Explore topic-wise InterviewSolutions in Current Affairs.

A diagonal matrix in which all the Principle diagonal Elements are equal is called scalar matrix.

The correct answer is (30,0) and Z = 120.

The linear function z = ax + by where a, b are constants which has to be maximised or minimized is called linear objective function.

Expanding along the first row, we get

Δ = cosα cosβ(cosβ cosα – 0) – cosα sinβ(–sinβ cosα) – sinα(–sinα sin²β – sinα cos²β)

= cos²α cos²β + cos²α sin²β + sin²α sin²β+ sin²α cos²β

= cos²α(cos²β + sin²β) + sin²α(sin²β + cos²β)

= cos²α· 1 + sin²α· 1 = 1

Chronological classification is the orderly arrangement of statistical data according to time. 

eg: Classification of population of India from 1971 to 2011

Column headings are called captions. 

Row headings are called stubs.

Row headings are called stubs and column headings are called captions of a table.

In two dimensional diagram, both height and width (X and Y – axes) are considered. 

Ogives/cumulative frequency curves. 

Extrapolation is a procedure of estimating the unknown value of a dependent variable for a given value of an independent variable which is outside the limits or the range of the independent variable.

Price and demand. 

Mode (z) = 2 (which is repeated more times).

The regression coefficient of x on y = bxy = γ δx/δy.

In a class if lower limit as well as upper limits are included in the same class, such a class is called inclusive class interval.

Ex.C.I. = (0 – 9), (10 – 19)…. (40 – 49).

In order to use the space on the graph effectively a line, shown by vertical wavy line between zero and the first scale or the axes can be broken by kinked line.

Rise in prices of vegetables and sales.

B.C.S.K = (Q₃ + Q₁- 2Q₂/Q₃- Q₁).

\(\int\limits_e^{e^4} \sqrt{log\, x}\,dx\)

Let \(log \,x = t^2 \) ⇒ \(x = e^{t^2}\)

\(\frac 1x dx = 2t\,dt\)

\(dx = 2t.e^{t^2}dt\)

Then \(\int\limits_e^{e^4} \sqrt{log\, x}\,dx = \int\limits_1^2 t.(2te^{t^2})dt\)

\(=2\left[\int\limits_1^2 t^2.e^{t^2}dt\right]\)

\(= 2\left[[t^2]^2_1 \int\limits_1^2 e^{t^2} dt -\int\limits_1^2 (2t\int e^{t^2} dt)\right]\)

\(=2\left[(4-1).a - [2t]_1^2 \int\limits_1^2 a\,dt + \int\limits_1^22.a\right]\)      \(\left(\because \int\limits_1^2 et^2dt = a\right)\)

\(= 2\left[3a - (4 -1)a (2 -1) + 2a(2 -1)\right]\)

\(= 2(3a - 3a + 2a)\)

\(= 4a\)

\(\int\limits_0^1\frac1{[1-log_2(1-x)]}dx\)

 = \(\int\limits_0^1\cfrac1{[log_2\frac2{(1-x)}]}dx\) (\(\because log_22=1 \& log\,A- log\,B = log\frac{A}{B}\))

\(\therefore\) 0 < x < 1

⇒ 0 < 1 - x < 1

⇒ 2/(1-x) > 2

Now,

\(\int\limits_0^1\cfrac1{[log_2\frac2{1-x}]}dx\) = ....+ \(\int\limits_{15/16}^{7/8}\cfrac1{[log_2\frac2{1-x}]}dx\) + \(\int\limits_{7/8}^{3/4}\cfrac1{[log_2\frac2{1-x}]}dx\) + \(\int\limits_{3/4}^{1/2}\cfrac1{[log_2\frac2{1-x}]}dx\) + \(\int\limits_{1/2}^{1}\cfrac1{[log_2\frac2{1-x}]}dx\) 

 = .... + \(\int\limits_{15/16}^{7/8}\frac1{4}dx\) + \(\int\limits_{7/8}^{3/4}\frac1{3}dx\) + \(\int\limits_{3/4}^{1/2}\cfrac1{2}dx\) 

 = ....+ \(\frac14(\frac{14}{16}-\frac{15}{16})+\frac13(\frac68-\frac78)\) + \(\frac12(\frac24-\frac34)+\frac12(1-\frac12)\)

 = \(\frac14-\frac18-\frac1{24}-\frac1{64}-..... <4\) 

Hence, \(\int\limits_0^1\frac1{1-log_2(1-x)}dx<1/4\)

(A) Economic cost 

(D) All the above

The alternative name of opportunity cost is Economic cost.

Correct option is D) Out of sight - out of mind.

(d) All the above

(c) Both (a) and (b) 

(D) All of these

Correct option is E) precariously

Correct option is C) You cannot eat your cake and have it.

Some young people visited her to test her intelligence. They believed her to be a fraud and wanted to prove it.

Utility can be measured by money.

A R is shown as TR/Q 

(d) All of the above. 

Cinema combines various functions of poetry, music, painting, drama, architecture. It also combines the logic of science. 

Law of demand is based on following assumption:- 

1. Consumer’s income should remain constant. 

2. Consumer’s taste, nature etc. should remain constant. 

3. Price of related goods should remain constant. 

4. Consumer remains unknown with new substitutes. 

5. There is no possibility of price change in future.

Kaldor has suggested tax on expenditure.

When total utility becomes maximum, marginal utility is Zero.

In final equilibrium of firm MC cuts MR from below.

M R is shown as ΔTR/ΔQ.

Peace, freedom and democracy are the most important factors of welfare state. There must be a democratic government running by the people's representatives. For the development of humanity and mankind peace or freedom is essential and this can only be achieved through democracy. 

(c) Both (a) and (b) 

In monopoly and monopolistic competition AR > MR.

(a) Total expenditure - Total Receipt ( other than borrowings)

(d) AC = AFC + AVC

Now-a-days cinema is the most popular form of recreation and value, cinema has also a great educative value. It gives the masses of knowledge of many current events as well as historical and geographical pictures, forest thrills. These historical and geographical sites increase knowledge among children. 

b) Special Assessments

(c) Both (a) and (b) 

These days life has become so fast that people have least to enjoy the company of others. The pace has become so fast that it has given rise to competition in all walks of life. The world moves on tips of fingers and the world is connected. One can gather the information from any corner of the world. There is competition in the world to become super power which is giving rise to war threats. 

Answer is (c) 17.68%

(c) Both (a) and (b) 

(a) fallen by Rs. 3349