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(a) (0.25 ± 0.08) m

m₁ = 10kg, m₂ = 8kg

u₁ = 10m/s and u₂= 4m/s.

1. v₁ = v₂ = v, common velocity.

m₁u₁ +m₂u₂ = m₁v₁ + m₂v₂

10 × 10 + 8 × 4 = (10 + 8)v

or v = 7.33m/s

2. m₁u₁ – m₂u₂ = (m₁ + m₂)v

10 × 10 – 8 × 4 = (10 + 8)v

v = 3.778m/s.

The centripetal force required to keep the body in circular motion is \(\frac{mv^2}{r}\)

Here, v = 30 ms^-1

r = \(\frac {1.8 \times 10^3m}{2}\)

= 0.9 10³ = 900m

N cos θ = mg 

and \(\frac{mv^2}{r}\) = N sinθ

\(\frac{mv^2}{r}\) = \(\frac{mg}{cos \theta}\) sinθ

⇒ tan θ = \(\frac {v^2}{rg}\)

⇒ θ = tan^{-1 \(\frac {30^2}{900 \times 10}\)}

⇒ θ = tan^-1 (0.1) = 5.71°.

1. A mean solar day is the average time interval from one noon to the next noon.

Method for measurement of time:

2. The unit of time, the second, was considered to be \(\frac{1}{86400}\) of the mean solar day, where a mean solar day = 24 hours.

= 24 × 60 × 60

= 86400 s

3. However, this definition proved to be unsatisfactory to define the unit of time precisely because solar day varies gradually due to gradual slowing down of the Earth’s rotation. Hence, the definition of second was replaced by one based on atomic standard of time.

4. Atomic standard of time is now used for the measurement of time. In atomic standard of time, periodic vibrations of caesium atom is used.

5. One second is time required for 9,192.631,770 vibrations of the radiation corresponding to transition between two hyperfine energy states of caesium-133 (Cs- 133) atom.

a. kilogram/meter³ – meter, kilogram, second are basic units, kilogram/meter³ is unit of volume.

b. Volume – Volume is a derived quantity and others are basic quatities.

c. Mass – Mass is a basic quantity and others are derived quantity.

V_atom/V_nucleus = (4π(10^-10m)³)/(4π(10^-15m)³) = 10¹⁵

The unit of left hand side is metre so the units of ct² should also be metre. Since t² has unit of s², so the unit of c is m/s².

General donation is a revenue nature receipt so it will shown in income side of income & expenditure account.

Income & Expenditure Account is a nominal nature account, it shows organisation’s surplus or deficit. In it all revenue income and revenue expenditure are shown related to financial year with doing necessary adjustments.

• Depreciation on fixed assets.
• Outstanding income and outstanding expenses at the end of financial year.

Specific donation just like a capital nature receipt so it will shown in liabilities side of balance sheet not in Income & Expenditure A/c.

Sometimes Income and Expenditure A/c and Balance Sheet is given and required to prepare receipts and payments account and in such a situation. 

The following procedure may be followed:

• All expenditure whether capital or revenue irrespective of the periods are shown on the payments side.
• All receipts whether capital or revenue irrespective of the periods are shown on receipt side.
• Pick up opening and closing balance Cash and Bank A/c to the Receipt & Payment Account.
• Eliminate all adjustments made while preparing income and expenditure account.
• Purchase of assets may be calculated and shown on the payments side. For compare the values of assets at the beginning and closing of the period.
• Adjustments of prepaid exp., Advance Receipts and Outstanding Exp. should be keeping in mind regarding particular item.

Income Side:
Amount shown in income and expenditure account …………
Less: Closing outstanding subscription in current year ……….
Less: Advance subscription received in last year ……….
Add: Outstanding subscription of last year received in current year ……..
Add: Advance subscription received in current year ………….
Amount of subscription shown in receipts and payments account in current year ………..

Expenditure Items:
Amount of salary shown in income and expenditure account ……………
Less : Closing outstanding of current year …………..
Less: Advance salary paid last year (related to current year) ………..
Add: Outstanding salary of last year (which is paid this year) ………..
Add: Advance salary paid in current year related to next year ………….
Amount of salary shown in receipts and payments account ……….

Amount of Stationery Consumed:
Amount of stationery shown in income and expenditure account …………..
Less: Opening stock of stationery ………….
Add: Closing stock of stationery ………….
Less: Advance payment last year for stationery ………….
Add: Advance stationery paid in current year related to next year ………..
Less: Current year closing creditors of stationery …………
Add: Current year opening creditors of stationery ………..
Amount of stationery shown in receipts and payments account ………

(b) payment side Rs 20,000

• Set up to provide service to a specific group or the public at large.
• Managed by elected members.

Distinction between Receipts and Payments Account and Cash Book : Both receipts and payments accounts and cash book record cash transactions i.e., cash receipts and cash payments. Inspite of such similarity, 

There are some differences between the two which are enumerated below:

Distinction between Receipts and Payments Account and Income and Expenditure Account:

Steps in the Preparation of Receipts and Payments Account:

• Take the opening balances of cash in hand and cash at bank and enter them on the debit side. In case there is bank overdraft at the beginning of the year enter the same on the credit side of this account.
• Show the total amounts of all receipts on its debit side irrespective of their nature (whether capital or revenue) and whether they pertain to past, current and future periods.
• Show the total amounts of all payments on its credit side irrespective of their nature (whether capital or revenue) and whether they pertain to past current and future periods.
• Name of the receivable income and payable expenses is to be entered in this account as they do not involve inflow or outflow of cash.
• Find out the difference between the total of debit side and the total of credit side of the account and enter the same on the credit side as the closing balance of cash/bank. In case however, the total of the credit side is more than that of the total of the debit side. Show the difference on the debit as bank overdraft and close the account.

Correct answer is (a) real

• Cashbook,
• Ledger,
• Register of member,
• Register of Assets.

Correct answer is (b) nominal

• Receipts and Payments A/c
• Income and Expenditure Account
• Balance Sheet.

(b) public welfare work

Correct option (c) 3, 2   

Explanation:

The balanced chemical equation is

3CaCO₃ + 2H₃PO₄→  Ca₃(PO₄)₂ + 3H₂O + 3CO₂

Exercise equipment is any apparatus/device used during physical activity to enhance the strength or conditioning effects of that exercise. Or to otherwise enhance the experience or outcome of an exercise routine.

Exercise done by the use of equipment(s) is called as equipment based exercise. Exercise equipment must be used properly. Its inappropriate use can lead to injuries, from mild to extreme.

Exercises done without equipment like lathi; dumbells etc. is called free hands exercises.

(c) Simple and Cheap

Correct Answer is: (a) Vigil

(d) Trend analysis

(c) Trend analysis refers to the study of movement of figures for one year

The dand or lathi is a wooden stick which helps you to do physical exercises.

Activities which consume our physical or mental energy and are done intentionally or unintentionally are known as the exercises. For example, running, brooming, cooking etc are physical exercises and thinking, studying, solving problems etc are mental exercises. Different forms of exercises are physical or mental, formal or informal and general or specific.

(a) Copper (Cu) 

(b) Hydrogen (H₂) 

(c) Copper oxide (CuO) 

(d) Water (H₂O) 

(e) CuO + H₂ 

Cu + H O 

(f) Displacement reaction (which is also a redox reaction)

Exercise is good both for the body and mind. Exercises help in strengthening the various parts of the body, improve metabolism and the functioning of the body. It improves the immunity of the body too.

Exercise inculcate a sense of discipline and team spirit if done in a group as they do in schools.

A sound body also creates a sound mind. The mind is refreshed and able to work properly. This is particularly in the case of students who have to study their lessons.

(c) Glycerol

Above mentioned exercises are called general exercises which students can do it with free hands. Besides these, tradition of exercises with use of equipments are also in force. Under which students can do exercises in a more facilitated environment. These are

1. Dumbells exercise 

2. Dand (lathi) exercise 

3. Laziasm 

4. Flag exercise

In the above listed four exercises, the student can benefit his body. By doing any exercise (individually, at a time). They should not be done in groups, i.e., all at a time.

Silver (Ag) 

(b) Silver nitrate (AgNO₃) 

(c) Silver chloride (AgCl) 

(d) AgNO₃ (aq) + NaCl (aq)—–>AgCl (s) + NaNO₃ (aq) 

(e) Double displacement reaction.

(d)  Benzene

Two different initial positions for general exercises are : 

1. Stand in the position of attention. 

2. Hands up and feet together. All exercises with a jump.

Steps of exercise with initial position of attention are :

1. Stretch arms in front palms facing each other. 

2. Bring arms down and bend knees. 

3. Bring arms in front and straighten the legs. 

4. Return to the original position. 

5. Stretch arms in front. 

6. Raise arms above the shoulders, palms facing each other and bend knees. 

7. Bring arms in front and straighten the legs. 

8. Return to the original position.

Note : Repeat to the count of 16.

Steps of exercise with initially hands up and feet together and doing exercise with a jump are as follows :

1. Bend with a jump left leg ahead of right leg and raise the left arm up and stretch right arm towards back. 

2. Return with a jump to the original position. 

3. Repeat the first step with the opposite arms and legs. 

4. Return to the original position with a jump. Repeat the same process to the count of 16 set.

(c) Methanol

1. Exercise helps in building a team spirit and discipline in students. It also makes them mentally alert to study well. 

2. To activate and energise our body systems and organs as respiratory system, nervous system, circulatory system, digestive system etc. 

3. To strengthen muscles and to make the joints flexible. 

4. To make us look attractive and alert.

1. Independence Day 

2. Republic Day 

3. School Anniversary 

4. Special functions

General exercises are done regularly in the schools during the morning assembly and in the regular periods marked in time table. They are meant to promote all round development of different organs of the body.

Cumene is formed when benzene and propene is heated at 523 K

(a) 1° alcohol > 2° alcohol > 3° alcohol

(c) Dow’s process

Phenol is more acidic

Steps of Laziasm drill are as follows :

Exercise No. 1 

1. Eyes in front, step forward in the right direction with a push and strike the small iron rod in front of the left foot in the bending position. 

2. Straighten your body and bring Laziasm to the level of left thigh bone and hold together wooden rod and small iron rod. 

3. Repeat number one step. 

4. Return to the original position in the state of attention. 

5. Raise Laziasm above the head and open small iron rod in front with a turn. 

6. Strike Laziasm above the head to produce sound. 

7. Return to the position of step No. 1. 

8. Return to the original position of attention. Continue to the count of 16 set.

Exercise No. 2 

1. With a turn to the right, stretch right leg backward and open Laziasm at the back and strike rear right leg in the bending position. Keep small iron rod downward. 

2. Straighten waist without moving feet and bring small rod close to the big wooden handle. 

3. Strike Laziasm with a sound near left leg in the bending position. 

4. Gather Laziasm keeping waist straight. 

5. Bring right leg in front with a right turn and open Laziasm above the head keeping small iron rod in front. 

6. Strike Laziasm with a sound above the head remaining in the position of step No. 5. 

7. Join right leg with left leg and strike Laziasm in the bending position. 

8. Return to the original position and continue the process to the count of 16 set.

(a) Phloroglucinol

(c) 1, 3, 5 – trihydroxy benzene

The Republic.

c) Adam Smith