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Exam held on 25 october 2026

Mathematics, Indian History, Indian Polity and Elections

Question 6

The question statement is missing from the supplied text. The available options are:

A) 75

B) 80

C) 85

D) 90

Correct Answer: Cannot be determined without the question statement.

Question 7

A movie theater sold student and adult tickets for a special screening of a show. The prices of the tickets were ₹37 and ₹73, respectively. While preparing the revenue report, the accountant accidentally interchanged the numbers of student and adult tickets sold. Using the incorrect figures, the reported revenue was ₹4,040. After the mistake was corrected, the actual revenue was found to be ₹4,760.

If the ratio of the number of student tickets sold to the number of adult tickets sold is (1), what is the value of (k)?

A) 0.6

B) 0.75

C) 1.33

D) 1.66

Correct Answer: D) 1.66

Solution:

Let the number of student tickets be (S) and adult tickets be (A).

Actual revenue:

$$37S+73A=4760$$

Incorrect revenue:

$$37A+73S=4040$$

Subtracting the equations gives:

$$36(A-S)=720$$ $$A-S=20$$

Substituting (A=S+20) into the actual revenue equation:

$$37S+73(S+20)=4760$$ $$110S=3300 \\Rightarrow S=30$$

Therefore, (A=50), and

$$S\=30:50=1:1.666\\ldots$$

Hence, (k\approx1.66).

Question 8

A solid metallic sphere of radius 9 cm is melted and recast into (n) identical solid cylinders, each of radius 3 cm and height 6 cm. All these cylinders are then melted together and recast into (m) identical solid cones, each of radius 3 cm and height 9 cm.

Find the ratio (n).

A) 1 : 2

B) 1 : 4

C) 1 : 6

D) 1 : 8

Correct Answer: A) 1 : 2

Solution:

Volume of the sphere:

$$V=\\frac43\\pi(9)^3=972\\pi$$

Volume of one cylinder:

$$V=\\pi(3)^2(6)=54\\pi$$

Therefore,

$$n=\\frac{972\\pi}{54\\pi}=18$$

Volume of one cone:

$$V=\\frac13\\pi(3)^2(9)=27\\pi$$

Thus,

$$m=\\frac{972\\pi}{27\\pi}=36$$

Therefore,

$$n\=18:36=\\boxed{1:2}$$

Question 9

A cone with the same base radius and height is carved out from a solid cylinder of radius (r) and height (2r). What is the ratio of the remaining surface area to the remaining volume?

A) (\dfrac{3(5+\sqrt5)}{4r})

B) (\dfrac{3(5-\sqrt5)}{4r})

C) (\dfrac{5+\sqrt5}{8r})

D) (\dfrac{5+\sqrt5}{4r})

Correct Answer: A) (\dfrac{3(5+\sqrt5)}{4r})

Solution:

The cone has radius (r) and height (2r).

Its slant height is:

$$l=\\sqrt{r^2+(2r)^2}=\\sqrt5r$$

Remaining external surface area includes the cylinder's curved surface, its bottom circular base, and the curved surface of the conical cavity:

$$S=4\\pi r^2+\\pi r^2+\\pi r(\\sqrt5r)$$ $$S=(5+\\sqrt5)\\pi r^2$$

Remaining volume:

$$V=2\\pi r^3-\\frac13\\pi r^2(2r)$$ $$V=\\frac43\\pi r^3$$

Therefore,

$$\\frac{S}{V}= \\boxed{\\frac{3(5+\\sqrt5)}{4r}}$$

Question 10

The total surface area of a closed cylinder is (1232\text{ cm}^2). The height is three times its radius. The volume of the cylinder is:

A) (2587\text{ cm}^3)

B) (3234\text{ cm}^3)

C) (3326\text{ cm}^3)

D) (3696\text{ cm}^3)

Correct Answer: B) (3234\text{ cm}^3)

Solution:

Given (h=3r).

Total surface area of a closed cylinder:

$$2\\pi r(r+h)=1232$$

Substituting (h=3r):

$$2\\pi r(4r)=1232$$ $$8\\pi r^2=1232$$

Using (\pi=\frac{22}{7}), we obtain (r=7) cm.

Hence, (h=21) cm.

Volume:

$$V=\\pi r^2h$$ V=\\frac{22}{7}\\times49\\times21 \=\\boxed{3234\\text{ cm}^3}

Question 11

A right circular cylinder of radius 4 cm and height 6 cm is placed on the smaller circular face of a right circular frustum. The frustum has a bottom radius of 10 cm, a top radius of 4 cm, and a vertical height of 8 cm. Find the total external surface area of the combined solid, excluding the common circular base between the cylinder and the frustum.

A) (204\pi)

B) (288\pi)

C) (304\pi)

D) (320\pi)

Correct Answer: C) (304\pi\text{ cm}^2)

Solution:

The slant height of the frustum is:

$$l=\\sqrt{8^2+(10-4)^2}$$ $$l=\\sqrt{64+36}=10\\text{ cm}$$

Curved surface area of the frustum:

$$\\pi(R+r)l=\\pi(10+4)(10)=140\\pi$$

Bottom circular base of the frustum:

$$\\pi(10)^2=100\\pi$$

Curved surface area of the cylinder:

$$2\\pi rh=2\\pi(4)(6)=48\\pi$$

Top circular face of the cylinder:

$$\\pi(4)^2=16\\pi$$

Total external surface area:

140\\pi+100\\pi+48\\pi+16\\pi \=\\boxed{304\\pi\\text{ cm}^2}

Question 12

Which of the following best explains why the Revolt of 1857 failed to achieve its objective?

A) The revolt was confined entirely to southern India.

B) The uprising was localized, with different leaders pursuing separate aims.

C) The rebels had too many modern communication tools that caused confusion.

D) The British had already imprisoned all capable Indian leaders before 1857.

Correct Answer: B) The uprising was localized, with different leaders pursuing separate aims.

Explanation: The revolt lacked unified leadership, coordination and a common programme across the country. Many regions and groups did not participate.

Question 13

Which of the following factors are important for the rise of Indian nationalism?

I. The establishment of railways and telegraph helped promote communication and unification.

II. The vernacular press played no significant role in awakening national consciousness.

III. The contributions of social reformers like Raja Ram Mohan Roy to the cultural renaissance.

Which of the above statements are correct?

A) I only

B) II and III only

C) I and III only

D) I, II and III

Correct Answer: C) I and III only

Explanation: Statement I is correct because railways and telegraph improved communication. Statement II is incorrect because the vernacular press played an important role in spreading nationalist ideas. Statement III is correct.

Question 14

Match List I (Moderate Leaders) with List II (their significant contributions).

List I — Leaders

i. Dadabhai Naoroji

ii. Gopal Krishna Gokhale

iii. Surendranath Banerjee

iv. Pherozeshah Mehta

List II — Contributions

a) Founded Indian Association

b) Drain of Wealth Theory

c) Founded Servants of India Society

d) Founded Bombay Presidency Association

Choose the correct match:

A) i-b, ii-c, iii-a, iv-d

B) i-a, ii-d, iii-c, iv-b

C) i-a, ii-b, iii-d, iv-c

D) i-d, ii-b, iii-a, iv-c

Correct Answer: A) i-b, ii-c, iii-a, iv-d

Explanation: Dadabhai Naoroji is associated with the Drain of Wealth Theory; Gopal Krishna Gokhale founded the Servants of India Society; Surendranath Banerjee founded the Indian Association with Ananda Mohan Bose; and Pherozeshah Mehta was associated with the Bombay Presidency Association.

Question 15

Which of the following statements is NOT correct regarding the Partition of Bengal (1905)?

A) It was announced by Lord Curzon on the grounds of administrative convenience.

B) The partition created a western province with a Hindu majority and Eastern Bengal and Assam with a Muslim majority.

C) It was reversed in 1911 due to strong nationalist opposition.

D) It received unanimous support from the Indian National Congress.

Correct Answer: D) It received unanimous support from the Indian National Congress.

Explanation: The Indian National Congress opposed the partition. The decision was reversed in 1911.

Question 16

Arrange the following events in chronological order and select the correct sequence.

I. Salt March (Dandi March)

II. Non-Cooperation Movement

III. Quit India Movement

IV. Partition of Bengal

Options:

A) IV-I-II-III

B) IV-II-I-III

C) II-IV-I-III

D) IV-I-III-II

Correct Answer: B) IV-II-I-III

Explanation:

Partition of Bengal — 1905

Non-Cooperation Movement — 1920

Salt March — 1930

Quit India Movement — 1942

Therefore, the correct sequence is IV-II-I-III.

Question 17

Which of the following statements is NOT correct regarding the Swadeshi Movement?

A) The movement began as a direct response to the Partition of Bengal in 1905.

B) The movement was limited only to Bengal and did not spread to other parts of India.

C) The movement promoted the use of Indian-made goods and the boycott of British goods.

D) The movement inspired future national movements, including the Non-Cooperation Movement.

Correct Answer: B) The movement was limited only to Bengal and did not spread to other parts of India.

Explanation: Although it began in response to the Partition of Bengal, the Swadeshi Movement spread to other parts of India.

Question 18

The All-India Muslim League was founded during the annual session of the:

A) Indian Association

B) Indian National Congress

C) All-India Khilafat Conference

D) All-India Muhammadan Educational Conference

Correct Answer: D) All-India Muhammadan Educational Conference

Explanation: The All-India Muslim League was founded at Dhaka on 30 December 1906 during the session of the All-India Muhammadan Educational Conference.

Question 19

Which event led Mahatma Gandhi to withdraw the Non-Cooperation Movement in 1922?

A) Chauri Chaura incident

B) Jallianwala Bagh Massacre

C) Rowlatt Act

D) Simon Commission

Correct Answer: A) Chauri Chaura incident

Explanation: The incident took place on 4 February 1922. After protesters set fire to a police station, resulting in the deaths of policemen, Gandhi withdrew the movement.

Question 20

Consider the following statements regarding the Quit India Movement.

I. It was launched on 8 August 1942 at the Bombay session of the All India Congress Committee.

II. Gandhi gave the slogan “Do or Die” during this movement.

III. It resulted in the immediate transfer of power to Indian leaders.

Which of the above statements are correct?

A) I only

B) II and III only

C) I and II only

D) I, II and III

Correct Answer: C) I and II only

Explanation: Statements I and II are correct. The movement did not result in the immediate transfer of power; India became independent in 1947.

Question 21

Match List I (Personalities) with List II (their roles during Independence and Partition).

List I — Personalities

i. Lord Mountbatten

ii. Cyril Radcliffe

iii. V. P. Menon

iv. Sardar Patel

List II — Roles

a) Drafted the boundary between India and Pakistan

b) Last Viceroy of British India

c) Architect of the integration of princely states

d) Constitutional adviser who helped with the transfer of power

Choose the correct match:

A) i-a, ii-d, iii-c, iv-b

B) i-b, ii-a, iii-d, iv-c

C) i-d, ii-b, iii-a, iv-c

D) i-b, ii-c, iii-a, iv-d

Correct Answer: B) i-b, ii-a, iii-d, iv-c

Explanation: Lord Mountbatten was the last Viceroy of British India; Cyril Radcliffe chaired the boundary commissions; V. P. Menon played a key advisory role in the transfer of power and integration process; and Sardar Patel played a leading role in integrating princely states.

Question 22

Which of the following Article–Fundamental Right pairs is correctly matched?

A) Article 14 — Right to equality before law

B) Article 19 — Right against exploitation

C) Article 23 — Right to freedom of religion

D) Article 25 — Right to freedom of education

Correct Answer: A) Article 14 — Right to equality before law

Explanation: Article 14 guarantees equality before the law and equal protection of the laws. Article 19 concerns specified freedoms; Article 23 prohibits trafficking and forced labour; Article 25 concerns freedom of conscience and religion.

Question 23

Which of the following is NOT a Fundamental Duty under Article 51A?

A) To abide by the Constitution and respect the National Flag and National Anthem

B) To protect and improve the natural environment

C) To promote harmony and brotherhood among all citizens

D) To vote compulsorily in every general election

Correct Answer: D) To vote compulsorily in every general election

Explanation: Compulsory voting is not listed as a Fundamental Duty under Article 51A of the Constitution of India.

Question 24

Which of the following countries integrates direct democracy with a federal republic structure?

A) India

B) United Kingdom

C) Switzerland

D) Canada

Correct Answer: C) Switzerland

Explanation: Switzerland is a federal republic known for direct-democratic mechanisms such as referendums and popular initiatives.

Question 25

Which of the following statements is NOT correct regarding Universal Adult Franchise?

A) It grants citizens the right to vote irrespective of caste, religion, gender or wealth, subject to the prescribed age and other legal conditions.

B) The voting age was reduced from 21 years to 18 years by the 61st Constitutional Amendment Act, 1988.

C) It ensures that the government derives its authority from the consent of the people.

D) The introduction of universal adult franchise in India reflects the principle of social hierarchy.

Correct Answer: D) The introduction of universal adult franchise in India reflects the principle of social hierarchy.

Explanation: Universal Adult Franchise reflects political equality, not social hierarchy. The 61st Constitutional Amendment reduced the voting age from 21 to 18 years.

Question 26

What is the importance of the Secret Ballot for democracy?

A) It allows the government to track how each citizen voted for security purposes.

B) It safeguards independent voting, without coercion or retaliation.

C) It increases the cost and complexity of conducting elections significantly.

D) It reduces the time taken to count votes during elections.

Correct Answer: B) It safeguards independent voting, without coercion or retaliation.

Explanation: A secret ballot protects the voter's choice from undue influence, intimidation and retaliation.

Question 27

Which of the following is NOT a feature available under the online nomination process through the Suvidha Portal?

A) Separate portal access for political parties/candidates and Election Commission officials

B) Submission of security deposits through multiple modes

C) Facility to choose a preferred date and time for physical verification

D) Facility to file multiple nominations from unlimited constituencies simultaneously

Correct Answer: D) Facility to file multiple nominations from unlimited constituencies simultaneously

Explanation: The Suvidha Portal facilitates election-related processes, including online nomination. It does not provide an unlimited, simultaneous nomination facility across constituencies. The precise portal features should be checked against the applicable Election Commission guidelines for the relevant election.

Question 28

Which of the following conditions must be fulfilled by a registered unrecognised political party to be eligible for allotment of a common election symbol?

I. The party must be registered with the Election Commission of India under Section 29A of the Representation of the People Act, 1951.

II. The party must have conducted its organisational elections as per the approved tenure.

III. The party must have submitted audited annual accounts and contribution reports for the last three financial years.

IV. The party must have won at least one seat in the previous General Election.

Which of the above statements are correct?

A) I and II only

B) I, II and III only

C) II, III and IV only

D) I, II, III and IV

Correct Answer: B) I, II and III only

Explanation: Under the conditions described in this question, statements I, II and III are treated as correct, while winning a seat in the previous general election is not a universal requirement for a registered unrecognised party to seek a common symbol. Exact eligibility requirements depend on the Election Commission's applicable symbol-allotment order and current guidelines.

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