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(2)

3° alcohols react fastest with ZnCl₂/conc.HCl due to formation of 3° carbocation and\2–methyl propan–2–ol is the only 3° alcohol

Pedicure Procedure 

Always remember to keep your implements clean: if they are left dirty they may harbor germs and cause infections.

Preparation 

• Before we begin, make sure you are properly prepared. Disinfect all hard surfaces, then wash your hands with soap and water and sanitize them with an instant hand sanitizer

• Make certain your rolling cart is fully stocked with a disinfection tray, Spa Pedicure products, other pedicuring products, implements, tools, towels and polishing products. 

Trim the nails 

• All pedicure clients should have filled out the consultation form (client profile) covering medical history and other important information. Remember, you must proceed with caution if a client is diabetic, calling the client’s physician for clearance if you have any doubts, and never perform a pedicure in an extreme situation, such as open sores or infections of the foot or leg. 

Filing of Nails 

• Plan on the service taking around an hour to complete. This includes a six to seven minute massage per leg. When you do the service in the salon, complete each step on all five toes before going on to the next step. 

Preparing the Bath 

• Fill the foot bath with warm water—this means under 37°C, or a comfortable temperature. Add the water to agitate as it fills to create light foam in the bath. 

• Let your client get settled in the chair with shoes, socks or nylons removed. You may provide a robe if the client so desires. 

• Submerge both the client’s feet in the warm water, adding more water if necessary to adjust the temperature to the client’s comfort. 

• Soak the clients feet for 5 minutes in the bath to take full advantage of the softening effects of Rice Bran and Vitamin E Oils. As they soak, remove your instruments from the disinfection unit and lay them on a clean, sanitized towel. 

Disinfect the foot 

Procedure 

• Begin by placing a clean, sanitized terry towel in your lap, and remove one foot from the water. Pat the foot dry and remove the enamel from the toenails. 

• Gently massage for 2 to 3 minutes, concentrating on areas of extreme dryness, then rinse and pat dry. • Wrap the foot in a clean towel. 

• Unwrap the first foot and run the Callus Smoother over all calluses to reduce and smooth. Use a circular motion to reduce calluses inlayers until the skin is pink and pliable. Rinse the foot and towel dry. 

Exfoliate the feet 

• Do not return the foot to the bath as you use the Callus Smoother on the other foot. when both feet are clean, exfoliated, and dry, you are ready to proceed to the next portion of the service. 

• Gently push back and remove non-living (true) cuticle from around the proximal and lateral nail folds, staying away from the eponychium. 

• Trim the corner of the big toenail at a 45° angle. Using firm ‘balance-point’ positioning and holding the toenail trimmer like scissors- between thumb and middle finger, leaving the index finger free for balance slide the tip of the trimmer under the corner at a 45° angle, so you can see the trimmer on the other side of the nail. Make sure you don’t leave a hook or spike behind on the lateral nail edge. 

• Guide a curette, small spoon tool or orangewood stick along the lateral nail edge in the direction of nail growth. Do this on both sides of the nail to remove non-living tissue and debris. 

• After all five toenails have been pedicured, rinse the foot in the bath and pat dry. 

Moisturize 

• Cover the entire foot up to the top of the ankle, leaving no bare spots. Then wrap it in a clean, dry terry towel and let this foot rest while you work on the other foot. 

• Pedicure the second foot in the same manner as the first. 

• Cover the second foot with moisturizer, wrap it in a clean, dry terry towel and let this foot rest while you return to the first foot. 

• Place the pedicure tools back into the disinfection unit. 

• Unwrap the first foot and completely rinse the entire masque from the foot, using a soft brush or cloth if needed. Pat dry. 

• Apply Nail Enamel – begin by placing toe Separators between the toes, apply one thin coat of base coat and allow it to dry, apply a thin coat of nail enamel and after it dries completely apply a one coat of top coat. 

• Allow enough time for enamel completely cure and then apply foot powder on the soles.

(2) q = 0, ΔT = 0 and w = 0 

free expansion of ideal gas 

P_ext = 0 

W_pv = 0 

q = 0 (adiabatic process) 

ΔE = q + w 

ΔE = 0 

ΔE = nC_vm ΔT = 0 

q = 0, ΔT = 0, w = 0 

Personality is shaped through family, culture, society, education and other environmental factors.

Entrepreneurship is a process of developing a business plan, launching and running a business using innovation to meet customer needs and to make a profit. 

A data type is a classification of the type of data that a variable or object can hold.

(1) (c) and (d) only 

Correct statement are (c) and (d) 

(c) use of zeolite (3d-silicate) 

(d) CO-neutral, colourless & odourless gas.

Methanamine > benzenamine > ammoxia

(c) NH₃

NH₃ is used as refrigerant in an ice plant.

Types of Skin 

• Normal 

• Dry 

• Oily

• Combination 

• Sensitive 

Oily skin is hereditary, and develops due to an overproduction of sebum from the sebaceous glands. There is always a tendency for clients to over treat their skin if it is oily; however, this can compound the problem as excessive stimulation results in stripping and irritating the skin, making it become dry and unbalanced. The skin’s natural protection mechanism will then respond by producing more oil. The client will usually report that their skin develops a ‘shine’ during the course of a day, their skin often feels 

Thick and dirty, due to the accumulation of the sebum and dead cells clogging the surface and suffer with blemishes.

Correct option is (a) 6.5

(a) Freezer

Evaporator of a refrigerator is also known as Freezer.

Correct option: (c) Plate type natural convection evaporator

\(12345 \times 12345 - 12345 \times 2345\)

\(= 12345 (12345 - 2345)\)

\(= 12345 \times 10000\)

\(= 123450000\)

\(= 1.2345 \times 10^8\)

Correct option: (b) Dry expansion evaporator

Going out for drinking with friends implies a gathering filled with fun and laughter, usually to celebrate good news, involving least decorum. Therefore, Option B is correct. The rest of the options express more formal settings, hence incorrect.

Hence, option B is the correct answer.

Correct option is A) coach

Correct option is (b) (3a, 2a, 3a), (a, a, a)

Explanation :

The given line L₁ is

x/1 = (y + a)/1 = z/1

P is a point on L₁. Therefore

P = (t, -a + t, t) ...(1)

and the given line L₂ is

(x + a)/2 = y/1 = z/1

Q is a point on L₂. Therefore

Q = (-a + 2s,s,s) ...(2)

From Eqs. (1) and (2), the DRs of vector PQ are 

(2s - a - t,s - t + a,s - t) 

Therefore, by hypothesis, we have

(2s - a - t)/2 = (s - t + a)/1 = (s - t)2

Hence

(2s - a - t)/2 = (s - t + a)/1

t = 3a

(s - t + a)/1 = (s - t)/2 

s - t = - 2a

s = a (∵ t = 3a)

Therefore, P = (3a, 2a, 3a) and Q = (a, a, a)

Concept:

A relation R in a set A is called 

(i) Reflexive, if (a, a) ∈ R, for every a ∈ A.

(ii) Symmetric, if (a, b) ∈ R implies that (b, a) ∈ R, for all a, b ∈A.

(iii) Transitive, if (a, b) ∈ R and (b, c) ∈ R  implies that (a, c) ∈ R, for all a, b, c ∈A.

Calculation:

Given: R = {(a, b): a2 ≥ b}

We know that a2 ≥ a

Therefore (a, a) ∈ R, for all a ∈ Z.

Hence, relation R is reflexive.

Let (a, b) ∈ R

⇒ a2 ≥ b but b2 \(\ngeqslant\) a for all a, b ∈ Z.

So, if (a, b) ∈ R then it does not implies that (b, a) also belongs to R.

Hence, relation R is not symmetric.

Now let (a, b) ∈ R and (b, c) ∈ R.

⇒ a2 ≥ b and b2 ≥ c

This does not implies that a2 ≥ c, therefore (a, c) does not belong to R for all a, b, c ∈ Z.

Hence, relation R is not transitive.

Hence, option 4 is the correct answer.

Concept:

If A, B and C are three sets such that  \(R\subseteq A\times B\) and \(S\subseteq B\times C\) then (SOR)-1 = R-1 O S-1. It is clear that if a R b, b S c ⇒ a S O R c.

If R is a relation from set A to set B, then inverse relation of R to be denoted by R-1, is a relation from set B to set A.

Symbolically R-1 = {(b, a): (a, b) ∈ R for all a ∈ A and b ∈ B}.

A relation R on a set A is said to be identity relation on A if R = {(a, b): a ∈ A, b ∈ A and a = b}.

A relation R from A to B is said to be the universal relation, if \(R = A\times B\).

A relation R from A to B is called an empty relation or a void relation from A to B if R = ø.

Calculation:
Given that,  A = {2, 3, 4} and B = {5, 6, 7} 

Relation R = {(a, b): a ∈ A, b ∈ B and b = a + 3}

Roster form R = {(2, 5), (3, 6), (4, 7)}

R^-1 =  {(5, 2), (6, 3), (7, 4)}

we see that,

2 → 5 → 2 ⇒ (2, 2) ∈ R^-1OR

3 → 6 → 3 ⇒ (3, 3) ∈ R-1OR

4 → 7 → 4 ⇒ (4, 4) ∈ R-1OR

Hence R-1OR = {(2, 2), (3, 3), (4, 4)}

we see that R-1OR is identity relation.

The correct answer is 11101.

• The binary equivalent of decimal 29= 11101.
• Step 1: Perform the successive modulo operation by 2 for the given decimal number 29 and note down the remainder (either 0 or 1) for each operation.
  • 29 / 2 = 14: Remainder = 1 → LSB
  • 14/ 2 = 7: Remainder = 0
  • 7 / 2 = 3: Remainder = 1
  • 3 / 2 = 1: Remainder = 1
  • 1 / 2 = 0: Remainder = 1 → MSB.
  • LSB(least significant bit): The last remainder.
  • MSB(most significant bit): The first remainder.
• Step 2: Write the remainders from MSB to LSB to provide the equivalent binary number.
• 2910= 111012 

Consider a binary relation on a set A has {a, b, c} 

A x A = { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }

Option a:  The smallest reflexive relation is {(a,a) (b,b) (c,c)}

True,  A relation R on set A is said to be reflexive, all diagonal relation have to present. So the smallest reflexive relation is {(a,a) (b,b) (c,c)} and The largest reflexive relation is { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }

Option b: The largest symmetric relation is {(a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }

True, The smallest symmetric relation is { } and The largest symmetric relation is { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }.

Option c: The largest equivalence relation is A x A.

True, An Equivalence relation is always Reflexive, Symmetric, and Transitive. The largest symmetric relation is { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) } and it Reflexive, and Transitive. And it also  A x A relation.

Option d: The number of partially ordered relations on set A (1,2) is 5.

False, A relation is partially ordered relation iff Reflexive, Antisymmetric and Transitive. So the number of partaially ordered relations on set A is 3 are,

• {(1,1) (2,2)}
• {(1,1) (1,2) (2,2)}
• {(1,1) (2,2) (2,1)} 

So only d  is False.

Hence the correct answer is only d.

Concept:

Divide number into the whole number part (32) and decimal number part (0.25).

Divide the whole number part by 2 and note down the remainder in each step. Keep doing this until the result of the division is 1.

For the decimal part, keep on multiplying the decimal number by 2 and note down the digit before the decimal point in each step. Keep doing this until the result is a whole number.

Then, just join the whole number and the decimal part to find the binary number.

Calculations:

Divide number into the whole number part (32) and decimal number part (0.25).

Divide the whole number part by 2 and note down the remainder in each step. Keep doing this until the result of the division is 1.

32/2 = 16, remainder 0

16/2 = 8, remainder 0

8/2 = 4, remainder 0

4/2 = 2, remainder 0

2/2 = 1, remainder 0

Now, write down the remainders in reverse order. Hence, binary of 32 is 100000.

For the decimal part, keep on multiplying the decimal number by 2 and note down the digit before the decimal point in each step. Keep doing this until the result is a whole number.

0.25 × 2 = 0.5, digit before decimal is 0

0.5 × 2 = 1, digit before decimal is 1

Now, write down the digits. Hence, the binary of 0.25 is 0.01.

Then, just join the whole number and the decimal part. Hence, binary of 32.25 = 100000.01

Sometimes, planets in our solar system are classified with their position relative to the asteroid belt, which lies approximately between Mars and Jupiter. With this scenario, "inner" planets are Mercury, Venus, Earth and Mars. "Outer" planets are Jupiter, Saturn, Uranus and Neptune.

Thallophytes are a polyphyletic group of non-mobile organisms that are grouped together on the basis of similarity of characteristics, but do not share a common ancestor. They were formerly categorized as a sub-kingdom of kingdom Plantae. These include lichens, algae, fungus, bacteria and slime moulds and bryophytes.

Characteristics of Thallophyta

• They are usually found in moist or wet places. 
• This is due to the absence of “true roots” and vascular tissue that is needed to transport water and minerals. Hence they are found in moist or wet places. 
• They are autotrophic in nature. 
• Most members in this group manufacture their own food. But a few members like fungi are dependent on other sources of food., 
• Reserve food is generally starch. 
• After photosynthesis, glucose is produced and consumed almost immediately, the remaining glucose is converted into complex compounds called starch. 
• They have a cell wall composed of cellulose around their cells. 
• Absence of vascular tissue. 
• Unlike other plants, xylem and phloem are absent. etc 
• Sex organs are simple, single-celled, there is no embryo formation after fertilization.

Correct option is (4) Viruses are facultative parasite

In colder countries it reduces the energy bill significantly. The cost of lightning is reduced as the glass helps with better natural illumination and also the heating due to green house effect reduces the need for extra heating. These are essentially the same reasons that lead to higher energy consumption in the hotter countries like India. As the sunlight is very hot the curtains and blinds remain perpetually drawn resulting in a need for extra illumination and the green house effect increases the need for higher cooling. The Air Conditioning systems feel inadequate most of the time. It is like living inside a large inefficient Solar Cooker.

Correct option  (4) More than 2R

Explanation:

V = (G + R) I_g

To increase the range of voltmeter, resistance R must be increases.

V ∝ R 

If we want to double the range, more than 2R, added

HCOOH > CH₃COOH > Cl₂CHCOOH > ClCH₂COOH

If R is increased, the current through the potentiometer wire will decrease. Due to it, the potential gradient of potentiometer wire will also decrease. AS a result of it, the balancing length will increase i.e. the position of J will shift on potentiometer wire towards B.

Correct answer is (a)

We have 

m² + a₁m + b₁ = n² + a₂n + b₂ 

n² + a₁n + b₁ = m² + a₂m + b_2. 

Hence 

(a₁ - a₂)(m + n) = 2(b₂ - b₁); (a₁ + a₂)(m - n) = 2(n² - m²).

This shows that a₁ + a₂ = -2(n + m). 

Hence 

4(b₂ - b₁) = a²₂ - a²₁. 

Since a₁ + a₂ and a₁ - a₂ have same parity, it follows that a₁ - a₂ is even.

If a fraction is simultaneously in the forms (7k - 5)/(5k - 3) and (6l - 1)/(4l - 3), 

we must have 

(7k - 5)/(5k - 3) = (6l - 1)/(4l - 3),

This simplies to kl + 8k + l - 6 = 0. We can write this in the form

(k + 1)(l + 8) = 14:

Now 14 can be factored in 8 ways: 1 x 14, 2 x 7, 7 x 2, 14 x 1, (-1) x (-14), (-2) x (-7),(-7) x (-2) and (-14) x (-1). 

Thus we get 8 pairs:

(k; l) = (13;-7); (6;-6); (1;-1); (0; 6); (-15;-9),(-8;-10); (-3;-15); (-2;-22):

These lead respectively to 8 fractions:

43/31, 31/27, 1, 55/39, 5/3, 61/43, 19/13, 13/9.

d = {"January":31, "February":28, "March":31, "April":30, "May":31, "June":30, "July":31, "August":31, "September":30, "October":31, "November":30, "December":31}

a = input("Enter the name of the month: ")

for i in d.keys():

    if i==a:

        print("There are ",d[i],"days in ",a)

print()

print("Months arranged in alphabetical order: ", end="")

b=[]

for i in d.keys():

    b.append(i)

b.sort()

print(b)

print()

print("Months with 30 days: ", end="")

for i in d.keys():

    if d[i]==30:

        print(i, end="")

print()

print()

c = [("February",28)]

for i in d.keys():

    if d[i]==30:

        c.append((i,30))

for i in d.keys():

    if d[i]==31:

        c.append((i,31))

print(c)

Code:

a = []

for i in range(1, 101):

    if i%3==0 or i%5==0:

        a.append(i)

print(a)

Given:

If a product is sold at a 10% discount, the selling price is Rs. 72.

Formula used:

S.P = M.P × (100 – D)/100

Where,

S.P → Selling price

M.P → Marked price

D → Discount%

Calculations:

Suppose marked price = Rs. x

S.P = x × (100 – 10)/100

⇒ 0.9x = 72

⇒ x = Rs. 80

On discount of 25%:

S.P = 80 × (100 – 25)/100

⇒ 80 × 0.75

⇒ Rs. 60

Given:

CP = Rs. 30000, Discount = 50% and Profit = 25%

Formula used:

S.P = C.P × (100 + P)/100

M.P = S.P × 100/(100 – D)

Where,

S.P → Selling price

C.P → Cost price

M.P → Marked price

P → Profit%

D → Discount%

CALCULATION:

Applying the formula:

SP = 300000 × (100 + 25)/100

⇒ 30000 × 1.25 = 37500

Marked price = 37500 × 100/(100 – 50)

⇒ 37500 × (100/50) = Rs. 75000

Calculation:

Ratio of investment of Jay and Diya  40000 : 60000

⇒ Jay : Diya = 2 : 3

⇒ Let be total profit = x

⇒ profit left after Rs x(100 - 30)% = 0.7x

⇒ Jay share in profit = Rs.14000 = (profit left after taxes) × (ratio of Jay share)

⇒ 14000 = 0.7× 2/5 

⇒ 1400 × 5 = 1.4x

⇒ (14000× 5) /1.4x = 50,000

∴ Total profit = 50,000 

Let the C.P be Rs x 

1st S.P=125% of x =125x/100=5x/4; 2nd S.P=80% of x=80x/100=4x/5 

2nd S.P=130% of 4x/5=(130/100*4x/5)=26x/25  

=>5x/4-26x/25=10.50

x=(10.50*100)/21=50 

hence C.P=Rs.50

Given:

Cost price of 12 pens = Selling price of 10 pens

Formula Used:

Profit percentage = {(S.P – C.P)/C.P} × 100

Calculation:

Let the C.P. of each pen = Rs. 1

C.P. of 12 pens = Rs. 12

S.P. of 10 pens = Rs. 12

C.P of 10 pens = Rs. 10

Profit = Rs. (12 – 10) = Rs. 2

Profit % = (2/10) × 100 = 20%