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(d) B implies A but A does not imply B.

Explanation: 

Position of CoM is given by R =(1/M)Σ_im_ir_i . If we differentiate both sides w.r.t. time t, we get, dR/dt =(1/M)Σ_im_i.dr_i/dt vcm=(1/M)Σ_im_iv_i Now if 

(B) is true, it means vcm = 0, 

→ Σ_im_iv_i = 0 =Constant. 

So (B) implies (A). 

Now let us check if (A) is true but not equal to zero 

→ Σ_im_iv_i = k Then vcm=(1/M)k =k/M =not equal to zero. i.e. CoM of the system is not at rest. So (A) does not imply (B).

(d) both A and B are false.

Explanation: 

With the application of pseudo force in a noninertial frame of reference velocities change, so do linear momentum and kinetic energy because both depend on velocity. Hence both statements are false.

The force of attraction between molecules of different substances is called adhesion.

(a) [M¹L²T^-1] = [M¹L²T^-2] x [T] → Joule-sec which are the units of Planck's constant.

(b) [M¹L²T^-1] is the dimensional formula of work or energy.

(c) [M¹L^-3T⁰] is the dimensional formula of density.

(i) Planck's constant, or angular momentum.

(ii) Work or energy or torque.

C) brightness reduced

 C) \(\cfrac{R}2\)

(i) Principal focus of a convex mirror: The principal focus of a convex mirror is a point on its principal axis from which a beam of light rays, initially parallel to the axis, appears to diverge after being reflected from the convex mirror.

(ii) Focal length of a concave mirror: The focal length of a convex mirror is the distance from the pole (P) to its principal focus (F).

1. frictional force 

2. applied force

The force applied when it is in contact with the object.

The bouncing back of light when it hits an opaque surface is called reflection of light. The two types of reflection are regular and irregular reflection.

Population ecology is an important area of ecology because it links ecology to population dynamics, genetics and evolution.

The soil characteristics along with pH, mineral composition and topography, and climatic factors determine the vegetation of an area

Correct answer is (a) Ability to concentrate urine.

Correct answer is (b) Temperature

The J-shaped growth curve indicates the minimum or absence of environmental resistance.

Correct answer is (d) Migration

Correct answer is (a) stenothermal

Species that tolerate wide range of salinity are called Euryhaline.

Characteristics of the soil are soil composition, grain size, the percolation and water holding capacity, pH, mineral composition of the soil.

Correct answer is (d) types of microorganisms

• Neurons are the functional unit and are excitable cells. 

• Neuroglia cells make up more than half the volume of neural tissue. They protect and support neurons.

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:
1. 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.

2. Fixed rate of interest:
Debenture holders are paid interest at fixed-rate at a pre-decided time.

3. 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.

4. Satisfy need:
Debenture is a useful tool to satisfy the needs of medium term and long-term finance.

5. Registration at stock-exchange:
If the debentures are listed at stock-exchange, one can trade them just like shares.

6. 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.

7. 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.

Types of debentures:
1. Secured debentures:
Debentures that are secured against company’s assets are called secured debentures. This means that at the time of dissolution if the company does not . have sufficient funds to repay the debentures than it will sell the mortgaged assets to repay. These assets carry floating charge when mortgaged.

2. Convertible debentures:

• If a company has announced that after a specific time debentures will be converted fully or partly into equity shares then such debentures are known as convertible debentures.
• If the company has made a provision of converting debentures in its Memorandum of Association then the company would give equity shares against the debentures in a pre-decide ratio.

3. Non-convertible debentures:
Debentures that are not converted into shares and whose money is returned to the debenture holders as per specific conditions and time frame are called non-convertible debentures.

Preference shares:
The shares that get the first preference to obtain dividend and during liquidation the first right to get the capital back are called preference shares. Types:
(A) Preference shares redeemable before 20 years
(B) Preference shares redeemable after 20 years

Characteristics of preference shares:
1. Dividend:
Preference share-holders possess the right to obtain dividend that too at a fixed rate irrespective of the volume of profit.

2. Right to vote:
Generally, preference share-holders do not have voting rights except for matters related to their interests.

3. Preference:
Investors prefer to buy these shares because they get a fixed income and security for their capital.

4. Market price:
The price of these shares generally remains steady i.e. it neither increase nor decrease. Their prices may change only when the rate of interest changes in the market.

5. Proportion of risk:
The risk is quite less in preference shares because holders of these shares are first paid their capital back during liquidation of company.

6. Repayment of capital:
In case the company is wound up and its assets are sold, the money that comes n this sale is first given to the preference share-holders.

Equity shares:
An equity share, commonly known as ordinary share represents the fractional or part ownership of the person i.e. share-holder in the company. Equity shares have ‘ the right to obtain dividend (i.e. earn income) as per company’s laws and right to claim repayment of share value after the company has made all its payments. After paying all the business expenses, taxes, etc. the company may earn profit. The equity share-holders have a right to claim a share in this profit. The company based on its policy may distribute a part of residual income in the form of dividends to the share-holders. The equity share-holders have a right to claim this dividend.

A company can invite people to buy its shares. The share-holders become part owners and the company gets its capital.
Characteristics of equity shares:
1. True owners:
Owners of equity shares i.e. equity share-holders are considered as true owners of the company or faithful companions because they take much higher risk on their head by investing in equity shares as compared to preference share-holders.

2. Kight to vote:
Equity share holders have right to vote for electing directors of the company. One share is equal to one vote. Thus, higher the number of shares held, higher the votes one can cast.

3. Dividend:
Whether to distribute the dividend or not and how much to distribute depends upon the company.

4. Dividend is based on profit:

• The dividend a share-holder gets depends on the profit a company makes.
• A company earning higher profit may distribute higher dividend and that making lesser profit or loss may distribute lesser dividend or may not distribute at all.

5. General meeting:
Share-holders have the right to attend general meetings and also have right to vote and elect the directors.

6. Repayment of capital:
Share capital is not repaid to the share-holders as long as the company exists. If the company winds up it returns the share capital after paying off all its business debts.

7. Dissolution (Liquidation):
At the time of liquidation the company first pays off capital of preference share¬holders and all other business debts and then if it has money, it pays to equity share-holders.

8. Share qualification:
If there is a provision in the memorandum and directors have given consent that if a particular person holds a specific number of shares decided by the company then he can become the director of the company then the shares are considered as share qualification.

9. Capital benefits:
Share-holders get various capital benefits by owning the shares. They earn dividend, company may also give them bonus shares, they earn by selling the shares whose prices have increased, etc.

10. Registration of shares:
Equity shares are registered in recognized share markets or say stock exchange. Investors can buy/sell the shares in these markets freely.

The normal content of urea in blood is 0.01 to 0.03 %.

• Sharks retain more urea in their body fluid (blood) to make their blood isotonic to surrounding marine water (in order to maintain osmotic balance). 
• This helps them to prevent possible loss of water by exosmosis.

Different DNA marker systems such as Restriction Fragment Length Polymorphisms (RFLPs), Random Amplified Polymorphic DNAs (RAPDs), Amplified Fragment Length Polymorphisms (AFLPs), Simple Sequence Repeats (SSRs) which also called as microsatellites, Single Nucleotide Polymorphisms (SNPs) and others have been developed.

Significance of inflorescence: 

1. Inflorescence makes a flower more conspicuous to attract the insects and birds for pollination. 

2. It provides more chances for cross pollination. 

3. An insect can pollinate many flowers in inflorescence in a single visit. 

4. In an inflorescence, flowers open successively and not simultaneously. This improves chances of pollination as flowering period is longer.

A specialised axis or branch over which flowers are produced or borne in definite manner is known inflorescence.

The correct answer is (B) Peduncle

The correct answer is (C) Caesalpinia

(c) introducing bone marrow cells producing ADA into cells at early embrayonic stages

Correct answer is (b) atherosclerosis

The answer is (c) Fabaceae

Microbes are also used for production of enzymes. Lipases are used in detergent formulations and are helpful in removing oily stains from the laundry. Lipases are produced by Candida lipolytica (fungus).

(i) Nucleopolyhedrovirus: Used as bio-control agents.

(ii) Saccharomyces cerevisiae: Used in bread making and in brewing industry.

(iii) Monascus purpureus: Cholesterol lowering agent

(iv) Trichoderma polysporum: Produces Cyclosporin-A

(v) Penicillium notatum: Produces antibiotic penicillin

(vi) Propionibacterium sharmanii: Produces large amount of CO₂ in Swiss cheese.

The San Andreas Fault Zone in North America.

Correct option is (B) 9 : 20

A : B = 5 : 8 and B : C = 18 : 25

A : C = \(\frac{A:B}{C:B}=\frac{5:8}{25:18}\)

\(=\frac58\times\frac{18}{25}\) \(=\frac{18}{8\times5}\)

\(=\frac9{4\times5}\) \(=\frac9{20}\)

= 9 : 20

Thus, A : C = 9 : 20

Correct option is  B) 9 : 20

1. Admissions to the students without any differences of caste/creed / religion. 

2. Elections to elect SPL / CPL 

3. Parents, teachers, associations 

4. Social clubs 

5. Community participation 

6. Equality in teaching etc.

• The Himalayas
• The Alps
• The Andes
• The Atlas

The plate margins are generally vulnerable to earthquakes, volcanoes, and faults. This is because the plate margins are weaker than other areas.

If the inequalities are vanished, the chess board will change.

Fold mountains → Plates

Himalayas → Between the Indo-Australian Plate and the Eurasian plate.

The Andes → Between South American and the Nasca plates.

The Alps → Between Eurasia and African plates.

The Atlas → Between Eurasia and African plates.

Correct option is (D) 10

x : 6 : : 5 : 3

\(\Rightarrow\) x : 6 = 5 : 3

\(\Rightarrow\) \(\frac x6=\frac53\)

\(\Rightarrow\) \(x=\frac53\times6=5\times2\) = 10

Correct option is  D) 10

Correct option is (D) 15 : 24

The compound ratio of 3 : 4 and 5 : 6 is \(\frac34\times\frac56\)

\(=\frac{15}{24}\) = 15 : 24.

Correct option is  D) 15 : 24

Correct option is (B) 200

Given that 24% value of x is 48.

i.e., \(\frac{24\times x}{100}\) = 48

\(\Rightarrow\) \(x=\frac{48\times100}{24}=200\)

Correct option is  B) 200

Speed of the train = 75 km/hr 

i) The distance travelled in 20 min. 

d = s x t = 75 x 20 min 

= 75 x 20 min = 25 km

=75 x 20/60 =75/3 =  25 km

ii) Time taken to travel 250 km

t = d/s = 250/75

t = 10/3 hrs

Correct option is (A) \(112\frac12\,km/hrs\)

Distance covered by train in \(2\frac12\) hrs = speed \(\times\) time

= 90 \(\times\) \(2\frac12\) km = 90 \(\times\) \(\frac52\) km

= 45 \(\times\) 5 km = 225 km

\(\therefore\) Speed required to covered same distance (225 km) in 2 hours \(=\frac{Distance}{Time}\)

\(=\frac{225}2\,km/hrs\) \(=112\frac{1}2\,km/hrs\)

A) 112 1/2 km/hrs

Nearly 80 percent of the world’s volcanoes are situated around the Pacific Ocean. This zone containing more than 452 volcanoes is therefore known as ‘the Pacific Ring of Fire’.

Correct option is (C) 3/8

37.5% \(=\frac{37.5}{100}\)

\(=\frac{375}{1000}\) \(=\frac{15}{40}\)

= \(\frac{3}{8}\)

Correct option is  C) 3/8