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(B) P-(ii), Q-(iii), R-(iv), S-(i) 

In chemistry an element is indicated by its symbol.

(1) Oils and fats are allowed to stand in air for a long time – Rancid

(2) NaOH dissolves in water – Exothermic reaction

(3) Zinc is added to CuSO₂ solution – Colourless solution

(4) Rusting of iron – Slow reaction.

Symbols of some elements are 

• Hydrogen – H 
• Helium – He 
• Boron – B 
• Carbon – C 
• Aluminium – Al

The symbols of given elements are as follows:

•  Antimony – Sb 
• Iron – Fe 
• Gold – Au 
• Silver – Ag 
• Mercury – Hg
• Lead – Pb 
• Sodium – Na

Correct answer: (b) 2 and 3

Cr₂O₇^2-/CrO₄^2-/K₂Cr₂O₇/K₂CrO_4.

Given planes are 

vector r.(2i - 7j + 4k) = 3

2x – 7y + 4z – 3 = 0 and 3x – 5y + 4z + 11 = 0 

Equation of a plane which passes through the line of intersection of the planes 

(2x – 7y + 4z – 3) + λ(3x – 5y + 4z + 11) = 0 … (1)

This passes through the point (-2, 1, 3). 

(1) ⇒ (-4 – 7 + 12 – 3) + λ(-6 – 5 + 12 + 11) = 0 

-2 + λ(12) = 0 ⇒ 12λ = 2 

λ = 2/12 ⇒ λ = 1/6

The required equation is

(1) ⇒ (2x – 7y + 4z – 3) + (1/6)(3x – 5y + 4z + 11) = 0 

12x – 42y + 24z – 18 + 3x – 5y + 4z + 11 = 0 

15x – 47y + 28z – 7 = 0

(c) vector[α,β,γ] = 0

Since vector[α,β,γ] are lie in the same plane 

So vector[α,β,γ] = 0

The required plane is perpendicular to vector(4i + 2j - 3k)

So, it is parallel to the plane 4x + 2y – 3z = k 

∴ the equation of the plane is 4x + 2y – 3z = k 

The plane passes through the point (2, -1, 1)

⇒ (4)(2) + 2(-1) – 3(1) = λ i.e. λ = 8 – 2 – 3 = 3 

So, the equation of the plane is 4x + 2y – 3z = 3.

The normal vectors are

vector n₁ = vector(2i - j + k) and vector n₂ = vector(i - j - 3k)

vector(n₁.n₂) = (2)(1) + (-1)(-1) + (1)(-3) = 2 + 1 – 3 = 0 

⇒ vector(n₁ ⊥r to n₂), i.e., the normals to the planes are at right angles. So, the planes are at right angles.

Correct option is b. PF₅

Phosphorus contains 5 electrons is its valence shell (3s² 3p³). One of the electrons is excited from 3p to vacant 3d orbital and these orbitals undergo hybridisation leading to sp³d hybrid orbitals.

Since the planes are perpendicular, the angle between the normals = 90°. 

The normals are vector n₁ = vector(2i + λj - 3k) and vector n₂ = vector(λi + 3j + k)

vector(n₁.n₂) = 0 [∵ θ = π/2] 

⇒ (2)(λ) + (λ)(3) + (-3)(1) = 0 ⇒ 2λ + 3λ – 3 = 0 

5λ – 3 = 0 ⇒ 5λ = 3 ⇒ λ = 3/5

Creativity and intelligence are positively correlated because high ability is component of creativity, A highly intelligent person may not be creative but all the creative persons are definitely high in intelligence. _

(i) Creativity is the ability to produce ideas, objects, or problem solutions that are novel, appropriate and useful.

(ii) Intelligence is subset of creativity.

(iii) Terman found that persons with high IQ were not necessarily creative. The same time, creative ideas could come from persons who did not even one of those identified as gifted, followed up through out their adult life, had become well known for creativity in some field.

(iv) Researchers have found that both high and low level of creativity can be found in highly intelligent children and also children of average intelligence. The same person can be creative as well as intelligent but it is not necessary that intelligent once must be creative.

Creative tests are different from intelligence tests:

(i)Creative tests measure creative thinking ability whereas intelligence tests measure general mental ability.

(ii) Creative tests measure convergent and divergent thinking whereas intelligence test measure convergent thinking only.

(iii)Creative tests measure imagination and spontaneous expression to produce new ideas, to see new relationship, to guess causes and consequences and ability to put things in a new context. Intelligence tests measure potential.

(iv)In creative tests questions are open-ended that have no specified answers whereas intelligence tests mostly use close-ended questions.

(i) IQ is a good predictor of potential.

(ii) EQ is a good predictor of success.

-Researchers had proved that—EQ helps in dealing with students who are stressed and face

challenges of the outside world.

-It improves the academic performance.

-It is very useful in preparing students to face the challenges of life outside the classroom.

-They are less anti-social and more co-operative.

Here AD is median. 

Therefore ar (∆ABD) = ar (∆ACD) …(i)

Reason:

(Median divides the triangle in two parts equal in areas)

Again PD is a median of ∆BPC

ar (∆BPD) = ar (∆CPD) …(ii)

Subtracting (ii) from (i), we get

ar (∆ABD) – ar (∆BPD) = ar (∆ACD) – ar (∆CPD)

⇒ ar (∆ABP) = ar (∆ACP)

The right to use the asset in lieu of specific prepayment for a specific time period.

(c) Collects the clients debt or account receivable

Factoring is a financial service under which the factor of discounting of the bills of exchange of the clients and collects his debts and also provides him information on credit worthiness of perspective client. He charges fees for the services rendered.

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.

(c) Collects the client’s debt or account receivables 

Sources of Short Term Finance: 

1. Loans and Advances 

2. Bank Overdraft 

3. Discounting Bills of Exchange

4. Trade Credit 

5. Pledge 

6. Hypothecation 

7. Mortgage 

8. Loans Against the Securities 

9. Clean Loan 

10. Commercial Paper (CP) 

11. Hire Purchase Finance 

12. Factoring

Sources of Long Term Finance:

1. Shares (i) Equity Shares (ii) Preference Shares 

2. Debentures 

3. Retained Earnings 

4. Public Deposits 

5. Long Term Loan from Commercial Banks 

6. The Loans from Financial Institutions

Artificial fibres or synthetic fibers are made of chemicals obtained from wood pulp or petroleum.

1. Artificial fibres are generally made of chemicals. 

2. Generally they are toxins. So, they mostly cause skin allergies.

1. Thermoplastic means becomes soft on absorbing heat. 

2. Artificial fibres are thermoplastic in nature.

1. To remove shrinkage silk sarees are being wrapped around a uniform wooden lag. 

2. It is kept dried for six to eight hours. 

3. Then they are allowed to steam iron. 

4. This process of removal of shrinkage from silk clothes is called ‘Rolling’.

Bleach : To remove the colour from, as by means of chemical agents or sunlight.

The cloth that is wrapped around the rod looks fine without shrinkage and wrinkles.

1. Nylon is the first fully synthetic fibre manufactured in 1931. 

2. It was prepared from coal and water. 

3. Nylon fibre is strong, elastic and light. 

4. Socks, ropes, tooth brush bristles, tents are made from Nylon. 

5. It is also used for making strong ropes for parachutes and those used for rock climbing.

1. Polyester does not get wrinkled easily. 

2. Shirts and other common dresses commonly worn by people are made from polyester.

3. Terylene is a type of polyester used for sarees and dress materials.

Wrinkles : Formation of foldings in animal fibres (wool and silk) due to poor maintenance.

1. Insects can readily feed on the protein substance present in fibres. 

2. So, we should protect silk and wool fabrics by placing phenolphthalein ball which have strong fragrance. 

3. Boric acid, fragrant oils like sandal oil and lavender oil can successfully repel the insects. 

4. By keeping these substances between the clothes we can protect silk and woolen clothes from insects. 

Polyester : It is used to make shirts, sarees and other dresses. It- doesn’t get wrinkled easily.

Recycle : The process of waste products to regain materials for human use.

Correct option is A) blending

Synthetic fabrics : The artificial fibres made from wood pulp or petroleum.

1. We wear silk fabrics during special occasions like marriages, dinners etc their beauty lustre and fine texture make thefti a symbol of aesthetic sense and pious feeling. 

2. We feel cool when we wear cotton clothes during summer. 

3. We buy woolen clothes specially for winter. 

4. Wearing clothes of natural fibres not only reflects our traditions and cultures but also eco-friendly and helping hand to the weavers too.

C) blended fibres

Correct option is A) nylon

We would find terriwool are more comfortable in winter. The reason is terriwool is similar to wool so protect us from cold.

Correct option is C) rayon

Nylon fibres are strong. So they are difficult to cut. So they are not preferable for sanitory diapers and bandages.

Given that length of the diaper = 50 cm

Breadth of the diaper = 17 cm

Area of cloth to make 1 diaper = Length x Breadth

= 50 cm x 17 cm

= 850 cm²

Thus, Area of 25 such diapers = (25 x 850) cm² 

= 21,250 cm²

Area of total cloth = Area of 25 diapers = 21,250 cm²

It is given that width of a cloth = 170 cm

Length of the cloth = Area of cloth

We have width of cloth = 170 cm

Length of a cloth = 21,250/170 cm = 125 cm

Hence, length of the cloth will be 125 cm.

(c)  y = x

dy/dx = 1, d²y/dx² = 0

d²y/dx² - x²dy/dx + xy = 0

(i) Given 

f(x) = x⁴ – 8x³ + 22x² – 24x + 5 at x = 0, -2 

f'(x) = 4x³ – 24x² + 44x – 24 

At x = 0, f'(0) = -24 < 0 

∴ f(x) is decreasing at x = 0 

At x = -2, f'(-2) = 4(-2)³ – 24(-2)² + 44 (-2) – 24 < 0 

= 32 – 96 – 88 – 24 <0 (negative) 

∴ f(x) is decreasing at x = -2 

(ii) Given 

f(x) = 4x³ – 15x² + 12x – 2 at x = 1,-1 

f'(x) = 12x² – 30x + 12 

At x = 1, f'(x) = 12 – 30 + 12 = -6 < 0 

∴ f(x) is increasing at x = 1

At x = -1, f'(-1) = 12(-1)² – 30 (-1) + 12 = 54 > 0 

∴ f(x) is increasing at x = -1 

(iii) Given 

f(x) = (x – 1) (x – 2)² at x = 1, 3 

f'(x) = (x – 1) (2 (x – 2) + (x – 2)²) 

At x = 1, f'(1) = 0 + (-1)² = 1 > 0 

∴ f(x) is increasing at x = 1 

At x = 3, f'(3) = 2 × 2(1) + 1 = 5 > 0 

∴ f(x) is increasing at x = 3.

The study of man and machine interactions and control methods are known as Cybernetics.

• Causative Pathogen: Virus. 
• Mode of infection: Through blood and semen of infected person and milk of mother suffering from AIDS. 
• Preventive measure: Safe sexual contact, avoid resuse of needles and injections.