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The first 8 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, and 24.

Answer: (r + s)* = (r*s*)*

Explanation.
Let take string” rrssrs”
Take + as either one of the path and * as the loop either 0 or more times.
Option (A)  (r + s)* = r* s*
left side  may be
While()
{
Either r or s
};
Left side realize the string. Where as right side fails to realize the string. Because r* s*=
While()
{r}
While()
{s}.
Option (B) (r + s)* = r* + s*
Left side realize the string where as r* + s* =
If()
{
while()
{r
}
Else
{
while()
{s}
}
So right side fails to realize the string “rrssrs”.
Option (C)    (r + s)* = (r*s*)* .

While()
{
While()
{
R
}
While()
{
S
}
}

Right side also realize the string. Hence the answer.

Logical matrix

The lines in atomic spectra can be used to identify unknown atoms, just like finger prints are used to identify people.

The light ray travelling from air into water bends towards the normal. 

Reason : Light ray bends towards the normal when it travels from rarer medium to denser medium.

(1) Take a magnet.

(2) Rotate the magnet in the sand.

(3) Magnet attracts in the iron dust.

(a) Liquation. 

(C) l.p - l.p > l.p - b.p > b.p - b.p

(i) 1 – hexyne 

(ii) Butanaldehyde

The number of ions of opposite charge that surround a given ion of given charge known as coordination number of that given ion.

The Ammeter.

(1) DE

(2) Here the temperature of water is not changed.

i – c, ii – a, iii – b

d_{x² – y²} orbital does the given diagram represent.

(A) a – ii, b – i, c – iii

C_nH_2n–2 is A .

Height of the real image is taken as Negative.

 The focal length of a convex lens is Positive.

(1) "Whenever there is a continuous change of magnetic flux linked with a closed coil, a current is generated in the coil". This is a law of induced emf or a Faraday's law. 

(2) There are so many devices are working with this principle. 

Those are (1) Induction stove, (2) ATM cards, 

(3) Security alarms, 

(4) Taperecorders, etc. 

(3) So, I appreciate the role of induced emf.

The speed of light in that medium 2 × 10⁸ m/s.

In First Plan was the growth rate target exceeded.

Sorensen introduced pH scale.

(d) neither exports nor imports take place

Correct option: (a) Roll up and down

(b) Both A and R are true ; R is correct explanation to A.

(c) the public, private, joint and Cooperative sectors

(a) in the Union List 

(a) Planning Commission

National Development Council was set up in 1952.

Correct option: (c) Current Tracer

South to North.

(a) Metals of group 'B' are moderately reactive. 

Because, they are found in the Earth crust mainly as oxides, sulphides and carbonates. 

(b) Metals of group 'A' are never found in nature in free state. 

Because they are highly reactive. 

(c) Zn : Incite (ZnO) and Zincblende (ZnS). 

Fe : Haematite (Fe₂O₃) and Magnetite (Fe₃O₄). 

(d) Metals of group 'C' are used to make jewellary. 

Because, they donot oxidize in normal weather conditions.

• What happens to light wave falling normally to glass slab?
• State the laws of reflection and refraction?
• Why does refraction occur when light passes from one medium to another?
• Define critical angle for an interface of two media?
• A rod immersed partially or obliquely in water appears to be bent. Explain.
• Differentiate between optical density and mass density?
• Why are rays falling over a mirror or a lens considered to be paraxial?
• Derive the mirror equation?
• Explain the illusion, mirage seen on a hot summer day in desert?
• Explain the term photometry?
• Derive the Len’s maker’s formula?
• How do thin prisms deviate light?
• Write a short note on:

a) Compound Microscope 

b) Telescope 

c) Human Eye 

d) Formation of rainbow

y² dx = (1 - 3xy) dy 

dx/dy = 1/(y²) - 3x/y

dx/dy + 3x/y = 1/y² 

This is a first order linear differential equation of the form x' + P(y)x = Q(y) where the integrating factor = e^{(∫P(y) dy)} = e^{(∫3/y dy)} = y³ 

Multiplying both sides by integrating factor: 

y³(dx/dy) + 3y^2x = y 

Note that the left hand side equals d/dy[x*y^3], so: d/dy[xy³] = y 

Integrating both sides: 

xy³ = (y²)/2 + C 

x = 1/(2y) + C/(y³)

The country’s great, liberal constitution was supposed to end the millennia-old obsession with the idea that your place in life, including your occupation, is set at birth. It abolished “untouchability”—the practice whereby others in society exclude so-called untouchables, or Dalits, as polluting—which has now mostly disappeared from Indian society. Various laws forbid discrimination by caste. At the same time (it is somewhat contradictory) official schemes push “positive” discrimination by caste, reserving quotas of places in higher education, plus jobs in government, to help groups deemed backward or deprived. In turn, some politicians have excelled at appealing to voters by caste, promising them ever more goodies. For example Mayawati, formerly chief minister of Uttar Pradesh state (population: over 200m) and just possibly a future prime minister, leads a Dalit party. In another northern state, Bihar, parties jostle to build coalitions of caste groups. Everywhere voters can be swayed by the caste of candidates.

But don’t blame politicians alone. Strong social actors—such as leaders of “khap panchayats” (all-male, unelected village councils) or doughty family elders—do much more to keep caste-identity going. Consider marriages. In rural areas it can be fatal to disregard social rules and marry someone of a different, especially if lower caste. Haryana, a socially conservative state in north India, is notorious for frequent murders of young men and women who transgress. Even in town, caste is an important criterion when marriages are arranged. Look at matrimonial ads in any newspaper, or try registering for a dating site, and intricate details on caste and sub-caste are explicitly listed and sought (“Brahmin seeks Brahmin”, “Mahar looking for Mahar”) along with those on religion, education, qualifications, earning power and looks. Studies of such sites suggest that only a quarter of participants state that “caste is no bar”. Such attitudes also reflect the anxieties of parents, who are keen for children to marry within the same group, because marriages bring extended families intimately together.

As long as marriages are mostly within the same caste, therefore, don’t expect any law or public effort to wipe away the persistent obsession with it. That seems set to continue for a long time: a survey in 2005 found that only 11% of women in India had married outside their caste, for example. What is changing for the better, if too slowly, is the importance of caste in determining what jobs, wealth, education and other opportunities are available to an average person. No caste exists for a call-centre worker, computer programmer or English teacher, for example. The more of those jobs that are created, and the more people escape India’s repressive villages, the quicker progress can come.

The depletion of ecosystems is often due to the over-exploitation of their resources. Although these activities may serve a short-term economic goal, this kind of exploitation can actually lead to direct adverse effects on social welfare in the medium and long terms.

 In the case of tropical forest degradation, population growth, poverty, environmentally damaging government subsidies, environmentally unsustainable export policies, failure to appreciate the ecology of natural systems and, as a consequence, failure to value the ecological services that the ecosystem provides can lead to degradation.

Human activity is causing environmental degradation, which is the deterioration of the environment through depletion of resources such as air, water and soil; the destruction of ecosystems; habitat destruction; the extinction of wildlife; and pollution.

At present, there is no reservation in Civil Posts and Services under the Government of India and admission to Central Educational Institutions for Minority Communities declared by the Central Government under Section 2(c) of National Commission of Minorities Act, 1992.

Answer: True

Explanation:

Since there's only two possibilities. the probability of either of the two possible outcomes will be 1/2.

Correct option (D) Statement – 1 is False, Statement – 2 is True

Explanation:

f(x) = 0 represents an identity if a² – a – 6 = 0 

⇒ a = 3, –2 

 a² – a – 6 = 0

⇒ a = 3, –2

a² – a = 0 

⇒ a = 3, –3 

 a² – 2a –3 =0 

⇒ a = 3, –1

⇒ a = 3 is the only values.