MCSCCE • Paper-II
The least value of 2sin^2θ + 3cos^2θ is:
A)
3
B)
4
C)
1
D)
2
Rewriting the expression: 2*sin^2(θ) + 3*cos^2(θ) = 2*(sin^2(θ) + cos^2(θ)) + cos^2(θ) = 2 + cos^2(θ). Since 0 <= cos^2(θ) <= 1, the minimum value is 2 + 0 = 2 (at θ = 90°).
MCSCCE • Paper-II
The largest number of five digits which, when divided by 16, 24, 30 or 36, leaves the same remainder 10 in each case is:
A)
99999
B)
99350
C)
99880
D)
99370
LCM(16, 24, 30, 36) = 720. The largest 5-digit multiple of 720 is 99999 - (99999 mod 720) = 99999 - 639 = 99360. Adding the required remainder 10 gives 99360 + 10 = 99370.
MCSCCE • Paper-II
Consider the following statements about the NISAR (NASA-ISRO Synthetic Aperture Radar) satellite mission launched in 2025: (i) NISAR is a joint collaboration between ISRO and NASA. (ii) The satellite is designed to map Earth’s surface every 12 days and track climate threats. (iii) NISAR is India’s first geostationary satellite dedicated to climate observation. Select the correct answer using the code below:
A)
(i) and (ii) only
B)
(ii) and (iii) only
C)
(i) and (iii) only
D)
All of the above
Statements (i) and (ii) are correct: NISAR is a joint NASA-ISRO mission using dual-frequency radar to map Earth's land and ice surfaces globally every 12 days. Statement (iii) is incorrect because NISAR operates in Low Earth Orbit (LEO, ~747 km altitude), not geostationary orbit.
MCSCCE • Paper-II
Mizoram Sustainable Investment Policy, 2024 aims to attract-
A)
Public investors, particularly from outside the State.
B)
Private investment, particularly from outside the State.
C)
Public Sector Undertaking, particularly from outside the State.
D)
Both private and public investors operating in the State of Mizoram
The Mizoram Sustainable Investment Policy, 2024 was formulated to provide incentives and ease of business to attract private investment, particularly from external domestic and international investors.
MCSCCE • Paper-II
Number of elements in the periodic table is:
A)
112
B)
114
C)
116
D)
118
The current officially recognized periodic table, as maintained by the IUPAC (International Union of Pure and Applied Chemistry), contains 118 elements. These elements range from Hydrogen (atomic number 1) to Oganesson (atomic number 118). Options a (112), b (114), and c (116) are incorrect as they represent incomplete versions of the table from previous years before the final elements of the 7th period were officially named and confirmed.
MCSCCE • Paper-II
Which of the following was/were the causes behind the 1857 Revolt? (i) Sepoys would not be given the foreign service allowance (batta) when serving in Sind or Punjab. (ii) General Services Enlistment Act required sepoys to serve overseas. (iii) The British imposed a new law requiring sepoys to pay income tax on their salaries. Select the correct answer using the code given below.
A)
(i) and (ii) only
B)
(ii) and (iii) only
C)
(ii) only
D)
(i), (ii) and (iii)
Withdrawal of foreign service allowance (batta) in Sindh/Punjab and the enactment of the General Services Enlistment Act (1856) requiring overseas service were major causes of resentment among Bengal sepoys. Income tax was introduced later in 1860 by James Wilson, not prior to 1857.
MCSCCE • Paper-II
What is meant by personal disposable income?
A)
Personal Income + Subsidies
B)
Personal Income – Subsidies
C)
Personal Income – Direct Taxes
D)
Personal Income – Indirect Taxes
Personal disposable income is the amount of income available to individuals after deducting personal direct taxes (like income tax) from personal income.
MCSCCE • Paper-II
The Chauri-Chaura incident during non-cooperation movement (February, 1922) relates to
A)
Burning of police post by a mob
B)
A major offensive by underground revolution
C)
Large scale looting of government property
D)
Massive police firing on unarmed satyagrahis
The Chauri Chaura incident occurred on 4 February 1922 in Gorakhpur, UP, when a large crowd of protesters set fire to a police station, leading Mahatma Gandhi to call off the Non-Cooperation Movement.
MCSCCE • Paper-II
In a row of girls Sawmi is 10th from the left and Rini is 11th from the right. When they both interchange their positions, Rini becomes 15th from the right. What will be Sawmi’s new position from the left?
A)
17th
B)
16th
C)
14th
D)
13th
After interchanging positions, Rini is 10th from left and 15th from right, giving total girls = 10 + 15 - 1 = 24. Sawmi is now at Rini's former position (11th from right), so Sawmi's new position from the left is 24 - 11 + 1 = 14th.
MCSCCE • Paper-II
Consider the following statements regarding the Presidential Reference under Article 143 of the Constitution of India: (i) The President can refer any question of law or fact to the Supreme Court for its advisory opinion. (ii) The opinion given by the Supreme Court is binding on the President and other authorities. (iii) The President can refer a question even when Parliament is not in session. Select the correct answer using the code below:
A)
(i) and (ii) only
B)
(i) and (iii) only
C)
(ii) and (iii) only
D)
(i), (ii) and (iii)
Under Article 143, the President may consult the Supreme Court on questions of law or fact of public importance (statement i). The advisory opinion is purely consultative and not binding on the President (statement ii is false). The President can make a reference at any time, including when Parliament is in recess (statement iii is true).
MCSCCE • Paper-II
The sum of all 2-digits number divisible by 3, is:
A)
1678
B)
1458
C)
1669
D)
1665
The two-digit numbers divisible by 3 are 12, 15, ..., 99. This is an AP with a = 12, d = 3, l = 99. Number of terms n = (99 - 12)/3 + 1 = 30. Sum S = (30/2) * (12 + 99) = 15 * 111 = 1665 (option d).
MCSCCE • Paper-II
Gaza strip lies along the coast of
A)
Dead Sea
B)
Mediterranean Sea
C)
Persian Gulf
D)
Red Sea
The Gaza Strip is a small Palestinian territory located on the eastern coast of the Mediterranean Sea.
MCSCCE • Paper-II
Environmental Impact Assessment (EIA) in India became mandatory under which Act?
A)
Environment (Protection) Act, 1986
B)
Forest Conservation Act, 1980
C)
Water Act, 1974
D)
Forest (Conservation) Amendment Act, 2023
Environmental Impact Assessment (EIA) in India was made statutory and mandatory under Section 3 of the Environment (Protection) Act, 1986 through the 1994 EIA Notification.
MCSCCE • Paper-II
The area of a circle is 176 square cm. What will be the area of square inscribed in this circle?
A)
56 cm2
B)
50 cm2
C)
112 cm2
D)
100 cm2
Area of circle = πr² = 176 cm². With π = 22/7, r² = 176 × (7/22) = 56. The diagonal of an inscribed square equals the diameter of the circle (d = 2r). If the square has side length s, then s² + s² = (2r)² ⇒ 2s² = 4r² ⇒ Area of square s² = 2r² = 2 × 56 = 112 cm².
MCSCCE • Paper-II
A coin and a dice are thrown at random. What is the probability that a composite number turns up on the dice and tail turns up on the coin?
A)
1/6
B)
1/5
C)
1/4
D)
1/3
The composite numbers on a fair 6-sided die {1, 2, 3, 4, 5, 6} are 4 and 6, so P(composite) = 2/6 = 1/3. For a fair coin, P(tail) = 1/2. Since these are independent events, P = (1/3) * (1/2) = 1/6.
MCSCCE • Paper-II
In traditional Mizo society, which head ornament was worn only by men who had killed an enemy?
A)
Dartawnsuk
B)
Chhawn
C)
Vakul chang
D)
Vakiria
In traditional Mizo society, the 'Chhawn' (a plume of hair/feathers worn on the head) was an exclusive warrior badge of honor worn only by a Pasaltha (brave warrior) who had slain an enemy.
MCSCCE • Paper-II
The ‘Evil Quartet’ refers to the primary causes of species extinction. Which of the following are included in it? (i) Habitat loss (ii) Overexploitation of species (iii) Introduction of invasive species (iv) Eutrophication Select the correct answer using the code below:
A)
(i), (ii) and (iii) only
B)
(i) and (iv) only
C)
(ii), (iii) and (iv) only
D)
All of the above
The 'Evil Quartet' includes Habitat loss, Overexploitation, Alien/Invasive species introduction, and Co-extinction. Eutrophication is not part of this specific term.
MCSCCE • Paper-II
A solid cone of radius 21 cm and height 10/7 of its radius is melted to form four equal solid cylinders of radius 7 cm. What is the difference between the height of the cone and height of each of the solid cylinders?
A)
9 cm
B)
6 cm
C)
7.5 cm
D)
5.5 cm
Cone: radius R = 21 cm, height H = (10/7) * 21 = 30 cm. Volume of cone = (1/3) * pi * 21^2 * 30 = 4410 * pi cm^3. Four identical cylinders of radius r = 7 cm have total volume = 4 * pi * 7^2 * h = 196 * pi * h. Equating volumes: 196 * pi * h = 4410 * pi => h = 4410 / 196 = 22.5 cm. Difference in height = 30 - 22.5 = 7.5 cm.
MCSCCE • Paper-II
From 1972 until the Assembly Constituency was redrawn and renamed in 2008, Dampa Assembly Constituency was known as:
A)
Zawlnuam Assembly Constituency
B)
Kawrthah Assembly Constituency
C)
West Phaileng Assembly Constituency
D)
Phuldungsei Assembly Constituency
From 1972 until the 2008 delimitation of constituencies in Mizoram, Dampa Assembly Constituency was designated as the West Phaileng Assembly Constituency.
MCSCCE • Paper-II
If 5^(2x-1) = 59/125^x then the value of x will be:
A)
1
B)
5
C)
2
D)
4
From the exponential equation 5^(2x-1) = 5^9 / 125^x = 5^9 / 5^(3x) = 5^(9-3x), equating exponents gives 2x - 1 = 9 - 3x => 5x = 10 => x = 2.
MCSCCE • Paper-II
With respect to Lakpati Didi Scheme, consider the following: (i) It is implemented by Ministry of Rural Development. (ii) Its goal is to increase the annual household income of SHG women to at least 1 lakh. (iii) It is an initiative and an outcome of DAY-NULM. Based on the code given below, select the correct statement:
A)
(i) and (ii) only
B)
(ii) and (iii) only
C)
(i) and (iii) only
D)
(i), (ii) and (iii)
Under the Lakhpati Didi initiative: (i) It is implemented by the Ministry of Rural Development; (ii) It aims to enable rural women self-help group members to earn at least ₹1 lakh annually; (iii) It is an initiative of DAY-NRLM (National Rural Livelihoods Mission), not DAY-NULM (National Urban Livelihoods Mission). Thus, only (i) and (ii) are correct.
MCSCCE • Paper-II
If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60°, respectively, then the ratio, AB : BC, is:
A)
3: 2
B)
1: 3
C)
2:3
D)
3:1
Let the height of the tower be h. The distances of collinear points A, B, C from the base are h/tan 30° = h√3, h/tan 45° = h, and h/tan 60° = h/√3. Thus AB = h(√3 - 1) and BC = h(1 - 1/√3) = h(√3 - 1)/√3. The ratio AB : BC = h(√3 - 1) / [h(√3 - 1)/√3] = √3 : 1 (represented in the options as 3:1).
MCSCCE • Paper-II
Which right was described by Dr. B.R Ambedkar as ‘The heart and soul of the constitution’?
A)
Right to property
B)
Right to Equality
C)
Right to constitutional remedies
D)
Right to freedom of religion
Dr. B. R. Ambedkar described Article 32 (Right to Constitutional Remedies) as the 'heart and soul of the Constitution' because it guarantees the judicial enforcement of all Fundamental Rights.
MCSCCE • Paper-II
In an examination, A obtained 27% marks and failed by 77 marks. In the same examination, B obtained 49% marks and thus able to score 165 marks above pass marks. Find the pass percentage of the examination.
A)
32%
B)
33%
C)
34%
D)
35%
Let total marks be M. Passing marks P = 0.27M + 77 = 0.49M - 165 => 0.22M = 242 => M = 1100. Passing marks P = 0.27(1100) + 77 = 297 + 77 = 374. Pass percentage = (374 / 1100) × 100% = 34%.
MCSCCE • Paper-II
Two different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number that will be on the face opposite to the one showing ‘3’.
A)
4
B)
1
C)
6
D)
2
From the two views of the dice, faces 4 and 6 are common in both positions. According to standard dice logic, the third remaining faces in both views must be opposite each other, meaning 3 is opposite to 1.
