MCSCCE
The radii of the ends of a frustum of a cone 40 cm high are 20 cm and 11 cm. Its slant height is:
A)
√(521) cm
B)
41 cm
C)
20 √5 cm
D)
49 cm
Slant height of frustum l = sqrt(h^2 + (R - r)^2) = sqrt(40^2 + (20 - 11)^2) = sqrt(1600 + 9^2) = sqrt(1681) = 41 cm.
MCSCCE
In a two digit number, if ‘a’ is the digit in the unit’s place and ‘b’ in the ten’s place, then the two digit number must be -
A)
ab
B)
10 ab
C)
10a+b
D)
10b+a
In standard decimal place value notation, a number with tens digit 'b' and units digit 'a' has the algebraic value 10 * b + a = 10b + a.
MCSCCE
If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is:
A)
9 cm
B)
6 cm
C)
3 cm
D)
1 cm
Let chord length be 2x. In the right triangle formed with concentric radii: x = sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3 cm. Total chord length = 2 * 3 = 6 cm (option b).
MCSCCE
If sec²θ ( 1 + sinθ) (1 – sinθ) = k, the value of k is:
A)
1
B)
– 1
C)
0
D)
2
Step-by-step derivation:
1. Start with the given expression: k = sec²θ (1 + sinθ)(1 – sinθ).
2. Use the algebraic identity (a + b)(a – b) = a² – b². Here, (1 + sinθ)(1 – sinθ) = 1² – sin²θ = 1 – sin²θ.
3. According to the fundamental trigonometric identity sin²θ + cos²θ = 1, we know that 1 – sin²θ = cos²θ.
4. Substitute this back into the expression: k = sec²θ × cos²θ.
5. Since secθ is the reciprocal of cosθ (secθ = 1/cosθ), then sec²θ × cos²θ = (1/cos²θ) × cos²θ = 1.
6. Therefore, k = 1.
Why other options are incorrect:
- Option b (-1), c (0), and d (2) are incorrect because the product of a trigonometric function and its reciprocal squared always results in 1, not any other constant.
MCSCCE • Paper-IV
It has come to your notice that one of the staff members in your office is a regular drunkard and a wife beater. His wife and children approached you to intervene in this matter. Out of the following options which one action will you choose giving reasons for your selection.
A)
Leave the matter to take its course- you would not want to and it is actually not appropriate for you to intervene in what is essentially a family matter.
B)
Call the other staff members and ask them to intervene in the matter.
C)
Call the staff member and counsel him.
D)
Counsel the staff member and arrange for his de-addiction treatment if required.
In workplace ethics and administrative leadership, addressing employee alcoholism and domestic misconduct through counseling and facilitating medical rehabilitation/de-addiction provides a constructive, empathetic, and responsible solution.
MCSCCE • Paper-I
In the Balance of Payment, Trade or Visible account includes
A)
Banking charges and freight
B)
Export and import of goods
C)
FDI and sales of assets
D)
Insurance and remittances
The 'Trade' or 'Visible' account in the Balance of Payment specifically records the export and import of tangible goods.
MCSCCE • Paper-I
National Rural Employment Programme (NREP) was launched in
A)
1980
B)
1982
C)
2002
D)
2003
The National Rural Employment Programme (NREP) was launched in October 1980 during the Sixth Five Year Plan (option a).
MCSCCE • Paper-I
The first complete and synchronous census in India for providing vital demographic data was conducted in:
A)
1901
B)
1881
C)
1891
D)
1911
While censuses were attempted earlier, the 1901 census was the first to be conducted in a complete and synchronous manner across India.
MCSCCE • Paper-I
Small Scale Industry is one which has fixed investment in plant and machinery
A)
not exceeding 1 Crore rupees and number of worker less than 50, but it uses electricity
B)
not exceeding 2 Crore rupees and number of worker less than 50, but it uses electricity
C)
not exceeding 3 Crore rupees and number of worker less than 20, but it uses electricity
D)
not exceeding 1 Crore rupees and number of worker less than 25, which does not use electricity
Under classic industrial policy definitions in India, a Small Scale Industry (SSI) was defined as having investment in plant and machinery not exceeding Rs. 1 Crore (option a).
MCSCCE • Paper-I
Indian National Congress had been formed in the year
A)
1895
B)
1885
C)
1875
D)
1892
The Indian National Congress was founded in December 1885 in Bombay by A.O. Hume and prominent Indian nationalist leaders.
MCSCCE • Paper-I
The Election Commission of India functioned as a single member body till
A)
1989
B)
1990
C)
1991
D)
1992
From its establishment in 1950 until 15 October 1989, the Election Commission of India functioned as a single-member body consisting solely of the Chief Election Commissioner. On 16 October 1989, two additional Commissioners were first appointed.
MCSCCE • Paper-I
Which of the following are the types of authority attributed to the President of India?
A)
Real and popular
B)
Titular and de - jure
C)
Constitutional and nominal
D)
Political and nominal
Under the parliamentary system of the Indian Constitution, the President of India is the Constitutional and nominal (de jure) head of state, whereas the Prime Minister and Council of Ministers hold de facto (real) executive authority.
MCSCCE • Paper-I
Muslim League was founded in
A)
1905
B)
1906
C)
1907
The All India Muslim League was established on 30 December 1906 in Dhaka (present-day Bangladesh) under the leadership of Nawab Salimullah, Aga Khan III, and others.
MCSCCE • Paper-I
The aggregate money value of all goods and services produced by the residents of a country within its domestic territory is called
A)
NNP
B)
Personal Income
C)
GDP
D)
DPI
Gross Domestic Product (GDP) is the aggregate monetary value of all goods and services produced within a country's domestic territory in a given period.
MCSCCE • Paper-I
“Go back to the Vedas” was a slogan of the
A)
Arya Samaj
B)
Brahmo Samaj
C)
Rama Krishna Mission
'Go back to the Vedas' was the famous clarion call given by Swami Dayanand Saraswati, the founder of the Arya Samaj (established in 1875).
MCSCCE • Paper-I
Judicial Review in the Indian Constitution is based on
A)
Procedure established by law
B)
Due process of law
C)
Rule of law
D)
Precedents and Conventions
Unlike the US Constitution's 'Due process of law', the scope of judicial review in India was originally textually grounded on the principle of 'Procedure established by law' borrowed from the Japanese Constitution under Article 21.
MCSCCE • Paper-I
The first Indian Universities were set up in the year
A)
1857
B)
1858
C)
1859
The first three modern universities in India—Calcutta, Bombay, and Madras—were founded in the year 1857 following Wood's Despatch.
MCSCCE • Paper-I
Which one of the following was not included in the Fundamental Rights as given in the Constitution of 1950?
A)
Right to freedom of speech
B)
Right to property
C)
Right against exploitation
D)
Right to education
Right to Education was inserted into Part III as Article 21A by the 86th Constitutional Amendment Act in 2002; it was not present in the original 1950 Constitution (option d).
MCSCCE • Paper-I
The term isohyets refer to:
A)
Equal temperature
B)
Equal Rainfall
C)
Equal Pressure
D)
Equal Sunshine
An isohyet is a line on a meteorological map connecting places having equal amounts of rainfall/precipitation over a given period.
MCSCCE • Paper-I
Which of the following is a committee on Panchayati Raj institution?
A)
Balwant Rai Mehta Committee
B)
GVK Rao Committee
C)
LM Singhvi Committee
D)
Ashok Mehta Committee
Balwant Rai Mehta Committee (1957) was the pioneer committee that recommended the establishment of a 3-tier Panchayati Raj system in India (option a).
MCSCCE • Paper-I
Per Capita Income is
A)
Total Income of the family/Number of family members
B)
Total number of population/National income of a country
C)
Total budget income/Number of families
D)
National Income/Total number of population
Per Capita Income (PCI) is a measure of the average income earned per person in a given area (usually a country) in a specified year. It is calculated by dividing the total National Income of the country by its total population.
- Option (d) is correct as it follows the standard economic formula: Per Capita Income = National Income / Total Population.
- Option (a) describes 'Average Family Income', not the national economic indicator of Per Capita Income.
- Option (b) is the inverse of the correct formula (Population divided by Income), which is mathematically incorrect.
- Option (c) refers to budget distribution per family, which is not the definition of Per Capita Income.
MCSCCE • Paper-I
The Hindustan – Tibet Road connecting Shimla with Gantok passes through:
A)
Shipki La
B)
Nathu La
C)
Jelep La
D)
Thag La
The historic Hindustan-Tibet Road connecting Shimla to Tibet (Gartok) passes through the Shipki La pass on the India-China border.
MCSCCE • Paper-I
Indian Councils Act passed in 1909 was the
A)
Morley-Minto Reforms
B)
Montague-Chelmsford Reforms
C)
Regulating Reforms
The Indian Councils Act 1909 is widely known as the Morley-Minto Reforms after Secretary of State John Morley and Viceroy Lord Minto (option a).
MCSCCE • Paper-I
The proclaimed leader of the Revolt of 1857 was
A)
Tantia Tope
B)
Rani Lakshmi Bai
C)
Bahadur Shah II
During the 1857 revolt, the mutineers marched to Delhi and proclaimed the Mughal Emperor Bahadur Shah II (Zafar) as the leader of the rebellion.
MCSCCE • Paper-I
Relatively narrow bands of high velocity winds moving from west to east usually found in the middle latitudes in the upper troposphere at a height of about 12 km are called:
A)
Jet stream
B)
Hurricane
C)
Cyclone
D)
Tornado
High-velocity westerly upper-tropospheric wind currents moving across mid-latitudes are called Jet Streams (option a).
