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F(X,Y,Z)= X’Y’Z’+X’Y’Z+XY’Z’+XYZ

OR F(X,Y,Z)=∑(0,1,4,7)

The angle made by a line parallel to z axis with x, y and z axis are 90°, 90° and 0° respectively.
The direction cosines of the line are cos 90°, cos 90°, cos 0° i.e, 0, 0, 1.

The correct option is (c) p + 9q.

10th term = p + (10 – 1)q 

a₁₀ = p + 9q

The correct option is (a) 6.

2x, (x + 10), (3x + 2) are in A.P. 

x + 10 – 2x = 3x + 2 – x – 10 

x = 6

Given A.P. 

24, 21, 18,..... 

First term = 24 = a 

and common difference = – 3 = d ...(i) 

Let no. of terms is n. 

Sum of n terms = \(\frac{n}{2} [2a + (n - 1)d]\)

According to question

\(78 = \frac{n}{2} [2 \times 24 - 3 \times (n -1)]\) [from (i) and given]

\(78 = \frac{n}{2} [51- 3n]\)

n² – 17n + 52 = 0

n² – 13n – 4n + 52 = 0 

n(n – 13) – 4 (n – 13) = 0 

(n – 13) (n – 4) = 0 

n = 13, 4 

For first 4 terms and first 13 terms in both case we get sum 78.

Accidentally, when live and neutral wires of an electric circuit comes into direct contact, it is called short circuiting.

1. Ba(N₃)₂ \(\overset{Heat}{\longrightarrow}\) Ba + 3N₂
2. 2NH₄Cl + Ca(OH)₂ → 2NH₃ ↑ + CaCl₂ + H₂O

1. Osmotic pressure : It is the pressure applied on higher concentration side of a semipermeable membrane so that there is no net flow of solvent molecules in either side of the membrane.
2. Hypertonic solution : The solution having an osmotic pressure more than the reference solution is known as Hypertonic solution.

Analgesics: They are the drugs used for relieving pain. Analgesics are classified into two categories:

(a) Narcotics (addictive) drugs (b) Non-narcotics (non-addictive) drugs

(a) Narcotics: Narcotic drugs are recommended for cardiac pain, post operative pains, terminal cancer and in child birth.

(b) Non-narcotics: Non-narcotic drugs are effective in relieving skeletal pain, reducing fever, preventing heart attack.

At equilibrium AD = AS or C + I = Y 200 + 0.5 Y + 1500 = Y 

1700 = 0.5Y , 

Y = 3400 

Putting the value of Y in the eq

C = 200 + 0.5 x 3400 , 200 + 1700, C = 1900

(c) Capital expenditure

We know that C = c + bY , by putting value We get 

C = 500 + 0.4 x 5000, C = 2500

Y = C + I

5000 = 2500 + I 

I = 2500

(a) Value Addition is the contribution of the enterprise to the current flow of goods and service. In other words, value added can be defined as the difference between value of output of a firm in a n accounting year and value of inputs brought from other firms (or value of intermediate consumption). Value added = Value of Output – Value of Inputs 

(b) Gross Domestic Product (GDP) : Gross Domestic Product (GDP) is the market value of all the final goods and services produced within the domestic territory of a country during a year. 

(c) Flow Variables : A flow is a quantity of any economic variable which is measured during a period of time (or per unit of time) say, a week, a month or a year. For example, monthly wages of a worker, the per hour speed of a train, production of cloth during a year etc. 

(d) Income from property and entrepreneurship in the form of rent, royalty, interest and profit is termed as operating surplus. 

(i) Income from Property : There are two principal forms of the income from property : 

(a) rent and royalty and (b) interest. 

(ii) Income from Entrepreneurship (Profit) : Profit is a residual factor payment to the owners of an enterprise.

We know that C = c + bY , by putting value

 C = 200 + 0.75 x 1000 = 950

We also know that Y = C + I

1000 = 950 + I 

∴ I = 50.

(a) Revenue receipt, it is a kind of transfer receipt. 

(b) Capital receipt, It is an example of Dis-investment. It reduced the assets of the government therefore, it is a Capital Receipts. 

(c) Revenue receipt, it neither creates liability nor reduced the assets for the government therefore it is Revenue Receipts. 

(d) Capital Receipts, it creates liability for the government therefore it is Capital Receipts 

We know that C = c + bY , by putting value we get

1100 = c + 0.8 x 1200 (MPC = 1 – 0.2)

1100 – 960 = 140 

∴ c = 140

Controller of Money Supply and Credit : The Central Bank controls the money supply and credit in the best interests of the economy. By this central bank can control inflationary and deflationary situation in the economy. Central bank uses various instruments to perform this function which can be categorised in - 

(a) Qualitative instruments such as margin requirement, moral suasion, consumer credit, rationing of credit, differentiated rate of interest and direct action.(aims to influence the use of credit and direction of credit). 

(b) Quantitative instruments such as bank rate, open market operations, CRR and SLR.(aims at controlling cost of credit and availability of credit).

When there is a difference between the commodities produced by different firms then it is known as product differentiation. This difference may be of colour, shape, size, weight, taste, texture, trademark, brandname, packing, etc. Goods produced by different firms are similar but not identical. There is mark of identification on commodity so that the consumer or producer can differentiate. Therefore consumers show personal attachment with particular firms. This feature of market can be found in monopolistic competition or oligopoly market. For e.g. Toothpaste, Soap etc.

There are variety of Toothpaste available in the market which has difference in taste brandname, packing, colour, size etc.

We know that Y = C + I By putting value 

we get 1500 = C + 100 , C = 1500 -100 = 1400

C = c + b Y by putting value 1400 = 300 + b 1500

1400 -300 / 1500 = b = 0.73 

∴ MPC = 0.73

As the Gross Domestic Product Increases, availability of goods and services also increases. But it is not always true to say that per capita availability of goods in the economy increases with the Increase in Gross Domestic Product. It is only possible when rest of the factors which can affect the welfare are assumed to be remains constant. Means there are some Limitations of Real GDP as an Index of per capita availability of goods, such as : 

(i) Growth of Population : If the growth rate of population is more than the growth rate of GNP, then the per capita real GDP and economic welfare decreases even with the increase in output. 

(ii) Change of Composition of National Income : If the production of War Material or Capital Goods increases in comparison to Consumer Goods, then it will Decreases the capita availability of goods. 

(iii) Distribution of National Income: If the distribution of National income becomes unequal with the increase in National income then it will decrease economic welfare. 

(iv) Government Expenditure on Law and Order and Defence : Expenditure on law and order and defence is termed as non–development expenditure. These expenditure does not promote economic welfare of the masses, but it will increase the National income etc. 

Y = C + I by putting the value we get  

2000 = C + 100 , C = 2000 -100 = 1900 

C = c + by

1900 = 200 + b 2000

1900 -200 /2000 = b = 0.8

∴ MPC = 0.8

At equilibrium : AD = AS OR C+ I = Y (c+ b Y) + I = Y

(100 + b. 1000) + 120 = 1000

1000 -220 = 1000 b

b= 780/1000 = 0.78

MPS = 1 – 0.78 ( MPC+MPS =1)

MPS = 0.22 

When in an economy aggregate demand falls short of aggregate supply at full employment level, the demand is said to be as deficient demand.

(a) Ex-ante saving : The saving which the firms or entrepreneur desire to maker in the economy during a period is called ex-ante (planned savings). 

(b) Full employment: refers to the situation when all the workers who are willing and able to work at prevailing wage rate are actually employed. 

(c) Autonomous consumption : When income is zero, consumption is not zero because consumption can never be zero even at zero level of income; there are some basic needs which need to be fulfilled even at zero level of income and to fulfil those basic needs we use past savings. This consumption at zero level of income is termed as “Autonomous consumption” and is denoted as bar C.

(a) Reduce Cash Reserve Ratio

All the final goods & services which are produced in a country in an economy is Aggregate Supply. It is equal to National Income of the economy, which is either consumed or saved. The curve is positively sloped starting from origin AS = C + S.

When in an economy aggregate demand exceeds “aggregate supply at full employment level”, the demand is said to be an excess demand and the gap is called inflationary gap.

Ex ante aggregate Demand refers to the total amount of money which all the sections (Household, Government, firm) are expected to spend on purchase of goods and services produced in an economy during a given period. 

When the primary cash deposits in the banking system leads to multiple expansion in the total deposits, it is called money multiplier

Money multiplier = Total deposits/primary cash deposits

or 1/Legal reserve ratio

(b) Negative

(d) Fiscal deficit is equal to interest payment

Ex-ante saving refers to amount of savings which household intended or planned to save at different levels of income in the economy.

If MPC and MPS are equal, value of multiplier is  2.

Ex-ante Investment is more than Ex-ante savings: Suppose the industrialists wish to invest Rs 50,000 crores while the family units makes a saving of Rs 45,000 crores. In such a condition, the aggregate demand is more the aggregate supply. To supply this demand, the industrialists will use more raw material and more means of production to increase their production. This will lead to an increase in the national income, the saving and investment will become equal and a state of equilibrium will be achieved. 

Moral suasion is exercised through discussion letters and speeches to banks. 

(b) Decreases

(a) Fall in the propensity to consume

(a) Fall in aggregate demand 

(b) Fiscal policy

Dogs are faithful pets. They are always human friendly. They always help human beings at the time of their need. So happens with Mrs. Beena also. Mrs. Beena keeps a pet dog. Its species is Labrador. They dog protects their house at the time of night and accompanies them whenever and wherever they go. His name is Snowy. She gets her dog vaccinated regularly. Yesterday, she took her pet dog for vaccination. She was inside the dog clinic. When the dog got vaccinated, she came out of the clinic. Her purse was dangling from her shoulder. She was busy in her day dream. In fact, she is a social activist and her mind is always filled with the reformative ideas for the society. During her thought process, she could not see a young man approaching her. The young man swiftly came near her and snatched her purse. Before she could think or do any thing, the young man took an opportunity and near disappeared in the street. She was taken aback. She could not think what to do. But Snowy did not waste a single moment. He ran after the thief. Now the thief was extremely panicked. He tried to disappear in the narrow lanes and streets but Snowy was perfect in smelling. So, he continued chasing the thief. At last, the thief was tired and could run no longer. He caught hold of the thief and began to bark. A large crowd gathered there. A police van was also there. After some time Mrs. Beena also reached the spot. The thief was arrested. Once again, Snowy had proved his faithfulness.

(a) Co²⁺ : [Ar]3d⁷ Sc³⁺ : [Ar]3d⁰ Cr³⁺ : [Ar]3d³

Co²⁺ and Cr³⁺ have unpaired electrons. Thus, they are coloured in aqueous solution.Sc³⁺ has no unpaired electron. Thus it is colourless.

(b) Metal copper has high enthalpy of atomisation and enthalpy of ionisation. Therefore the high energy required to convert Cu(s) to Cu²⁺(aq) is not balanced by its hydration enthalpy.

(c) Due to lanthanoid contraction the size of lanthanoid ion decreases regularly with increase in atomic size. Thus covalent character between lanthanoid ion and OH^- increases from La³⁺ to Lu³⁺. Thus the basic character of hydroxides decreases from La(OH)₃ to Lu(OH)₃

(a) NaCN is used as depressants to separate two sulphide ores ( ZnS and PbS) in Froth Floatation Method.

(b) Carbon monoxide forms a volatile complex of nickel, nickel tetracarbonyl.

(c) Coke is used as a reducing agent to reduce zinc oxide to zinc.

Cocaine has a potent stimulating action on central nervous system, producing a sense of euphoria and increased energy. Certain sports persons misuse it to enhance their performance.

The fuel was CNG or compressed natural gas. CNG is considered better because of the following reasons: 

(i) CNG burns more efficiently unlike diesel or petrol.

(ii) Very little of it is left unburnt. 

(iii) It cannot be adulterated. 

(iv) It is cheaper than petrol or diesel.

Error            Correction 

(a) over         on 

(b) knew       know 

(c) their       his 

(d) the        a

Error             Correction 

(a) a               an 

(b) of              off/from 

(c) in               with 

(d) looking      looked

Error                Correction 

(a) as               even 

(b) cannot        couldn’t 

(c) drive          drove 

(d) thank        thanked