Inspector of Statistics • Paper-III
At (0,0), the function f(x,y) = xy, where x and y are real numbers is:
A)
Differentiable and both the partial derivatives fx and fy exist
B)
Differentiable but both the partial derivatives fx and fy do not exist
C)
Not differentiable but both the partial derivatives fx and fy exist
D)
Not differentiable and both the partial derivatives fx and fy do not exist
f(x,y)=xy is a polynomial, so it is differentiable everywhere and both partial derivatives exist at (0,0).
Inspector of Statistics • Paper-III
The first order partial differential equation obtained from z = f(x^2 + y^2) by eliminating the arbitrary function is:
A)
x(dz/dx) - y(dz/dy) = 0
B)
x(dz/dx) + y(dz/dy) = 0
C)
y(dz/dx) + x(dz/dy) = 0
D)
y(dz/dx) - x(dz/dy) = 0
For z=f(x²+y²), y z_x − x z_y =0 because z_x=2x f' and z_y=2y f'.
Inspector of Statistics • Paper-III
The equation of the integral surface of the equation 4yzp + q + 2y = 0 and passing through y^2 + z^2 = 1, x + z = 2 is given by:
A)
y^2 + z^2 + x + z = 3
B)
x^2 + z^2 + y + z = 3
C)
y^2 + z^2 + x + z = 0
D)
x^2 + y^2 + x + z = 0
The surface y²+z²+x+z=3 contains the given initial curve and satisfies the PDE.
Inspector of Statistics • Paper-III
The set {1, -1, 1/2, -1/2, 1/3, -1/3, ...} is:
A)
Is closed
B)
Is open
C)
Is both open and closed
D)
Neither closed nor open
The set is neither open nor closed in R: it has no interior, and 0 is a limit point not contained in the set.
Inspector of Statistics • Paper-III
The derivative of ln(3x^2 + 1) is:
A)
6x / (3x^2 + 1)
B)
3x / (3x^2 + 1)
C)
6x / (x^2 + 1)
D)
1 / (3x^2 + 1)
d/dx ln(3x²+1)=6x/(3x²+1).
Inspector of Statistics • Paper-III
The directional derivative of f(x,y) = x^2 sin(2y) at the point (1, pi/2) in the direction of v = 3i - 4j is:
A)
2/5
B)
3/5
C)
8/5
D)
9/5
At (1,π/2), ∇f=(0,−2). The unit direction is (3/5,−4/5), giving directional derivative 8/5.
Inspector of Statistics • Paper-III
Let z = x + iy. Then the function f(z) = 1/(z-5)^3 has:
A)
A pole of order 3 at z = 5
B)
An isolated essential singularity at z = 5
C)
A removable singularity at z = 5
D)
Has no singularity at z = 5
1/(z−5)^3 has a pole of order 3 at z=5.
Inspector of Statistics • Paper-III
Which of the following sets is not a neighbourhood of each of its points?
A)
The set of real numbers
B)
The set of rational numbers
C)
The empty set
D)
The open interval (a, b) where a and b are real numbers
The rationals are not a neighbourhood of each of their points in the usual topology on R because no open interval around a rational lies entirely in Q.
Inspector of Statistics • Paper-III
If u = xyz, then d^2u / (dx dy) =
A)
yz
B)
xz
C)
z
D)
0
For u=xyz, first ∂u/∂x=yz, then ∂²u/(∂x∂y)=z.
Inspector of Statistics • Paper-III
When inflation goes out of control and the rate of inflation is more than 100 %, what is it called?
A)
Reflation
B)
Running inflation
C)
Stagflation
D)
Hyper-inflation
Option D is correct: Hyper-inflation.
Inspector of Statistics • Paper-III
The basis of determining dearness allowance (DA) to employees in India is
A)
National Income
B)
Consumer Price Index
C)
Per Capita Income
D)
GDP at factor cost
Option B is correct: Consumer Price Index.
Inspector of Statistics • Paper-III
What is the Most important Rabi crops in India?
A)
Wheat
B)
Rice
C)
Maize
D)
Barley
Option A is correct: Wheat.
Inspector of Statistics • Paper-III
According to the Forest report of India 2015, which state has the highest percentage area under forest cover?
A)
Madhya Pradesh
B)
Maharastra
C)
Arunachal Pradesh
D)
Mizoram
Option D is correct: Mizoram.
Inspector of Statistics • Paper-III
Dalal street is situated at -
A)
London
B)
Paris
C)
Mumbai
D)
New Delhi
Option C is correct: Mumbai.
Inspector of Statistics • Paper-III
What is the position of India in terms of milk production?
A)
First
B)
Second
C)
Third
D)
Fourth
Option A is correct: First.
Inspector of Statistics • Paper-III
Ad Valorem tax is a tax levied :
A)
According to value
B)
According to weight
C)
According to size
D)
According to advertisement cost
Option A is correct: According to value.
Inspector of Statistics • Paper-III
Who are very senior citizens in the context of collection of income tax in India?
A)
Above the age of 60
B)
Above the age of 65
C)
Above the age of 70
D)
Above the age of 80
Option D is correct: Above the age of 80.
Inspector of Statistics • Paper-III
India is regarded as a country with “ Demographic Dividend “ . This is due to -
A)
its high population in the age group below 15 years
B)
its high population in the age group of 15-64 years
C)
its high population in the age group above 65 years
D)
its high total population
Option B is correct: its high population in the age group of 15-64 years.
Inspector of Statistics • Paper-III
‘Zero Based Budgeting’ means -
A)
Infinite deficit financing
B)
Preparation of new budget every time
C)
No Appraisal of new programmes
D)
No curtailment in unproductive expenditure
Option B is correct: Preparation of new budget every time.
Inspector of Statistics • Paper-III
Which year is known as the year of great divide in India’s population history?
A)
1911
B)
1921
C)
1951
D)
1971
Option B is correct: 1921.
Inspector of Statistics • Paper-III
What is the agency responsible for publishing National income in India?
A)
National Sample Survey
B)
SEBI
C)
Central Statistics Organisation
D)
TRAI
Option C is correct: Central Statistics Organisation.
Inspector of Statistics • Paper-III
Which of the following Agency regulates the working of the share markets in India -
A)
MRTP Act
B)
FERA
C)
SEBI
D)
FEMA
Option C is correct: SEBI.
Inspector of Statistics • Paper-III
Which article of the Indian constitution contains the central budget?
A)
Article 110
B)
Article 111
C)
Article 112
D)
Article 202
Option C is correct: Article 112.
Inspector of Statistics • Paper-III
In the spot exchange market, foreign exchange transactions are settled:
A)
After one month
B)
After three months
C)
After one year
D)
Immediately or within two working days
Spot FX transactions are normally settled immediately or within the standard short settlement window, commonly T+2.
Inspector of Statistics • Paper-III
According to Marx, the extra labour that a labourer puts in and for which he receives nothing is called:
A)
Surplus labour
B)
Surplus value
C)
Capitalist’s profit
D)
Socialist bonus
Surplus labour is labour performed beyond what is necessary to reproduce the worker's wage-equivalent value.
