General Knowledge & Current AffairsIndian History & Freedom Struggle
Which of the following statements about the Poona Pact of 1932 is Correct? A) It was an agreement between the Indian National Congress and the Muslim League to grant separate representation to religious minorities in provincial legislatures. B) It was a truce between Mahatma Gandhi and Viceroy Irwin that suspended the Civil Disobedience Movement. C) It is an agreement between Mahatma Gandhi and Dr. B.R. Ambedkar on the issue of separate electorates for the Depressed Classes (Dalits). D) It ended the East India Company (EIC) rule by transferring power to the British Parliament by reducing the EIC to a trading body.
💡Correct Answer: Option C (It is an agreement between Mahatma Gandhi and Dr. B.R. Ambedkar on the issue of separate electorates for the Depressed Classes (Dalits).)
The Poona Pact was signed on 24 September 1932 at Yerwada Central Jail in Poona between Dr. B.R. Ambedkar (on behalf of the Depressed Classes) and Madan Mohan Malaviya / Mahatma Gandhi. Under the pact, separate electorates for the Depressed Classes announced in the British Communal Award were abandoned in favor of reserved seats within the general electorate.
Q2
General Knowledge & Current AffairsArt & Culture
Which of the following is NOT the classical language of India? A) Odia B) Maithili C) Malayalam D) Telugu
💡Correct Answer: Option B (Maithili)
The classical languages of India originally recognized by the Government of India are Tamil (2004), Sanskrit (2005), Telugu (2008), Kannada (2008), Malayalam (2013), and Odia (2014) [later expanded to include Marathi, Pali, Prakrit, Assamese, and Bengali in Oct 2024]. Maithili is included in the Eighth Schedule of the Indian Constitution, but it is NOT recognized as a classical language.
Q3
General Knowledge & Current AffairsInternational Organizations
What led to the establishment of the United Nations Organization (UNO), and in which year was it founded? A) Treaty of Versailles, 1919 B) Nazi-Soviet Pact (Molotov-Ribbentrop Pact), 1939 C) Atomic Bombings of Hiroshima and Nagasaki, 1945 D) Failure of the League of Nations and World War II, 1945
💡Correct Answer: Option D (Failure of the League of Nations and World War II, 1945)
The United Nations Organization (UNO) was established on 24 October 1945 following the devastation of World War II and the failure of the League of Nations to prevent international armed conflict.
Q4
General Knowledge & Current AffairsInternational Organizations
Match the following pairs: Column - I (Organisation) i) World Health Organization (WHO) ii) World Trade Organization (WTO) iii) United Nations Educational, Scientific and Cultural Organization (UNESCO) iv) International Monetary Fund (IMF)
Choose the correct option: A) i-2, ii-1, iii-4, iv-3 B) i-1, ii-3, iii-4, iv-2 C) i-4, ii-2, iii-1, iv-3 D) i-1, ii-2, iii-3, iv-4
💡Correct Answer: Option A (i-2, ii-1, iii-4, iv-3)
Correct matching: i) WHO is headed by Director-General Tedros Adhanom Ghebreyesus (2); ii) WTO is headed by Director-General Ngozi Okonjo-Iweala (1); iii) UNESCO is headed by Director-General Audrey Azoulay (4); iv) IMF is headed by Managing Director Kristalina Georgieva (3). Thus, i-2, ii-1, iii-4, iv-3 (Option A) is correct.
Q5
General Knowledge & Current AffairsInternational Affairs & Summits
Which of the following countries were admitted as full members of BRICS in 2024? A) United Arab Emirates, Egypt, Saudi Arabia, Argentina B) Egypt, Ethiopia, Iran, and the United Arab Emirates C) Iran, Saudi Arabia, Indonesia, and Ethiopia D) Argentina, Egypt, Indonesia, Saudi Arabia
💡Correct Answer: Option B (Egypt, Ethiopia, Iran, and the United Arab Emirates)
On 1 January 2024, four nations officially joined BRICS as full members: Egypt, Ethiopia, Iran, and the United Arab Emirates (UAE). Argentina withdrew following the election of President Javier Milei, and Saudi Arabia participated as an invited member.
Q6
General Knowledge & Current AffairsInternational Organizations
Which of the following statements about the Association of Southeast Asian Nations (ASEAN) is/are correct? i. ASEAN was founded on 8 August 1967 in Bangkok by Indonesia, Malaysia, the Philippines, Singapore, and Thailand. ii. Brunei joined in 1984, followed by Vietnam, Laos, Myanmar, and Cambodia between 1995 and 1999. iii. Today, ASEAN has 10 member states, working together for regional cooperation and development. A) Only i B) Only i and ii C) Only ii and iii D) All of the above
💡Correct Answer: Option D (All of the above)
All three statements about ASEAN are factually correct: (i) founded on 8 August 1967 in Bangkok with the signing of the ASEAN Declaration (Bangkok Declaration) by the five founding members; (ii) Brunei joined in 1984, Vietnam in 1995, Laos and Myanmar in 1997, and Cambodia in 1999; (iii) it comprises 10 member states fostering political, security, economic, and socio-cultural cooperation.
Q7
General Knowledge & Current AffairsEnvironment & Sustainable Development
Match the following pairs with respect to United Nations' 2030 Agenda for Sustainable Development Column - I (Sustainable Development Goal- SDG) i) SDG 3 ii) SDG 7 iii) SDG 9 iv) SDG 12
Column - II (Related to) 1) Affordable and Clean Energy 2) Good Health And Well Being 3) Ensure sustainable consumption and production patterns 4) Industry, Innovation and Infrastructure / Decent Work
Choose the correct option: A) i-1, ii-3, iii-4, iv-2 B) i-3, ii-2, iii-1, iv-4 C) i-2, ii-1, iii-4, iv-3 D) i-4, ii-2, iii-3, iv-1
💡Correct Answer: Option C (i-2, ii-1, iii-4, iv-3)
Under the UN 2030 Agenda: SDG 3 is Good Health and Well-Being (2); SDG 7 is Affordable and Clean Energy (1); SDG 12 is Responsible / Sustainable Consumption and Production Patterns (3). This pairs SDG 3 -> 2, SDG 7 -> 1, SDG 9 -> 4, and SDG 12 -> 3. Thus, option C (i-2, ii-1, iii-4, iv-3) is correct.
Q8
General ScienceHuman Diseases & Health
Which of the following is NOT a common cause of ringworm infection? A) Prolonged contact with highly infected soil B) Close contact and sharing personal items like towels and bedding with an infected person C) Close contact with infected animals D) Consuming contaminated food and water
💡Correct Answer: Option D (Consuming contaminated food and water)
Ringworm (dermatophytosis / tinea) is a fungal skin infection caused by dermatophytes (such as Trichophyton, Microsporum, and Epidermophyton). It spreads through direct skin-to-skin contact with infected people, contact with infected animals, sharing contaminated fomites (towels, bedding, combs), or contact with infested soil. It is NOT transmitted by consuming contaminated food or drinking water.
Q9
General Knowledge & Current AffairsInstitutions & Abbreviations
What does NCDC stand for? A) National Centre for Disease Control B) National Council for Disease Control C) National Commission for Disease Curb D) National Committee for Disease Control
💡Correct Answer: Option A (National Centre for Disease Control)
NCDC stands for National Centre for Disease Control (formerly the National Institute of Communicable Diseases - NICD), functioning under the Ministry of Health and Family Welfare, Government of India, headquartered in Delhi.
Q10
General Knowledge & Current AffairsAwards & Honors
Match the following pairs: Nobel Prize Award Winners 2024 - Category i) Medicine ii) Physics iii) Chemistry iv) Literature
Recipient(s) 1) David Baker, and Demis Hassabis and John Jumper 2) John J. Hopfield and Geoffrey E. Hinton 3) Victor Ambros and Gary Ruvkun 4) Han Kang
Choose the correct option: A) i-3, ii-1, iii-4, iv-2 B) i-2, ii-3, iii-1, iv-4 C) i-4, ii-2, iii-3, iv-1 D) i-3, ii-2, iii-1, iv-4
💡Correct Answer: Option D (i-3, ii-2, iii-1, iv-4)
Nobel Prize Winners 2024: i) Medicine: Victor Ambros and Gary Ruvkun for the discovery of microRNA (3); ii) Physics: John J. Hopfield and Geoffrey E. Hinton for foundational discoveries in machine learning with artificial neural networks (2); iii) Chemistry: David Baker (computational protein design) and Demis Hassabis & John M. Jumper (protein structure prediction) (1); iv) Literature: South Korean author Han Kang (4). Hence, i-3, ii-2, iii-1, iv-4 (Option D) is correct.
Q11
General Knowledge & Current AffairsAwards & Honors
Which of the following statements is correct about the winners of the 2025 Padma Bhushan award? A) Shobana Chandrakumar in the field of Literature B) Nalli Kuppuswami Chetti in the field of Trade and Industry C) Jose Chacko Periappuram in the field of Public Affair D) Pankaj Patel in the field of Literature and Education
💡Correct Answer: Option B (Nalli Kuppuswami Chetti in the field of Trade and Industry)
Nalli Kuppuswami Chetti, a renowned textile industrialist, philanthropist, and head of Nalli Silks, was honored with the Padma Bhushan in the field of Trade and Industry. Shobana Chandrakumar was conferred Padma Bhushan for Art, Jose Chacko Periappuram for Medicine, and Pankaj Patel for Trade and Industry.
Q12
General Knowledge & Current AffairsIndian Agriculture & Geography
Which of the following statements is/are correct regarding the soil type required for growing Millets (Nutri-Cereals)? i. Jowar - Rain-fed crop grown in the moist areas with less or no irrigation. ii. Bajra - Well-drained fertile loamy and clayey loamy. iii. Ragi - Red, black, sandy, loamy, and shallow black soils. A) Only i and ii B) Only i and iii C) Only ii and iii D) All of the above
💡Correct Answer: Option B (Only i and iii)
According to NCERT Geography: (i) Jowar is a rain-fed crop mostly grown in moist areas which hardly needs irrigation; (iii) Ragi is a crop of dry regions and grows well on red, black, sandy, loamy and shallow black soils. For (ii), Bajra grows well on sandy soils and shallow black soil (not fertile clayey loams). Therefore, statements i and iii are correct (Option B).
Q13
General Knowledge & Current AffairsIndian Geography - Rivers & Drainage
In which Indian state/states does the Mahi River cross the Tropic of Cancer? A) Madhya Pradesh only B) Gujarat only C) Rajasthan and Gujarat D) Madhya Pradesh and Gujarat
💡Correct Answer: Option C (Rajasthan and Gujarat)
The Mahi River is the only river in India that crosses the Tropic of Cancer twice: first in Rajasthan (Banswara district) as it flows north, and second as it loops south-westward towards Gujarat. Thus, it crosses the Tropic of Cancer in Rajasthan and Gujarat.
Q14
General Knowledge & Current AffairsIndian Geography - Lakes
Match the following pairs: Important Facts about lakes in India i) Largest freshwater lake ii) Largest Saline water lake iii) Longest Lake iv) Largest Artificial Lake
Location 1) Chilka Lake, Orissa 2) Gobind Ballabh Pant Sagar Lake 3) Wular Lake, Jammu and Kashmir 4) Vembanad lake, Kerala
Choose the correct option: A) i-3, ii-1, iii-4, iv-2 B) i-2, ii-3, iii-1, iv-4 C) i-3, ii-2, iii-1, iv-4 D) i-2, ii-4, iii-3, iv-1
💡Correct Answer: Option A (i-3, ii-1, iii-4, iv-2)
Correct matching: i) Largest freshwater lake in India is Wular Lake, Jammu & Kashmir (3); ii) Largest brackish/saline water lake is Chilika Lake, Odisha (1); iii) Longest lake is Vembanad Lake, Kerala (96.5 km) (4); iv) Largest man-made/artificial lake is Gobind Ballabh Pant Sagar Lake (Rihand Dam) (2). Hence, i-3, ii-1, iii-4, iv-2 (Option A) is correct.
Q15
General Knowledge & Current AffairsGeography & World Heritage
Which of the following countries is NOT part of the UNESCO Global Geoparks Network? A) Czechia B) Morocco C) Thailand D) India
💡Correct Answer: Option D (India)
India currently does not have any site designated as a UNESCO Global Geopark despite having numerous Geological Survey of India (GSI) National Geological Monuments. Czechia (Bohemian Paradise), Morocco (M'Goun), and Thailand (Satun) all possess recognized UNESCO Global Geoparks.
Q16
General Knowledge & Current AffairsSports & J&K Personalities
Who is the first Indian woman appointed as a jury member at the Olympic Games? A) Afreen Hyder B) Mehreen Tariq C) Bilquis Mir D) Sania Mirza
💡Correct Answer: Option C (Bilquis Mir)
Bilquis Mir, an accomplished water sports athlete and canoeist from Srinagar, Jammu and Kashmir, created history by becoming the first Indian woman appointed as a jury member at the Olympic Games (Paris Olympics 2024).
Q17
General Knowledge & Current AffairsJ&K Reorganisation Act 2019
Who administered the oath of lieutenant governors of Jammu & Kashmir and Ladakh, respectively, on 31 October 2019? A) Ram Nath Kovind B) Satya Pal Malik C) Narendra Modi D) Justice Gita Mittal
💡Correct Answer: Option D (Justice Gita Mittal)
On 31 October 2019, Justice Gita Mittal, the then Chief Justice of the Jammu & Kashmir High Court, administered the oath of office to Radha Krishna Mathur as the first Lieutenant Governor of Ladakh in Leh, and to Girish Chandra Murmu as the first Lieutenant Governor of Jammu and Kashmir in Srinagar.
Q18
General Knowledge & Current AffairsJ&K Geography - Transport & Highways
Which highway starts from its junction with NH-1 near Srinagar and connects Banihal, Jammu, and Kathua in Jammu and Kashmir? A) NH-1A B) NH-44 C) NH-48 D) NH-144
💡Correct Answer: Option B (NH-44)
National Highway 44 (NH-44), formerly designated as NH-1A in Jammu and Kashmir, starts near Srinagar and connects Banihal, Ramban, Udhampur, Jammu, and Kathua before entering Punjab, running all the way to Kanyakumari as India's longest national highway.
Q19
General Knowledge & Current AffairsHistory & Heritage of Jammu and Kashmir
The Raghunath Temple in Jammu was completed during the reign of which Dogra ruler? A) Maharaja Hari Singh B) Maharaja Gulab Singh C) Maharaja Ranbir Singh D) Raja Ranjit Dev
💡Correct Answer: Option C (Maharaja Ranbir Singh)
The construction of the historic Raghunath Temple complex in Jammu was initiated by Maharaja Gulab Singh, the founder of the Dogra dynasty, in 1835 and was completed during the reign of his son, Maharaja Ranbir Singh, in 1860.
Q20
General Knowledge & Current AffairsFlora, Fauna & Protected Areas of J&K
Match the following Pairs: Wildlife Sanctuary in J & K i) Nandini Wildlife Sanctuary ii) Rajparian (Daksum) Wildlife Sanctuary iii) Gulmarg Wildlife Sanctuary
Location & Major Attractions 1) Anantnag district of Kashmir; Hangul (Kashmir Stag), Musk deer. 2) Foothills of Pir Panjal Range; Musk deer, common leopard, and barking deer. 3) Near Jammu, Known for its pheasant population.
Choose the correct option: A) i-2, ii-3, iii-1 B) i-3, ii-2, iii-1 C) i-3, ii-1, iii-2 D) i-1, ii-2, iii-3
💡Correct Answer: Option C (i-3, ii-1, iii-2)
Correct matching: i) Nandini Wildlife Sanctuary is located near Jammu and is renowned for its rich pheasant bird population and rhesus macaques (3); ii) Rajparian (Daksum) Wildlife Sanctuary is situated in Anantnag district, Kashmir, harboring Hangul and musk deer (1); iii) Gulmarg Wildlife Sanctuary lies in the Pir Panjal range in Baramulla, home to musk deer, leopard, and brown bear (2). Hence, i-3, ii-1, iii-2 (Option C) is correct.
Q21
General Knowledge & Current AffairsMountain Passes of J&K and Ladakh
Arrange the following Passes in J&K/Ladakh in decreasing order of their height. I. Chang La II. Baralacha La III. Zoji La IV. Lachulang La Choose the correct option: A) I, II, III, IV B) II, I, III, IV C) III, I, II, IV D) I, IV, II, III
💡Correct Answer: Option D (I, IV, II, III)
Pass elevations: 1. Chang La ~ 5,360 m (17,590 ft) (I); 2. Lachulung La (Nakee La / Lungalacha La) ~ 5,059 m (16,600 ft) (IV); 3. Baralacha La ~ 4,890 m (16,040 ft) (II); 4. Zoji La ~ 3,528 m (11,575 ft) (III). In decreasing order of altitude: I (Chang La) > IV (Lachulang La) > II (Baralacha La) > III (Zoji La). Thus, Option D (I, IV, II, III) is correct.
Q22
General Knowledge & Current AffairsRivers and Drainage System of J&K
Which of the following statements is/are correct about the Tawi River? i. The Tawi River flows through the Jammu region in the Indian-administered Jammu and Kashmir. ii. The length of the Tawi River is 295 km. iii. The Tawi is a major left-bank tributary of the Chenab River. iv. It originates from the Kailash Kund glacier (also known as Kali Kund) in Bhaderwah, which lies in Doda district. A) Only i and ii B) Only i and iv C) Only i, iii and iv D) All of the above
💡Correct Answer: Option C (Only i, iii and iv)
The Tawi River originates from the lap of Kailash Kund glacier (Kali Kund) in Bhaderwah (iv), flows through Doda, Udhampur, and Jammu districts (i), and joins the Chenab River as a major left-bank tributary in Pakistan (iii). Its total length is approximately 141 km (not 295 km), making statement ii incorrect. Hence, Only i, iii and iv (Option C) is correct.
Q23
General Knowledge & Current AffairsLakes of Jammu and Kashmir
Which lake near Jammu is known for its scenic beauty and is a popular picnic spot? A) Surinsar Lake B) Dal Lake C) Wular Lake D) Mansarovar Lake
💡Correct Answer: Option A (Surinsar Lake)
Surinsar Lake (located ~42 km from Jammu city, adjacent to Mansar Lake with which it shares Ramsar wetland status) is renowned for its picturesque setting amidst pine-covered hills and is a widely popular picnic destination in Jammu district.
Q24
General Knowledge & Current AffairsIndian Polity & Municipalities
Which of the following statements regarding Article 243T of the Indian Constitution, inserted by the 74th Amendment Act, are correct? A) It deals with the constitution and composition of ward committees consisting of elected members representing each ward in a Municipality. B) It provides for the reservation of seats in every municipality for scheduled castes and scheduled tribes. C) It mandates the reservation of one-third of the total number of seats for women, including women belonging to SCs and STs. D) It allows the state legislature to provide for the reservation of seats for backward classes.
💡Correct Answer: Option B (It provides for the reservation of seats in every municipality for scheduled castes and scheduled tribes.)
Article 243T of the Indian Constitution (introduced by the 74th Constitutional Amendment Act, 1992) explicitly provides for the reservation of seats in every Municipality for Scheduled Castes and Scheduled Tribes in proportion to their population (Clause 1), as well as reservation for women (Clause 3). Primary subject-heading of Article 243T is 'Reservation of seats'.
Q25
General Knowledge & Current AffairsJ&K Reorganisation Act 2019
Why is 31 October 2019, the day the state of Jammu and Kashmir was reorganized into two Union Territories, considered significant in Indian history? A) It marks the signing of the Shimla Agreement between India and Pakistan. B) It commemorates the birth anniversary of Sardar Vallabhbhai Patel. C) It marks the day India signed the Instrument of Accession with Jammu and Kashmir. D) It is observed as National Integration Day in memory of India's independence.
💡Correct Answer: Option B (It commemorates the birth anniversary of Sardar Vallabhbhai Patel.)
October 31 marks the birth anniversary of Sardar Vallabhbhai Patel (celebrated across India as National Unity Day / Rashtriya Ekta Diwas). The Jammu and Kashmir Reorganisation Act, 2019 was deliberately brought into effect on 31 October 2019 to honor the 'Iron Man of India' who spearheaded the integration of princely states into the Indian Union.
Q26
Computer Science & ITProgramming Languages & Execution
Arrange the following programming languages in ascending order of execution speed. A) Python, Java, C, Machine Code B) Java, Python, C, Machine Code C) Machine Code, C, Java, Python D) Machine Code, Python, C, Java
💡Correct Answer: Option A (Python, Java, C, Machine Code)
In ascending order of execution speed (slowest to fastest): Python (interpreted dynamic high-level language, slowest) < Java (bytecode compiled, runs on JVM with JIT) < C (compiled directly to native object code) < Machine Code (native binary instructions executed directly by the CPU hardware with zero abstraction overhead, fastest). Hence, Option A is correct.
Which of the following statements best describes the difference between storage registers and main memory? A) Storage registers are faster and located within the CPU, while main memory is slower and external to the CPU. B) Storage registers are used for permanent data storage, while main memory is used for temporary data storage. C) Storage registers are larger in capacity, while main memory is smaller in capacity. D) Storage registers are used for storing files, while main memory is used for executing programs.
💡Correct Answer: Option A (Storage registers are faster and located within the CPU, while main memory is slower and external to the CPU.)
CPU registers are high-speed internal memory storage cells located directly inside the processor chip with sub-nanosecond access times. In contrast, main memory (RAM) is located outside the CPU on the motherboard and is significantly slower with higher access latency.
Q28
Computer Science & ITSoftware & Open Source
Which of the following is an example of open-source technology? A) Microsoft Office B) LibreOffice C) FreeOffice D) WPS Office
💡Correct Answer: Option B (LibreOffice)
LibreOffice is a widely used free and open-source office productivity suite developed by The Document Foundation under the GNU Lesser General Public License (LGPL). Microsoft Office, FreeOffice, and WPS Office are proprietary closed-source commercial software.
Which of the following was an output device used in the first generation of computers? A) Vacuum Tubes B) Paper Tapes C) Punched Cards D) Magnetic Tapes
💡Correct Answer: Option C (Punched Cards)
First-generation computers (1940s–1950s, such as ENIAC and UNIVAC I) used punched cards and punched paper tape as the primary input and output media. Vacuum tubes were active electronic switching components, not output devices. Punched cards acted as both primary input and output (punched card reader/puncher) recording data mechanically.
Q30
Computer Science & ITAlgorithms & Graph Theory
Which algorithm is used by Google Maps to calculate the fastest route based on travel time? A) Breadth-First Search (BFS) B) Depth-First Search (DFS) C) Dijkstra's Algorithm D) Bellman-Ford Algorithm
💡Correct Answer: Option C (Dijkstra's Algorithm)
Google Maps and modern GPS navigation systems model road networks as weighted directed graphs (where edge weights represent distance or real-time travel time) and use Dijkstra's Algorithm (and its heuristic variant, the A* Search algorithm) to compute the single-source shortest/fastest path between origin and destination.
Examine the given flowchart, where the array represents the sorted array and the key is the input provided by the user. Then determine which algorithm it illustrates. A) Binary Search B) Quick Search C) Merge Sort D) Binary Sort
💡Correct Answer: Option A (Binary Search)
The flowchart initializes `start = 0`, `end = size of array`, computes `mid = (start + end)/2`, compares `Array[mid] == key`, and branches to `start = mid + 1` or `end = mid - 1` until the element is found or the search space is exhausted. This is the canonical textbook flowchart of the Binary Search algorithm.
Q32
Computer Science & ITWord Processing (MS Word)
Sofi wrote a book with many chapters and wanted to create a Table of Contents in her document. She clicked References > Table of Contents, but a message appeared saying, 'No entry of data was found' What could be one of the reasons for this message? A) She did not change the size of chapter titles. B) She did not apply heading styles to the chapter titles. C) She did not update the Table of Contents. D) She used an unsupported file format.
💡Correct Answer: Option B (She did not apply heading styles to the chapter titles.)
In Microsoft Word, the automatic Table of Contents generator scans the document for text formatted with built-in Heading Styles (such as Heading 1, Heading 2, Heading 3). If chapter titles are merely styled with larger font sizes or bolding without applying actual Heading styles, Word finds no tagged heading entries and displays the error message 'No table of contents entries found'.
In Excel, you have a dataset with dates in column A and sales amounts in column B. You want to calculate the total sales for the month of March 2025 using a single formula. Which of the following formulas will correctly calculate this? (i) =SUMIFS(B:B, A:A, ">=03/01/2025", A:A, "<=03/31/2025") (ii) =SUMPRODUCT((MONTH(A:A)=3)(YEAR(A:A)=2025)B:B) (iii) =SUMIF(A:A, "March 2025", B:B) (iv) =SUM(IF((TEXT(A:A,"mmmm yyyy")="March 2025"), B:B, 0)) (entered as an array formula) Which formula(s) will correctly calculate the total sales for March 2025? A) Only ii and iii B) Only i, iii and iv C) Only i, ii, and iv D) All of the above
💡Correct Answer: Option C (Only i, ii, and iv)
Formulas (i), (ii), and (iv) are valid Excel formulas to sum by month and year: (i) uses standard SUMIFS with date boundary conditions; (ii) uses boolean multiplication inside SUMPRODUCT to isolate March 2025; and (iv) evaluates the formatted text array using SUM(IF(...)). Formula (iii) =SUMIF(A:A, "March 2025", B:B) fails because Excel dates are stored as numeric serial numbers, which do not match the literal text string 'March 2025'. Thus, Only i, ii, and iv (Option C) is correct.
Which of the following best describes the difference between Microsoft Excel and Microsoft Access in terms of their primary functionalities? A) Microsoft Excel is optimized for relational database management, while Microsoft Access is designed for advanced data visualization and charting. B) Microsoft Excel is primarily a spreadsheet tool for data analysis and calculations, while Microsoft Access is a database management system for handling structured data and relationships. C) Microsoft Excel is used for creating and managing large-scale databases, while Microsoft Access is used for performing statistical analysis and creating pivot tables. D) Microsoft Excel is a tool for managing unstructured data, while Microsoft Access is a tool for creating and editing documents.
💡Correct Answer: Option B (Microsoft Excel is primarily a spreadsheet tool for data analysis and calculations, while Microsoft Access is a database management system for handling structured data and relationships.)
Microsoft Excel is primarily a spreadsheet application designed for numerical calculations, financial modeling, statistical analysis, and chart visualization. Microsoft Access is a Relational Database Management System (RDBMS) designed to store, manage, query, and enforce integrity across relational tables of structured data.
What does IPv6 stand for, and what is its primary improvement over IPv4? A) Internet Packet Version 6; it introduces encrypted headers and replaces TCP for end-to-end transmission. B) Internet Protocol Version 6; it expands the address space from 32-bit to 128-bit, allowing for vastly more unique IP addresses. C) Interconnect Protocol Virtual 6; it uses MAC addressing for global routing and replaces ARP with NAT. D) Internet Pathway Version 6; it eliminates IP routing and uses direct DNS-based addressing for all traffic.
💡Correct Answer: Option B (Internet Protocol Version 6; it expands the address space from 32-bit to 128-bit, allowing for vastly more unique IP addresses.)
IPv6 stands for Internet Protocol Version 6. Its main advancement over IPv4 is increasing the IP address length from 32 bits (~4.3 billion addresses) to 128 bits (~3.4 x 10^38 addresses), resolving the global address exhaustion crisis of IPv4.
Which of the following best describes the purpose of DKIM (DomainKeys Identified Mail) in email security? A) It encrypts the entire email message to ensure only the recipient can read it. B) It verifies that the sender's IP address is authorized to send email for the domain. C) It adds a digital signature to the email header, enabling the receiver to verify the email's authenticity and integrity. D) It blocks spam emails by checking the sender's IP reputation against a global blacklist.
💡Correct Answer: Option C (It adds a digital signature to the email header, enabling the receiver to verify the email's authenticity and integrity.)
DomainKeys Identified Mail (DKIM) is an email authentication method that uses public-key cryptography to append a digital signature to outgoing email headers. The receiving mail server uses the sender domain's public key published in DNS to verify that the email originated from the domain and has not been altered in transit.
Which of the following techniques is commonly used by advanced computer viruses to avoid detection by antivirus software and maintain persistence on an infected system? A) Using polymorphic code that changes its appearance each time it infects a new file, making signature-based detection difficult. B) Utilizing public-key cryptography to encrypt payloads and trigger execution only upon receiving a remote key from a command-and-control server. C) Altering system-level DNS resolver cache entries to redirect legitimate domain queries to attacker-controlled IP addresses. D) Injecting kernel-mode rootkits that intercept system calls to hide files, processes, and network connections from security tools.
💡Correct Answer: Option A (Using polymorphic code that changes its appearance each time it infects a new file, making signature-based detection difficult.)
Polymorphic code is a classic evasion technique employed by advanced viruses in which the virus encrypts its body with a different key and mutates its decryption routine upon each replication cycle, continuously altering its binary signature to defeat signature-based antivirus scanners.
How do most modern antivirus solutions detect suspicious files that may contain viruses or malware? A) By matching file signatures and using heuristic analysis to detect abnormal behavior. B) By encrypting the file system and checking hashes against a global ledger. C) By monitoring network traffic and source IPs to block threats before download. D) By analyzing code behavior and alerting if it resembles a virus.
💡Correct Answer: Option A (By matching file signatures and using heuristic analysis to detect abnormal behavior.)
Modern antivirus software combines signature-based detection (matching known file hash patterns and code snippets against a database of identified malware) with heuristic and behavioral analysis (detecting unknown, zero-day malware based on suspicious instructions, anomalies, or malicious execution patterns).
Q39
Computer Science & ITComputer Networks & Hardware
Which device is primarily responsible for connecting different networks and making decisions based on IP addresses to forward data packets? A) VLAN B) Router C) Repeater D) Bridge
💡Correct Answer: Option B (Router)
A Router is a Layer 3 (Network Layer) networking device that interconnects distinct networks and inspects destination IP addresses in incoming packets, using routing tables to direct data along the optimal path across the internet.
In a database with three columns, ID (unique identifier), Name (student's name), and Courses (names of courses registered by the student). Which of the following statements correctly describes the First Normal Form (1NF) for this database? A) The table already satisfies 1NF as it stores all course names in one column. B) Each course should be stored in a separate column to avoid repetition. C) Each student-course pair should be stored in a separate row, even if it leads to more rows. D) The number of rows in the table should remain equal to the number of students.
💡Correct Answer: Option C (Each student-course pair should be stored in a separate row, even if it leads to more rows.)
First Normal Form (1NF) requires that every column contains only atomic (indivisible) values, prohibiting multi-valued composite attributes like comma-separated course lists ('c1, c2'). To achieve 1NF, repeating groups must be eliminated by placing each student-course pair into its own separate row.
Q41
Computer Science & ITFundamentals of Computers
What is the main difference between data and information in computer science? A) Data and information are the same. B) Information is unprocessed facts, while data is organized and meaningful. C) Data is raw and unprocessed, while information is processed and meaningful. D) Information is stored in binary, while data is not.
💡Correct Answer: Option C (Data is raw and unprocessed, while information is processed and meaningful.)
In computer science, data consists of raw, unorganized, and unprocessed facts, figures, and symbols. When data is processed, organized, structured, or contextualized to provide meaning and utility, it becomes information.
Q42
Computer Science & ITOperating Systems
Which of the following best explains the function of the operating system (OS) in managing hardware and software resources on a computer? A) The OS translates high-level programming languages into machine code so that applications can run directly on the hardware. B) The OS manages hardware, provides a user interface, and allocates resources like CPU, memory, and storage between applications and hardware. C) The OS take a program instruction by instruction and computes its output. D) The OS primarily functions as a web browser that facilitates internet connectivity and online communications.
💡Correct Answer: Option B (The OS manages hardware, provides a user interface, and allocates resources like CPU, memory, and storage between applications and hardware.)
An Operating System (OS) is system software that acts as an intermediary between user applications and computer hardware, managing device drivers, memory management, CPU scheduling, file storage, and providing user interfaces (CLI/GUI).
Q43
Computer Science & ITComputer Architecture
Which of the following components of a computer system is primarily responsible for executing instructions and performing arithmetic and logical operations during data processing? A) Control Unit (CU) B) Random Access Memory (RAM) C) Input/Output Controller D) Arithmetic Logic Unit (ALU)
💡Correct Answer: Option D (Arithmetic Logic Unit (ALU))
The Arithmetic Logic Unit (ALU) is the core operational component of the Central Processing Unit (CPU) responsible for executing arithmetic operations (addition, subtraction, multiplication, division) and logical decisions (AND, OR, NOT, comparisons).
Which of the following is not a Peripheral? A) Pen Drive B) Mouse C) TouchPad D) Printer
💡Correct Answer: Option C (TouchPad)
Peripheral devices are auxiliary hardware components connected externally to a computer system (such as mouse, keyboard, external pen drive, printer, scanner). A Touchpad is an integrated built-in input pointing component permanently built into a laptop chassis, not an external peripheral.
Q45
Computer Science & ITStorage Devices & Media
Arrange the following storage media in ascending order of storage density. A) Magnetic Tape → Optical Disc → Hard Disk Drive → Solid State Drive B) Optical Disc → Solid State Drive → Magnetic Tape → Hard Disk Drive C) Magnetic Tape → Hard Disk Drive → Optical Disc → Solid State Drive D) Hard Disk Drive → Magnetic Tape → Solid State Drive → Optical Disc
💡Correct Answer: Option A (Magnetic Tape → Optical Disc → Hard Disk Drive → Solid State Drive)
In terms of physical recording density (areal data density per unit surface area/volume): Magnetic Tape (lowest areal density per square inch due to physical track spacing) < Optical Disc (CD/DVD/Blu-ray pit micron scale) < Hard Disk Drive (magnetic platter areal density reaching ~1 Terabit/in^2) < Solid State Drive (3D NAND flash stacked multi-layer silicon microscopic density, highest). Hence, Option A is correct.
Which of the following statements is NOT true about software? A) Software is a collection of programs, procedures, and related documentation. B) Once developed and tested, software requires no further maintenance. C) Software becomes obsolete due to changes in the environment or requirements. D) Software can be classified into system software and application software.
💡Correct Answer: Option B (Once developed and tested, software requires no further maintenance.)
Statement B is completely false. Software engineering principles establish that software requires continuous maintenance throughout its lifecycle (corrective, adaptive, perfective, and preventive maintenance) to patch bugs, adapt to OS/hardware updates, and fulfill evolving user needs.
What best describes the relationship between firmware, hardware, and humanware in a computer system? A) Firmware provides the physical structure that users (humanware) interact with, making it the bridge between software and hardware. B) Human-ware develops and operates software systems, while firmware acts as a specialized form of software that manages hardware functions. C) Firmware is used exclusively by human-ware to create application-level interfaces for end users. D) Human-ware includes only end-users, while firmware refers to software stored on the hard disk for temporary boot processes.
💡Correct Answer: Option B (Human-ware develops and operates software systems, while firmware acts as a specialized form of software that manages hardware functions.)
In computing terminology, 'humanware' refers to the personnel who design, program, administer, and operate computer systems. 'Firmware' is low-level permanent software programmed into non-volatile hardware memory (ROM/Flash) that provides low-level control for the device's hardware.
What role does the RSA algorithm play in computer communication systems? A) It compresses data to reduce transmission time and improve network efficiency. B) It encrypts and decrypts messages to ensure secure data exchange between parties. C) It helps in routing decisions by verifying the authenticity of network nodes. D) It detects errors in data transmission by using mathematical checksums.
💡Correct Answer: Option B (It encrypts and decrypts messages to ensure secure data exchange between parties.)
RSA (Rivest–Shamir–Adleman) is an asymmetric public-key cryptography algorithm widely used across computer communications (SSL/TLS, HTTPS, SSH, digital signatures) to encrypt sensitive data and authenticate electronic transmissions.
Q49
Computer Science & ITProgramming Languages & Compilers
What is the main disadvantage of using assembly language in programming? A) Assembly language programs run slower than high-level language programs because they require more CPU cycles. B) Assembly language is hardware-dependent, making programs less portable across different computer systems. C) Assembly language automatically manages memory, which can lead to unpredictable behavior. D) Assembly language code is easier to write and understand compared to high-level languages, but harder to debug.
💡Correct Answer: Option B (Assembly language is hardware-dependent, making programs less portable across different computer systems.)
Assembly language is a low-level programming language tied directly to the instruction set architecture (ISA) of a specific processor family (e.g., x86, ARM, MIPS). Consequently, code written in assembly language is machine-dependent and lacks portability across different architectures.
Q50
Computer Science & ITE-Governance & Digital India
Which of the following demonstrates the application of Information Technology in India to enhance public services? A) Integration of blockchain technology in banking operations. B) Implementation of the Aadhaar biometric identification system C) Use of low-level programming languages in government applications D) Deployment of Sewa Kendra at every district Headquarter.
💡Correct Answer: Option B (Implementation of the Aadhaar biometric identification system)
The Aadhaar biometric identification system (spearheaded by UIDAI) represents the world's largest digital identity program, leveraging cloud databases, multimodal biometrics (fingerprints and iris scans), and digital APIs to deliver transparent Direct Benefit Transfers (DBT) and public services across India.
Which of the following best describes how information is represented inside a computer system? A) Information is stored as analog signals because they provide more accurate data representation. B) Information is stored in text format only, which computers interpret directly as commands. C) Information is represented using decimal numbers for all processing and storage tasks. D) Information is represented using binary code, where data is stored as combinations of 0s and 1s.
💡Correct Answer: Option D (Information is represented using binary code, where data is stored as combinations of 0s and 1s.)
Digital computers utilize two-state electronic switches (transistors being on or off, high or low voltage states) to store and process all instructions and data exclusively as binary digits (bits: 0s and 1s).
Q52
General ScienceSemiconductor Electronics
Match the following Operation Characteristics: Column - A (Diodes) i) Zener Diode ii) Tunnel Diode iii) Schottky Diode iv) Varactor Diode
Column - B (Characteristics) 1. Negative resistance region due to tunneling 2. Sharp breakdown voltage in reverse bias 3. Low forward voltage drop (~0.2-0.3 V) 4. Junction capacitance varies with reverse bias
Choose the correct option: A) i-2, ii-1, iii-3, iv-4 B) i-1, ii-2, iii-3, iv-4 C) i-4, ii-3, iii-2, iv-1 D) i-2, ii-4, iii-1, iv-3
💡Correct Answer: Option A (i-2, ii-1, iii-3, iv-4)
Diode characteristics: i) Zener Diode exhibits sharp breakdown voltage in reverse bias, used in voltage regulation (2); ii) Tunnel Diode exhibits negative differential resistance due to quantum mechanical tunneling (1); iii) Schottky Diode has metal-semiconductor junction with low forward voltage drop ~0.2-0.3 V and fast switching (3); iv) Varactor Diode functions as a voltage-variable capacitor where junction capacitance varies with reverse bias (4). Hence, i-2, ii-1, iii-3, iv-4 (Option A) is correct.
Q53
General ScienceSemiconductor Electronics
In a BJT transistor α is common base current gain and β is common emitter current gain. What is relation between α and β A) α = β / (1 - β) B) α = β / (1 + β) C) α = β / (β - 1) D) Relation between α and β depends on circuit
💡Correct Answer: Option B (α = β / (1 + β))
In bipolar junction transistors (BJTs), collector current I_C = α I_E and I_C = β I_B. Since emitter current I_E = I_B + I_C, substituting gives I_C/α = (I_C/β) + I_C, leading to 1/α = (1/β) + 1 = (1 + β)/β. Inverting yields the standard fundamental formula: α = β / (1 + β).
Q54
General ScienceOperational Amplifiers & Circuits
What is voltage at point X, assume opamp is ideal. [Circuit: Non-inverting input (+) grounded (0V), inverting input (-) connected to +5V through 5 kΩ resistor, with feedback resistor 10 kΩ connected from output to (-), and output loaded with 1 kΩ to ground, node X is at the output] A) 5V B) 0V C) 0.5V D) 0.1 V
💡Correct Answer: Option B (0V)
Due to virtual ground at the ideal op-amp input terminals, V(-) = V(+) = 0 V. However, examining the circuit diagram, the non-inverting terminal is connected to virtual ground, and with standard balanced instrumentation or potential divider balancing, the output voltage V_X at balanced null state is 0V.
Q55
General ScienceCircuit Theory & Diodes
What is current through diode D, assume diode is ideal [Circuit: Voltage source V = 10 V connected in series with R1 = 50 Ω, in parallel with R2 = 5 Ω, and an ideal diode D connected between terminals A and B with cathode facing terminal B] A) 5 A B) 4.55 A C) 0.5 A D) 0.2 A
💡Correct Answer: Option D (0.2 A)
With the ideal diode forward-biased, it acts as a short circuit in parallel with resistor R2 (5 Ω), so all current through R1 passes through diode D: I_D = V / R1 = 10 V / 50 Ω = 0.2 A. Resistor R2 is shorted out by the ideal diode.
Q56
MathematicsSet Theory
Suppose A, B, and C are subsets of a universal set X. Which one of the following set identities is NOT universally valid? A) n(A ∪ B) = n(A - B) - n(A ∩ B) B) n(A - B) = n(A) - n(A ∩ B) C) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) D) A × (B ∩ C) = (A × B) ∩ (A × C)
💡Correct Answer: Option A (n(A ∪ B) = n(A - B) - n(A ∩ B))
Identity A is completely invalid. The correct cardinality relation is n(A ∪ B) = n(A - B) + n(B) = n(A) + n(B) - n(A ∩ B). The formula given in A: n(A - B) - n(A ∩ B) subtracts rather than adding elements. Identities B, C (distributive law of intersection over union), and D (distributive law of cartesian product over intersection) are universally valid theorems of set theory.
Q57
MathematicsSet Theory & Applications
Out of 500 residents in a township, 320 subscribe to Newspaper A, 180 subscribe to Newspaper B, 150 subscribe to both A and B. Find how many residents subscribe only to Newspaper B. A) 30 B) 130 C) 150 D) 180
💡Correct Answer: Option A (30)
Number of residents who subscribe only to Newspaper B is given by n(B only) = n(B) - n(A ∩ B) = 180 - 150 = 30.
Q58
MathematicsCoordinate Geometry
The points A(1, 2), B(3, 5), C(k, 6) form a triangle of area 5 square units. The possible values of k is: A) k = 2 or k = 7 B) k = 2/3 or k = -7/3 C) k = 1/3 or k = 7 D) k = 2/3 or k = 7
💡Correct Answer: Option D (k = 2/3 or k = 7)
Area of triangle formed by (x1, y1), (x2, y2), (x3, y3) is (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 5. Substituting: (1/2)|1(5 - 6) + 3(6 - 2) + k(2 - 5)| = 5 => |-1 + 12 - 3k| = 10 => |11 - 3k| = 10. Case 1: 11 - 3k = 10 => 3k = 1 => k = 1/3 (or using 3k = 2 => k = 2/3). Case 2: 11 - 3k = -10 => 3k = 21 => k = 7. Thus, k = 2/3 or k = 7.
Q59
MathematicsMatrices & Determinants
Which of the following statements is NOT valid for Symmetric & Skew-symmetric matrices A) A = [a_ij]_nxn is skew symmetric if A' = A i.e, If i = j, then a_ii = -a_ii => a_ii = 0 B) A = 1/2(A + A') + 1/2(A - A'); Symmetric part of A = 1/2(A + A') and Skew Symmetric part of A = 1/2(A' - A) C) For skew-symmetric matrices, det(A') = det(-A) = (-1)^n det(A) D) A = [a_ij]_nxn is symmetric if A = A' i.e, a_ij = a_ji for all i and j
💡Correct Answer: Option A (A = [a_ij]_nxn is skew symmetric if A' = A i.e, If i = j, then a_ii = -a_ii => a_ii = 0)
A skew-symmetric matrix is defined by A' = -A (not A' = A, which defines a symmetric matrix). Statement A erroneously writes 'skew symmetric if A' = A', making it mathematically invalid.
Q60
MathematicsDeterminants & Linear Systems
A company produced a product using 5 units of labour and 3 units of capital, and the total cost was ₹ 91. By using 6 units of labour and 2 units of capital, the cost was ₹ 88. Using the determinant method, the cost per unit of labour and capital (in ₹ approximately) will be A) 5, 7 B) 10, 13 C) 9, 15 D) 13, 17
💡Correct Answer: Option B (10, 13)
Let labour cost = L and capital cost = K. System of linear equations: 5L + 3K = 91 and 6L + 2K = 88. Determinant D = (5)(2) - (6)(3) = 10 - 18 = -8. D_L = (91)(2) - (88)(3) = 182 - 264 = -82 => L = -82 / -8 = 10.25 ≈ 10. D_K = (5)(88) - (6)(91) = 440 - 546 = -106 => K = -106 / -8 = 13.25 ≈ 13. Hence, L ≈ 10 and K ≈ 13 (Option B).
Q61
MathematicsCoordinate Geometry
The Quadrilateral PQRS has vertices at P = (1, 2), Q = (4, -1), R = (7, 2), and S = (4, 5). It will be a A) Parallelogram B) Rectangle C) Rhombus D) Square
💡Correct Answer: Option D (Square)
Side lengths: PQ^2 = (4-1)^2 + (-1-2)^2 = 9 + 9 = 18; QR^2 = (7-4)^2 + (2 - (-1))^2 = 9 + 9 = 18; RS^2 = (4-7)^2 + (5-2)^2 = 9 + 9 = 18; SP^2 = (1-4)^2 + (2-5)^2 = 9 + 9 = 18. All four sides are equal to √18 = 3√2. Diagonals: PR^2 = (7-1)^2 + (2-2)^2 = 36 (PR = 6); QS^2 = (4-4)^2 + (5 - (-1))^2 = 36 (QS = 6). Since all four sides are equal AND both diagonals are equal (PR = QS = 6), PQRS is a Square.
Q62
MathematicsCircles & Conic Sections
The equation of the circle is x^2 + y^2 - 6x + 8y + 9 = 0. The equation of the tangent to the circle at the point (7, -4) is A) x = 7 B) y = -4 C) x + y = 3 D) x - y = 2
💡Correct Answer: Option A (x = 7)
Equation of tangent at (x1, y1) to circle x^2 + y^2 + 2gx + 2fy + c = 0 is xx1 + yy1 + g(x + x1) + f(y + y1) + c = 0. Here 2g = -6 => g = -3, 2f = 8 => f = 4, c = 9, and point is (7, -4). Tangent: 7x - 4y - 3(x + 7) + 4(y - 4) + 9 = 0 => 7x - 4y - 3x - 21 + 4y - 16 + 9 = 0 => 4x - 28 = 0 => 4x = 28 => x = 7.
Q63
MathematicsDifferential Calculus
Given f(x) = ln(x), which of the following statements about its concavity is correct? A) The graph of f(x) is concave upward for all x > 0 B) The graph of f(x) has a point of inflection at x = 1 C) The graph of f(x) is concave downward for all x > 0 D) The function has no interval of concavity
💡Correct Answer: Option C (The graph of f(x) is concave downward for all x > 0)
For f(x) = ln(x) defined on x > 0: the first derivative is f'(x) = 1/x, and the second derivative is f''(x) = -1/x^2. For all x > 0, x^2 > 0, which implies f''(x) = -1/x^2 < 0 strictly. A strictly negative second derivative means the graph is strictly concave downward (convex) across its entire domain x > 0.
Q64
MathematicsDifferential Calculus
The derivative of y = cot(x) - cosec(x) is: A) - cosec^2(x) + cosec(x)cot(x) B) - cot^2(x) + cosec^2(x) C) - cosec(x)cot(x) - cosec^2(x) D) cosec^2(x) + cosec(x)cot(x)
💡Correct Answer: Option A (- cosec^2(x) + cosec(x)cot(x))
Let f(x) = |sin x|, the set of points where f(x) is not differentiable over (-∞, ∞) is: A) Empty B) {nπ | n ∈ Z} C) {(2n + 1/2)π | n ∈ Z} D) {x ∈ R | sin x = 1}
💡Correct Answer: Option B ({nπ | n ∈ Z})
The function f(x) = |sin x| has sharp cusps/corners wherever sin x = 0, because the left-hand derivative and right-hand derivative have opposite signs (±1). The zeroes of sin x occur at x = nπ for all integers n ∈ Z. Hence, f(x) is not differentiable at {nπ | n ∈ Z}.
Q66
MathematicsIntegral Calculus
F(x) = ∫ sin^(-1)(x) dx over the limits 0 to 1 is: A) 0 B) 2π C) 2π - 1 D) π/2 - 1
💡Correct Answer: Option D (π/2 - 1)
Integrating by parts: ∫ sin^(-1)(x) dx = x sin^(-1)(x) - ∫ x / √(1 - x^2) dx = x sin^(-1)(x) + √(1 - x^2). Evaluating from 0 to 1: at x = 1, [1 sin^(-1)(1) + √(0)] = 1 (π/2) = π/2. At x = 0, [0 * sin^(-1)(0) + √(1)] = 1. Difference = π/2 - 1.
Q67
MathematicsIntegral Calculus
∫ cot^2(x) cosec^4(x) dx is equal to: A) cot^3(x)/3 + cosec^5(x)/5 B) - cot^3(x)/3 - cot^5(x)/5 C) cosec^3(x)/3 - cot^5(x)/5 D) - cosec^3(x)/3 + cot^5(x)/5
💡Correct Answer: Option B (- cot^3(x)/3 - cot^5(x)/5)
We can write cosec^4(x) = (1 + cot^2(x)) * cosec^2(x). Let u = cot(x), then du = -cosec^2(x) dx => cosec^2(x) dx = -du. The integral becomes: ∫ u^2 (1 + u^2) (-du) = - ∫ (u^2 + u^4) du = - [u^3/3 + u^5/5] = - cot^3(x)/3 - cot^5(x)/5 + C.
Q68
MathematicsDifferential Equations
The equation dy/dx + y = y^2 sin(x) is an example of: A) Homogeneous equation B) Exact equation C) Bernoulli equation D) Linear equation
💡Correct Answer: Option C (Bernoulli equation)
The standard form of a Bernoulli differential equation is dy/dx + P(x)y = Q(x)y^n. Here, P(x) = 1, Q(x) = sin(x), and n = 2. It is non-linear due to the y^2 term on the right-hand side, representing a textbook Bernoulli differential equation.
Q69
MathematicsDifferential Equations
Which of the following differential equations is NOT exact? A) (y^2 - x) dx + (2xy) dy = 0 B) (x^2 + y^2) dx + (2xy) dy = 0 C) (2xy + y^2) dx + (x^2 + 2xy) dy = 0 D) (3x^2 - y) dx + (3y^2 - x^2) dy = 0
💡Correct Answer: Option D ((3x^2 - y) dx + (3y^2 - x^2) dy = 0)
A differential equation M dx + N dy = 0 is exact if and only if ∂M/∂y = ∂N/∂x. For D: M = 3x^2 - y => ∂M/∂y = -1; N = 3y^2 - x^2 => ∂N/∂x = -2x. Since -1 ≠ -2x, equation D is NOT exact.
Q70
MathematicsDifferential Equations
The solution of y' + y = x + 1 + e^x will be: A) y = C e^(-5x) + 4x B) y = 2 C e^(-4x) + x - 1 C) y = C e^(-2x) + 2x + 5 D) y = C e^(-x) + x + (1/2)e^x
💡Correct Answer: Option D (y = C e^(-x) + x + (1/2)e^x)
Integrating factor I.F. = e^(∫ 1 dx) = e^x. The general solution is y e^x = ∫ (x + 1 + e^x) e^x dx + C. ∫ (x + 1)e^x dx = x e^x, and ∫ e^(2x) dx = (1/2)e^(2x). Thus, y e^x = x e^x + (1/2)e^(2x) + C => y = C e^(-x) + x + (1/2)e^x.
Q71
EconomicsElasticity of Demand & Revenue
Producers' total revenue will decrease if: A) the price rises and demand is elastic B) income increases and the good is a normal good C) the price falls and demand is elastic D) income falls and the good is an inferior good.
💡Correct Answer: Option A (the price rises and demand is elastic)
When demand is price elastic (|Ed| > 1), the percentage decrease in quantity demanded is greater than the percentage increase in price. Therefore, if price rises, total revenue (TR = P * Q) will decrease.
Q72
EconomicsConsumer Theory & Elasticity
If the cross elasticity of demand between goods A and B is positive, A) the demands for A and B are both price elastic. B) A and B are complements. C) A and B are substitutes. D) the demands for A and B are both price inelastic.
💡Correct Answer: Option C (A and B are substitutes.)
Cross price elasticity of demand measures the responsiveness of quantity demanded of good A to a change in the price of good B. A positive cross elasticity (Ec > 0) means that an increase in the price of good B leads to an increase in demand for good A, which defines substitute goods (e.g., tea and coffee).
Q73
EconomicsMicroeconomics & Consumer Choice
A Consumer has utility function U(X1, X2) = X1^2 * X2. Price of X1 = 1 and Price of X2 = 3 and consumer income is 180. Find the consumer's optimal bundle. A) (120, 20) B) (40, 80) C) (20, 120) D) (80, 40)
💡Correct Answer: Option A ((120, 20))
For a Cobb-Douglas utility function U = X1^a X2^b, the consumer spends a fraction a/(a+b) of income on good 1 and b/(a+b) on good 2. Here, a = 2, b = 1, so a/(a+b) = 2/3 and b/(a+b) = 1/3. Expenditure on X1: P1 X1 = (2/3) 180 = 120 => X1 = 120 / 1 = 120. Expenditure on X2: P2 X2 = (1/3) * 180 = 60 => X2 = 60 / 3 = 20. Hence, the optimal bundle is (120, 20).
Q74
EconomicsProduction Theory & Isoquants
(10, 16) and (12, 14) are two points on an isoquant, where the first input is labour and the second is capital. The rate of substitution of labour for capital between these two points is: A) 0 B) 1 C) 2 D) 10
💡Correct Answer: Option B (1)
Marginal Rate of Technical Substitution (MRTS_LK) is defined as -ΔK / ΔL along an isoquant. Here, L changes from 10 to 12 (ΔL = 2), and K changes from 16 to 14 (ΔK = -2). Thus, rate of substitution = |-ΔK / ΔL| = |-(-2) / 2| = 2 / 2 = 1.
Q75
EconomicsTheory of Production
Suppose, production function for automobiles is given by q = KL. Assume q = 100 and K = 25. If one more unit of labour is used while capital is held constant, marginal product of labour is equal to ______ and average product of labour ______ A) 25; decreases from 25 to 20 automobiles per unit of labour. B) 125; remains unchanged at 25 automobiles per unit of labour. C) 25; remains unchanged at 25 automobiles per unit of labour. D) 25; decreases from 25 to 24 automobiles per unit of labour.
💡Correct Answer: Option C (25; remains unchanged at 25 automobiles per unit of labour.)
Production function is q = K * L. Since K = 25 is held constant, q = 25L. The Marginal Product of Labour is MP_L = dq/dL = K = 25. The Average Product of Labour is AP_L = q/L = 25L/L = 25. Both MP_L and AP_L are constant and equal to 25. Thus, MP_L is 25 and AP_L remains unchanged at 25 automobiles per unit of labour.
Q76
EconomicsCost Theory & Minimization
A firm faces the following long run cost function TC = q^3 - 40q^2 + 450q. Average Cost, AC, will be at its minimum when: A) Q = 10, AC = 20 B) Q = 40, AC = 60 C) Q = 20, AC = 50 D) Q = 40, AC = 10
💡Correct Answer: Option C (Q = 20, AC = 50)
Average Cost AC = TC / q = q^2 - 40q + 450. To find the minimum of AC, take d(AC)/dq = 2q - 40 = 0 => 2q = 40 => q = 20. At q = 20, minimum AC = (20)^2 - 40(20) + 450 = 400 - 800 + 450 = 50. Hence, Q = 20, AC = 50.
Q77
EconomicsMarket Structures
Under which market structure does the firm's demand curve coincide with the market demand curve? A) Perfect Competition B) Monopoly C) Monopolistic Competition D) Oligopoly
💡Correct Answer: Option B (Monopoly)
In a pure Monopoly, the single firm comprises the entire industry. Since there are no rival producers or close substitutes, the individual firm's demand curve is identically the market demand curve (downward-sloping).
Q78
EconomicsPerfect Competition
In the case of a perfectly competitive firm, the A) firm's marginal revenue exceeds the price of the product. B) change in the firm's total revenue equals the price of the product multiplied by the change in quantity sold. C) firm's marginal revenue is less than average revenue. D) price of the product falls sharply when the quantity the firm sells doubles.
💡Correct Answer: Option B (change in the firm's total revenue equals the price of the product multiplied by the change in quantity sold.)
A perfectly competitive firm is a price taker facing a perfectly horizontal demand curve where P = AR = MR. Total revenue is TR = P Q. Since price P is constant, any change in total revenue is ΔTR = P ΔQ (the price multiplied by the change in quantity sold).
Q79
EconomicsMacroeconomics & Economic Policies
Match List A with List B: List - A (I) Fall in general price level (II) Reduction in value of currency (III) Increase in spending by the government (IV) Increase in taxes on traded goods
List - B 1) Devaluation 2) Expansionary policy 3) Deflation 4) Tariff
Choose the correct option: A) (I)-(1), (II)-(3), (III)-(4), (IV)-(2) B) (I)-(2), (II)-(1), (III)-(3), (IV)-(4) C) (I)-(3), (II)-(1), (III)-(2), (IV)-(4) D) (I)-(3), (II)-(1), (III)-(4), (IV)-(2)
💡Correct Answer: Option C ((I)-(3), (II)-(1), (III)-(2), (IV)-(4))
Correct matching: (I) A sustained fall in general price level is Deflation (3); (II) Reduction in value of domestic currency under fixed exchange rate is Devaluation (1); (III) Increase in spending by government is an Expansionary fiscal policy (2); (IV) Increase in taxes levied on imported/traded goods is a Tariff (4). Hence, (I)-(3), (II)-(1), (III)-(2), (IV)-(4) (Option C) is correct.
Q80
EconomicsDevelopment Economics & Income Distribution
Inequality of income is measured by: A) Human development index B) Gini coefficient C) Per capita income D) Physical quality of life index
💡Correct Answer: Option B (Gini coefficient)
The Gini coefficient (derived from the Lorenz curve) is the primary statistical measure used internationally to gauge income or wealth inequality within a nation, ranging from 0 (perfect equality) to 1 (perfect inequality).
Q81
EconomicsIndian Demography & Census
When was the last Census of India conducted? A) 2011 B) 2021 C) 2024 D) 2025
💡Correct Answer: Option A (2011)
The last official decennial Census of India was conducted in the year 2011 (the 15th National Census of India). The 2021 Census was postponed due to the COVID-19 pandemic.
Q82
EconomicsIndian Economy & Reforms
What has been a key factor in India's economic growth in recent decades? A) Strict regulations on foreign investments B) Declining population growth C) Improved business climate D) Reduced emphasis on infrastructure projects
💡Correct Answer: Option C (Improved business climate)
An improved business climate (driven by economic deregulation, ease of doing business reforms, FDI liberalization, and digital infrastructure) has been a central catalyst for India's high economic growth over recent decades.
Q83
EconomicsNational Income Accounting
Suppose, GDP in India in FY 2023-24 is 6,00,000 and we also assume the following: Mr. P, an Indian citizen, works in Tokyo and earns 50,000. Mr. Q, an Australian citizen, works in Mumbai and earns 30,000. Mrs. R, an Indian citizen, owns a restaurant in UK which she rents to a British family for 25,000. Mrs. S, a German citizen, owns a factory in New Delhi which she rents to an Indian firm for 60,000. Given above, GNP in India in FY 2023-24 will be: A) 5,85,000 B) 6,45,000 C) 4,80,000 D) 5,30,000
💡Correct Answer: Option A (5,85,000)
GNP = GDP + Net Factor Income from Abroad (NFIA). Factor income earned by Indian residents abroad: Mr. P (50,000) + Mrs. R (25,000) = 75,000. Factor income earned by non-residents in India: Mr. Q (30,000) + Mrs. S (60,000) = 90,000. NFIA = 75,000 - 90,000 = -15,000. Therefore, GNP = 6,00,000 + (-15,000) = 5,85,000.
Q84
EconomicsNational Income Accounting
Suppose the GDP at Market Price of a country in 2024 was 1000 crores. The values of Net factor income from abroad was 100 crores, net factor income paid to abroad was 50 crores, net indirect taxes were 100 crores and the national income was 700 crores. Calculate the total value of depreciation. A) 250 crores B) 450 crores C) 1850 crores D) 300 crores
💡Correct Answer: Option A (250 crores)
National Income is NNP_FC = 700 crores. GDP_MP = 1000 crores. NFIA = Factor income from abroad (100) - Factor income paid to abroad (50) = 50 crores. GNP_MP = GDP_MP + NFIA = 1000 + 50 = 1050 crores. GNP_FC = GNP_MP - Net Indirect Taxes = 1050 - 100 = 950 crores. Since NNP_FC = GNP_FC - Depreciation, we have 700 = 950 - Depreciation => Depreciation = 950 - 700 = 250 crores.
Q85
EconomicsMacroeconomic Identities
If Indian government is running a budget deficit and net exports are zero, then A) investment is greater than saving. B) saving is greater than investment. C) investment and saving are equal. D) None of the above.
💡Correct Answer: Option B (saving is greater than investment.)
From the macroeconomic identity: (S - I) = (G - T) + (X - M). Given budget deficit (G - T > 0) and net exports NX = (X - M) = 0, we have (S - I) = (G - T) > 0, which directly implies S > I (private saving is greater than private investment).
Q86
EconomicsTheory of the Firm & Profit Maximization
Hypothetically, a firm's profit margin and total profit are maximized at the same point when A) P - minimum ATC is the maximum B) when only P = MR = SMC C) when P = minimum ATC D) None of the above
💡Correct Answer: Option D (None of the above)
Profit margin is (P - ATC), which is maximized where ATC is minimized (or where d(P - ATC)/dq = 0), whereas total profit π = (P - ATC)*q is maximized where Marginal Revenue equals Marginal Cost (MR = MC). In general, the output that maximizes unit profit margin does NOT coincide with the output that maximizes total profit, making 'None of the above' correct.
Q87
EconomicsMonetary Policy & Banking
Match List A with List B: List - A (I) Bank Rate (II) Reverse Repo Rate (III) Statutory Liquidity Ratio (IV) Cash Reserve Ratio
List - B (1) Minimum percentage of a bank's deposits that must be maintained as reserves in liquid form with the RBI. (2) Minimum percentage of a bank's deposits that must be maintained as reserves in liquid form. (3) Rate at which the RBI borrows money from commercial banks. (4) Rate at which the RBI provides loans to commercial banks for long-term and without any collateral.
Choose the correct option: A) (I)-(3), (II)-(4), (III)-(1), (IV)-(2) B) (I)-(4), (II)-(3), (III)-(1), (IV)-(2) C) (I)-(3), (II)-(4), (III)-(2), (IV)-(1) D) (I)-(4), (II)-(3), (III)-(2), (IV)-(1)
💡Correct Answer: Option D ((I)-(4), (II)-(3), (III)-(2), (IV)-(1))
Correct matching: (I) Bank Rate is the rate at which RBI lends long-term without collateral (4); (II) Reverse Repo Rate is the rate at which RBI borrows funds from commercial banks (3); (III) Statutory Liquidity Ratio (SLR) is the percentage of NDTL maintained in liquid assets by banks themselves (2); (IV) Cash Reserve Ratio (CRR) is the percentage of deposits maintained with RBI in cash (1). Hence, (I)-(4), (II)-(3), (III)-(2), (IV)-(1) (Option D) is correct.
Q88
EconomicsForeign Exchange & International Trade
Identify which of the following statements is true? A) The flexible exchange rate system gives the government more flexibility to maintain large stocks of foreign exchange reserves. B) In the fixed exchange rate system, the government intervenes to buy and sell foreign currencies. C) In the managed floating exchange rate system, the central bank intervenes to moderate exchange rate fluctuations. D) In the fixed exchange rate system, market forces fix the exchange rate.
💡Correct Answer: Option C (In the managed floating exchange rate system, the central bank intervenes to moderate exchange rate fluctuations.)
Managed floating exchange rate system (also called a dirty float) is an international exchange rate arrangement where the currency exchange rate is primarily determined by market forces of demand and supply, but the central bank intervenes by buying or selling foreign currency to stabilize extreme short-term volatility.
Q89
EconomicsIndian Economic History & Planning
Arrange the following economic events in India in chronological order: i) Nationalization of 14 major banks ii) India's LPG reforms iii) Launch of the First Five-Year Plan iv) Formation of NITI Aayog Options: A) iii, i, ii, iv B) i, iii, ii, iv C) iii, ii, i, iv D) i, ii, iii, iv
💡Correct Answer: Option A (iii, i, ii, iv)
Chronological order of economic events: iii) Launch of the First Five-Year Plan: 1951; i) Nationalization of 14 major commercial banks: July 1969; ii) India's LPG (Liberalization, Privatization, Globalization) reforms: July 1991; iv) Formation of NITI Aayog: 1 January 2015. Thus, the sequence is iii, i, ii, iv (Option A).
Q90
EconomicsPoverty Estimation in India
Arrange the following committees related to poverty estimation in India in chronological order: i) Alagh Committee ii) Lakdawala Committee iii) Tendulkar Committee iv) Rangarajan Committee Options: A) ii, i, iii, iv B) i, iii, ii, iv C) ii, iii, i, iv D) i, ii, iii, iv
💡Correct Answer: Option D (i, ii, iii, iv)
Chronological timeline of poverty estimation committees in India: i) Y.K. Alagh Task Force (1979 - nutritional calorie norms); ii) D.T. Lakdawala Committee (constituted 1989, submitted report in 1993); iii) Suresh Tendulkar Committee (constituted 2005, submitted report in 2009); iv) C. Rangarajan Committee (constituted 2012, submitted report in 2014). Hence, i, ii, iii, iv (Option D) is correct.
Q91
EconomicsEconomic Systems
Which of the following best describes the main difference between a market economy and a planned economy? A) Both systems rely on government intervention for economic decisions. B) In a market economy, supply and demand determine production and pricing, while in a planned economy, the government makes these decisions. C) In a market economy, the government sets all prices, while in a planned economy, businesses do. D) There is no difference between the two systems.
💡Correct Answer: Option B (In a market economy, supply and demand determine production and pricing, while in a planned economy, the government makes these decisions.)
In a free market (capitalist) economy, resource allocation, production choices, and pricing are determined decentralised through the price mechanism of market supply and demand. In a command/planned (socialist) economy, a central government authority owns the means of production and determines what, how, and for whom goods are produced.
Q92
EconomicsPublic Finance & Fiscal Policy
The excess of total expenditure over total receipts, excluding debt capital receipts, is called: A) Revenue deficit B) Budgetary deficit C) Fiscal deficit D) Primary deficit
💡Correct Answer: Option C (Fiscal deficit)
Fiscal Deficit is defined as the excess of total government expenditure (revenue + capital) over total non-debt receipts (revenue receipts + non-debt capital receipts such as loan recoveries and disinvestment). It measures the total borrowing requirements of the government.
Q93
EconomicsIndian Agriculture & Green Revolution
What was the main technological innovation introduced during the Green Revolution? A) Use of green manure B) Organic farming C) Crop rotation D) High Yielding Variety (HYV) seeds
💡Correct Answer: Option D (High Yielding Variety (HYV) seeds)
The core technological cornerstone of the Green Revolution in the mid-1960s was the adoption of dwarf, semi-dwarf High Yielding Variety (HYV) seeds of wheat and rice (developed by Norman Borlaug and introduced in India under M.S. Swaminathan), accompanied by chemical fertilizers, pesticides, and assured irrigation.
Q94
EconomicsEconomic Reforms 1991
What was the main reason for introducing economic reforms in India in 1991? A) High agricultural output B) Increase in exports C) Political instability D) Balance of Payments crisis
💡Correct Answer: Option D (Balance of Payments crisis)
The immediate trigger for the 1991 Economic Reforms (LPG policy) was a severe Balance of Payments (BoP) crisis: foreign exchange reserves had dropped to barely two weeks of imports, inflation was soaring, fiscal deficits were unsustainable, and India had to pledge gold reserves to secure emergency IMF loans.
Q95
EconomicsEmployment & Unemployment
Unemployment that occurs due to a mismatch between the skills of workers and the requirements of jobs is called: A) Structural unemployment B) Frictional unemployment C) Seasonal unemployment D) Disguised unemployment
💡Correct Answer: Option A (Structural unemployment)
Structural unemployment arises from fundamental long-term shifts in an economy (such as technological advancement or industrial restructuring) creating a qualitative mismatch between the skills possessed by job seekers and the specific technical qualifications demanded by employers.
Q96
StatisticsCollection of Data
Which of the following statements is TRUE regarding the use of enumerators in collecting data through questionnaires? A) Less time consuming B) Less costly C) Less reliable D) Less chance of bias
💡Correct Answer: Option D (Less chance of bias)
In statistical data collection, trained enumerators directly guide respondents, clarify questions in person, and prevent misunderstandings, which yields standardized answers with less non-response error and lower non-sampling interpretation bias compared to unguided mail surveys.
Q97
StatisticsIndex Numbers & Purchasing Power
If the price index for the year 2024 is 105.5, and the purchasing power of money (in Rs.) of 2014 compared to 2024 is 1.11, then what is the price index for the year 2014? A) 0.01 B) 95.04 C) 117.11 D) 98.40
💡Correct Answer: Option B (95.04)
Purchasing power of money is inversely proportional to the price index: Purchasing Power = P_(2024) / P_(2014). Here 1.11 = 105.5 / P_(2014) => P_(2014) = 105.5 / 1.11 = 95.045 ≈ 95.04.
Q98
StatisticsMeasures of Skewness
For a certain frequency distribution, we calculated the following values: Mean = 62, Co-efficient of skewness = -0.6, Standard Deviation = 30 The median is equal to: A) 60 B) 66 C) 68 D) 70
💡Correct Answer: Option C (68)
Karl Pearson's coefficient of skewness based on median is Sk = 3(Mean - Median) / σ. Substituting given values: -0.6 = 3(62 - Median) / 30 => -0.6 = (62 - Median) / 10 => -6 = 62 - Median => Median = 62 + 6 = 68.
Q99
StatisticsProbability Theory
Let A, B and C be three events such that P(A ∩ B) = 1/4, P(A ∩ C) = 1/5, P(B ∩ C) = 1/5, and P(A ∩ B ∩ C) = 1/6. The probability that at least two events occur is equal to: A) 13/60 B) 19/60 C) 29/60 D) 31/60
💡Correct Answer: Option C (29/60)
The probability that at least two of the three events occur is given by: P(A ∩ B) + P(A ∩ C) + P(B ∩ C) - P(A ∩ B ∩ C) = 1/4 + 1/5 + 1/5 - 1/6 = (15 + 12 + 12 - 10)/60 = 29/60. Thus, Option C is correct.
Q100
StatisticsMeasures of Central Tendency
Given the following numbers: 1, 7, 8, 2, 4, 10, 14, 11, 37, 16, 17. The value of mean - median is: A) 11.5 B) 1.55 C) 10 D) 21.5
💡Correct Answer: Option B (1.55)
Total numbers n = 11. Sum = 1 + 7 + 8 + 2 + 4 + 10 + 14 + 11 + 37 + 16 + 17 = 127. Mean = 127 / 11 = 11.545 ≈ 11.55. Arranging in ascending order: 1, 2, 4, 7, 8, 10, 11, 14, 16, 17, 37. The median (6th element) is 10. Therefore, Mean - Median = 11.545 - 10 = 1.545 ≈ 1.55.
Q101
StatisticsLinear Functions & Demography
The life expectancy, E, of females is a linear function of time (in years). In 1995, the life expectancy was 72 years, and in 2015, it was 78 years. What would be the predicted life expectancy in the year 2025? A) 80 B) 82 C) 79 D) 81
💡Correct Answer: Option D (81)
Rate of increase = (78 - 72) / (2015 - 1995) = 6 years / 20 years = 0.3 years per calendar year. From 2015 to 2025 is 10 years. Predicted life expectancy in 2025 = 78 + (10 * 0.3) = 78 + 3 = 81 years.
Q102
StatisticsBayes' Theorem & Conditional Probability
A box contains a certain number of balls out of which 15% are red, 80% are yellow and 5% are green. All the balls of the same color are indistinguishable. Further, it is known that among all the yellow balls, x% are defective, among all the red, 6% are marked defective and among all the green balls, 9% are marked defective. A ball is chosen at random. If the conditional probability that the chosen ball is yellow, given that it is defective is 0.4, the value of x is: A) 1.12 B) 0.01 C) 0.05 D) 1.05
💡Correct Answer: Option A (1.12)
Using Bayes' Theorem: P(Yellow | Defective) = P(Yellow ∩ Defective) / P(Defective) = 0.4. P(Red ∩ Defective) = 0.15 0.06 = 0.009. P(Green ∩ Defective) = 0.05 0.09 = 0.0045. Non-yellow defective probability = 0.009 + 0.0045 = 0.0135. Let p = P(Yellow ∩ Defective) = 0.80 (x/100). Then p / (p + 0.0135) = 0.4 => p = 0.4p + 0.0054 => 0.6p = 0.0054 => p = 0.009. Since 0.80 (x/100) = 0.009 => x/100 = 0.009 / 0.80 = 0.01125 => x = 1.125% ≈ 1.12.
Q103
StatisticsTheory of Attributes
For two attributes A and B, we have the following information: N = 100; (A) = 50, (B) = 60, (AB) = 5. Which of the following is true about consistence of the data? A) Data are inconsistent B) Data are consistent C) Cannot be determined D) Both (A) and (B)
💡Correct Answer: Option A (Data are inconsistent)
For consistency of attributes, no class frequency can be negative. Consider (αβ): (αβ) = N - (A) - (B) + (AB) = 100 - 50 - 60 + 5 = -5. Since a frequency cannot be negative ((αβ) = -5 < 0), the given data is mathematically inconsistent.
Q104
StatisticsSet Theory & Probability
In a college, 75% of students passed Mathematics, and 80% of students passed English. What is the minimum percentage of students who must have passed both subjects? A) 25% B) 55% C) 20% D) 5%
💡Correct Answer: Option B (55%)
Since total percentage cannot exceed 100%: P(M ∪ E) ≤ 100%. By the inclusion-exclusion principle: P(M ∪ E) = P(M) + P(E) - P(M ∩ E) => P(M ∩ E) = P(M) + P(E) - P(M ∪ E) ≥ 75% + 80% - 100% = 155% - 100% = 55%. Thus, the minimum percentage who passed both subjects is 55%.
Q105
StatisticsCorrelation and Regression
If the line of regression of y on x is 5x - 8y + 14 = 0 then the correlation between y and x is: A) Positive B) Negative C) Zero D) Cannot be determined
💡Correct Answer: Option A (Positive)
Rewriting the regression line of y on x in slope form: 8y = 5x + 14 => y = (5/8)x + 14/8. The regression coefficient b_yx is +5/8 > 0. Since the correlation coefficient r has the exact same algebraic sign as the regression coefficients, b_yx > 0 directly implies r is Positive.
Q106
StatisticsCorrelation and Regression
If the two regression lines—one obtained by regressing y on x, and the other by regressing x on y—are 5x - 8y + 14 = 0 and 2x - 5y + 11 = 0, then x̄ + ȳ is: A) 2 B) 3 C) 5 D) 0
💡Correct Answer: Option C (5)
The two regression lines always intersect at the point of their means (x̄, ȳ). Solving the simultaneous equations: 1) 5x̄ - 8ȳ = -14, and 2) 2x̄ - 5ȳ = -11. Multiplying (1) by 2 and (2) by 5: 10x̄ - 16ȳ = -28 and 10x̄ - 25ȳ = -55. Subtracting gives 9ȳ = 27 => ȳ = 3. Substituting into (2): 2x̄ - 5(3) = -11 => 2x̄ - 15 = -11 => 2x̄ = 4 => x̄ = 2. Thus, x̄ + ȳ = 2 + 3 = 5.
Q107
StatisticsPermutations & Probability
In a random arrangement of the letters of the word 'STATISTICS', the probability that all the vowels come together is: A) 1/15 B) 3/28 C) 2/15 D) 5/28
💡Correct Answer: Option A (1/15)
Word STATISTICS has 10 letters: S(3), T(3), A(1), I(2), C(1). Total permutations = 10! / (3! 3! 2!) = 50,400. Vowels are A, I, I (3 vowels: one A, two I's). Treating the 3 vowels as 1 single block, we have 7 consonants + 1 block = 8 units. Consonants have S(3), T(3), C(1). Number of arrangements of the 8 units = 8! / (3! 3!) = 1,120. Inside the vowel block, the vowels can be arranged in 3! / 2! = 3 ways. Favorable permutations = 1,120 3 = 3,360. Probability = 3,360 / 50,400 = 1/15.
Q108
StatisticsCollection of Data
Interview is an example of which data? A) Primary B) Secondary C) Both (A) and (B) D) None of the above
💡Correct Answer: Option A (Primary)
Primary data is information collected firsthand directly from the original source for a specific research purpose. Conducting personal or structured interviews gathers original, firsthand responses, making it an example of Primary data.
Q109
StatisticsTabulation of Data
Zero should be used only to indicate the A) Quality of variable B) Non availability of data C) Quantity of variable D) All of these
💡Correct Answer: Option C (Quantity of variable)
In standard statistical tabulation rules, zero ('0') must strictly represent a null magnitude or nil quantity of a variable (i.e. zero frequency or count). Non-availability of data or missing observations should be denoted by dashes ('-') or 'N.A.', never by zero.
Q110
StatisticsQuestionnaire Design & Survey Sampling
'Do you own a vehicle? ______ Yes ______ No' is an example of what type of question? A) Loaded B) Leading C) Simple-dichotomy D) Open-ended response
💡Correct Answer: Option C (Simple-dichotomy)
A question that provides only two mutually exclusive and exhaustive response choices (such as Yes/No, True/False, Male/Female) is known in survey research methodology as a simple-dichotomy (or dichotomous) question.
Q111
StatisticsVital Statistics & Demography
Which of the following is a measure of mortality? A) Crude death rate B) Immunization rate C) Literacy rate D) Birth weight
💡Correct Answer: Option A (Crude death rate)
In vital statistics and demography, mortality refers to the incidence of death in a population. The Crude Death Rate (CDR), Infant Mortality Rate (IMR), and Age-Specific Death Rate (ASDR) are core measures of mortality.
Which is a demographic indicator of health? A) Oxygen level B) Life expectancy C) Literacy rate D) Blood group
💡Correct Answer: Option B (Life expectancy)
Life expectancy at birth (e_0) is the universally recognized demographic indicator of overall population health and socio-economic wellbeing, measuring the average number of years a newborn is expected to live under prevailing mortality rates.
Q113
StatisticsInterpolation & Numerical Methods
If x_0 = 5, x_1 = 6, x_2 = 9 and x_3 = 11, and f(x_0) = 12, f(x_1) = 13, f(x_2) = 14 and f(x_3) = 16 then the approximate value of f(10) using Lagrange's interpolation formula is: A) 15 B) 14.67 C) 16 D) 15.47
💡Correct Answer: Option B (14.67)
Applying Lagrange's interpolation formula at x = 10 with points (5,12), (6,13), (9,14), (11,16): L0(10)12 + L1(10)13 + L2(10)14 + L3(10)16 evaluates accurately to 14.67. Thus, Option B is correct.
Q114
StatisticsCombined Mean
The average height of male employees in a company is 68 inches and that of female employees is 63 inches. The average height of all the employees is 65 inches. The percentage of male employees in the company is: A) 40% B) 60% C) 50% D) 55%
💡Correct Answer: Option A (40%)
Let m be the proportion of male employees and f = (1 - m) be female employees. Combined mean: 68m + 63(1 - m) = 65 => 68m + 63 - 63m = 65 => 5m = 2 => m = 2/5 = 0.40 or 40%.
Q115
StatisticsIndex Numbers
If Laspeyres' price index is 100, Fisher's index number is 120, then Bowley's index number is: A) 122 B) 144 C) 110 D) 100
💡Correct Answer: Option A (122)
Fisher's ideal index is the geometric mean of Laspeyres and Paasche: F = √(L P) => 120 = √(100 P) => 14400 = 100 * P => Paasche's index P = 144. Bowley's index number is the arithmetic mean of Laspeyres and Paasche: B = (L + P) / 2 = (100 + 144) / 2 = 244 / 2 = 122.
Q116
StatisticsVital Statistics & Reproduction Rates
The population of a city is 12000. If the population size after 3 generations is 768000, then the net reproductive rate is: A) 3 B) 2 C) 8 D) 4
💡Correct Answer: Option D (4)
Population growth across generations is modeled by N_t = N_0 * (R_0)^t, where R_0 is the net reproductive rate and t is the number of generations. Here N_3 = 768,000, N_0 = 12,000, and t = 3. Thus: (R_0)^3 = 768,000 / 12,000 = 64 => R_0 = (64)^(1/3) = 4. Hence, the net reproductive rate is 4.
Q117
StatisticsDemography & Fertility Rates
If the gross reproductive rate is 1.08 per woman and the proportion of male births is 60%, then total fertility rate per woman is (assuming no mortality): A) 2.5 B) 2.7 C) 1.8 D) 2.2
💡Correct Answer: Option B (2.7)
GRR (Gross Reproduction Rate) counts only female births per woman: GRR = TFR (proportion of female births). If male births are 60%, female births are 100% - 60% = 40% = 0.40. Therefore, 1.08 = TFR 0.40 => TFR = 1.08 / 0.40 = 2.7 per woman.
Q118
StatisticsTests of Index Numbers
Fisher's Ideal Index Number does not satisfy: A) Unit Test B) Time Reversal Test C) Circular Test D) Factor Reversal Test
💡Correct Answer: Option C (Circular Test)
Fisher's Ideal Index Number satisfies the Time Reversal Test, the Factor Reversal Test, and the Unit Test. However, it does NOT satisfy the Circular Test (which is satisfied by simple geometric mean of price relatives and Kelly's fixed weight index).
Q119
StatisticsProperties of Correlation Coefficient
The class instructor calculated the correlation coefficient between the marks obtained by students in English and Hindi, and found it to be -0.5. Later, she realized that she had forgotten to include 1 grace mark for every student in the English scores. What will be the new correlation coefficient between the updated English marks and the Hindi marks? A) 0.5 B) -0.5 C) 0 D) 1
💡Correct Answer: Option B (-0.5)
The Pearson correlation coefficient is completely invariant to changes of origin and positive changes of scale. Adding a constant (+1 grace mark) to all scores of a variable shifts the origin equally without altering the covariance or standard deviation. Hence, the correlation coefficient remains unchanged at -0.5.
Q120
StatisticsMedian of Grouped Frequency Distribution
What is the value of x if the median wage is Rs. 4675 for the following salary distribution? Salary (in Rs.): 2000-3000 | 3000-4000 | 4000-5000 | 5000-6000 | 6000-7000 Number of Employees: 3 | 5 | x | 10 | 5 A) 8 B) 20 C) 12 D) 9
💡Correct Answer: Option C (12)
Median = 4675 lies in class 4000-5000. Lower limit L = 4000, class width h = 1000, frequency f = x. Cumulative frequency before median class c.f. = 3 + 5 = 8. Total N = 3 + 5 + x + 10 + 5 = 23 + x. Median formula: Median = L + [ (N/2 - c.f.) / f ] h. Substituting: 4675 = 4000 + [ ((23 + x)/2 - 8) / x ] 1000 => 675 = [ (7 + x) / (2x) ] 1000 => 675 = [ (7 + x) / (2x) ] 1000 => 1350x = 7000 + 1000x => 350x = 7000 => x = 7000 / 350 = 20. Exactly 20! Thus, Option B is correct.
🎯 Ready for a Timed Mock Test?
Simulate the real exam experience with a countdown timer, negative marking, and instant detailed scorecards.
About JKSSB Statistical Assistant 2025 Previous Year Paper
This page provides the full solved question paper for the JKSSB Statistical Assistant examination conducted in 2025. Every MCQ is presented with verified answer keys and detailed bilingual explanations to support concept building.
Key subjects covered in this paper include General Knowledge & Current Affairs, General Science, Computer Science & IT, Mathematics, Economics, Statistics. Practicing authentic previous year questions is the proven way to master question patterns and improve accuracy for upcoming exams across Jammu & Kashmir.
