company to public in order to obtain public money as loan.
• The way a company invites public to buy shares it can ask public to buy debentures.
• The basic difference between a share and a debenture is that a share-holder becomes the part owner of the company whereas a debenture holder becomes creditor of the company from whom the company has taken the money as loan.
• Debentures are issued when company is in need of additional capital but does not want to issue shares. The total capital needed is divided into small parts i.e. debentures and then public is invited to subscribe for them.
• Debenture is a liability to the company. Buyers of debentures become creditors of the company. The company needs to pay them interest at pre-decided rates and period. At the end of the pre-decided time frame the company as per conditions returns the entire money to the debenture holders or convert the money equal to the share value and gives shares to the debenture holders.
• Issuing debentures is a good medium-term as well as long-term nnance option for the company.
• When a company issues debentures it appoints trustees who work for protecting the interests of debenture holders as per the Trust Deed.

Characteristics:

• Creditors of company: Since the amount of debenture is considered as loan debenture is a debt of the company and the debenture holders are the creditors of the company.
• Fixed rate of interest: Debenture holders are paid interest at fixed-rate at a pre-decided time.
• Fixed burden and charge on asset: A Company mortgages assets as security to obtain capital through debentures.
• The company needs to pay interest on debentures to the debenture holders. This interest is considered as a ‘fixed charge on the assets’ or say on the profits. This means that the company has to pay this charge even if it makes no profit. Moreover, company cannot raise loan on such assets unless it fully pays up capital borrowed from debentures. However, it can use the assets.
• Satisfy need: Debenture is a useful tool to satisfy the needs of medium term and long-term finance.
• Registration at stock-exchange: If the debentures are listed at stock-exchange, one can trade them just like shares.
• Repayment: At the end of the duration, the company returns the debenture money to debenture holders either all at once or in installments as per the pre-decided conditions.
• First preference for payment: Since debentures are debt of the company the debenture holders get the preference to receive the money before the share-holders at the time of dissolution of the company.

Preference share holders.

Encourages monopoly:

When a company retains its profit too much it becomes economically quite strong. If can then dominate the market by over stocking very large amount of raw material, forcing vendors and suppliers to follow company’s policies, ask them to create artificial scarcity etc. and hence create monopoly.

c. long-term forecast.

b. operating budget 

The asexual phase of fungi is called anamorph. 

The sexual phase of fungi is called telomorph.

• The mycelium is organised into loosely or compactly interwoven fungal tissues called plectenchyma.
• It is further divided into two types: prosenchyma and pseudoparenchyma.

Methanol and acetone are added to denature the alcohol to prevent the misuse of alcohol.