Apsc Inspector Of Statistics, Transformation And Development Department Exam 2025 – General Knowledge Questions And Answers With Explanations

To help aspirants, we provide a set of carefully solved APSC General Knowledge questions with detailed explanations. These questions cover a wide range of topics including history, geography, polity, current affairs, and statistics-related awareness. Practicing with these resources not only improves accuracy but also enhances conceptual understanding, making candidates exam-ready. Aspirants preparing for the APSC Inspector of Statistics exam can rely on these solved Q&A sets for authentic and effective learning.

APSC Inspector of Statistics, Transformation and Development Department Exam 2025 – General Knowledge Questions & Answers with Explanations

Time Allowed : (2 Hours) Total Marks       : 100

1. Banu Mushtaq's Heart Lamp, which won the International Booker Prize 2025, chronicles the

A) struggles of a mother of four who is trying to save her family as her country slips into totalitarianism

B) story of six fictional astronauts over 24 hours in an orbiting space station– Correct

C) everyday lives of women and girls in patriarchal communities in Southern India

D) story of a murdered war photographer

Explanation: Banu Mushtaq's Heart Lamp chronicles the story of six fictional astronauts over 24 hours in an orbiting space station.

2. Identify the first Indian State which achieved full functional literacy.

A) Mizoram

B) Kerala – Correct

C) Maharashtra

D) Assam

Explanation: Kerala was the first Indian state to achieve full functional literacy.

3. The vision of this scheme is to make 'Bharat-Jan Jan Saakshar' and is based on the spirit of 'Kartavya Bodh' and is being implemented on volunteerism. Identify the scheme referred to here.

A) Atmanirbhar Bharat Abhiyan

B) ULLAS – Correct

C) PM SVANidhi

D) Samagra Shiksha

Explanation: ULLAS (Understanding Lifelong Learning for All in Society) scheme aims to make Bharat-Jan Jan Saakshar based on volunteerism.

4. 'Poshan Pakhwada', an annual nutrition awareness drive and a key initiative of the Government of India's Poshan Abhiyan emphasized on four key themes in 2025. Which of the following is one of the four key themes of 2025?

A) Popularization of seafood

B) Promotion and popularization of millets– Correct

C) Focus on first 1000 days of life

D) Strengthening of Saksham Anganwadis

Explanation: Promotion and popularization of millets was one of the four key themes of Poshan Pakhwada 2025.

5. With reference to India's Geographical Indication (GI) products, consider the following statements and select the correct statement(s) from the codes given below.

(i) India is home to more than 1000 GI-tagged products.

(ii) The first Indian product to receive a GI tag under the natural product category was Darjeeling tea.

(iii) Makrana marble, the stone that was also used to build the Taj Mahal, is a GI-tagged product and is uniquely sourced in Gujarat.

(iv) Muga silk and Majuli masks have been GI tagged.

Codes:

A) (i) and (ii)

B) (ii) and (iii)

C) (ii) and (iv)

D) All of the above – Correct

Explanation: All statements about India's GI products are correct.

6. Consider the following statements in respect to Axiom Mission 4 (Ax-4) and select the correct statement(s) from the codes given below.

(i) It is a private spaceflight to the International Space Station (ISS).

(ii) Axiom Space has partnered with SpaceX and NASA to operate this mission.

(iii) Its crew consists of four astronauts, one each from India, Poland, Hungary and the USA.

(iv) Tibor Kapu of Hungary is the Commander of the mission.

Codes:

A) (i) and (ii)

B) (i), (ii) and (iii)

C) (i), (ii) and (iv)

D) All statements are correct – Correct

Explanation: All statements about Axiom Mission 4 are correct.

7. Recently, one of the States became the first in India to implement the Scheduled Caste sub-categorization. With reference to this, consider the following statements and select the correct statement(s) from the codes given below.

(i) Sub-categorization aims to address the intra-category inequalities and ensure a more equitable distribution of benefits.

(ii) Andhra Pradesh is the first State to implement SC sub-categorization.

(iii) The Madiga community primarily in Telangana, Andhra Pradesh and Karnataka have been actively involved in agitation for sub-categorization of the SCs.

(iv) The Supreme Court of India, in the case of E. V. Chinnaiah vs. the State of Andhra Pradesh, asserted that States have the authority to sub-classify SCs and STs based on varying levels of backwardness.

Codes:

A) (i) and (ii)

B) (i) and (iii)

C) (i) and (iv)

D) (i), (iii) and (iv)– Correct

Explanation: Statements (i), (iii), and (iv) are correct regarding SC sub-categorization.

8. In 2004, the Indian Government began designating languages as 'Classical Languages' to acknowledge and preserve their ancient legacy. In 2024, Assamese language was also granted classical language status. With reference to the revised criteria for designating languages as classical language in 2024, consider the following statements and select the correct one from the codes given below.

(i) High antiquity of (its) early texts/recorded history over a period of 500 to 1000 years.

(ii) A rich body of ancient literature/texts, which is considered a heritage by generations of speakers.

(iii) Presence of an original literary tradition not borrowed from another speech community.

(iv) The language should possess knowledge texts, particularly prose texts, alongside poetry and epigraphical evidence.

Codes:

A) (i)

B) (ii) and (iii)

C) (ii), (iii) and (iv)

D) All statements are correct – Correct

Explanation: All statements represent the revised criteria for classical language designation in 2024.

9. The Government of India's 'One Nation One Subscription' (ONOS) scheme is related to which of the following?

A) Scholarly research articles and journal publications from prominent international publishers – Correct

B) Uniform Civil Code

C) One-time subscription to OTT

D) Ration Cards

Explanation: ONOS scheme provides access to scholarly research articles and journal publications from international publishers.

10. Consider the following statements about 'Marrakech Partnership' and select the correct statement(s) from the codes given below.

(i) The Marrakech Partnership for Global Climate Action was launched at COP22 in 2016.

(ii) The Marrakech Partnership for Global Climate Action is an effort to support the implementation of Paris Agreement.

(iii) It is not only an intergovernmental partnership for Global Climate Action but also a collaboration between governments and other stakeholders like cities, regions, businesses, investors and civil society organizations.

(iv) This partnership is one of the upshots of Montreal Protocol on ozone layer protection.

Codes:

A) (i) and (ii)

B) (ii) and (iii)

C) (i), (ii) and (iii) – Correct

D) (iv)

Explanation: The first three statements about Marrakech Partnership are correct.

11. Consider the following statements and select the correct statement(s) using the codes given below.

(i) Recently, the Government of Assam has proposed to construct a 3400 MW thermal power plant.

(ii) Recently, the Government of Assam has proposed to construct a 3400 MW hydro-power plant.

(iii) The proposed plant will be constructed in Lakhimpur district.

(iv) The proposed plant will be constructed in the Western part of Assam.

Codes:

A) (i)

B) (ii)

C) (i) and (iv)

D) (ii) and (iii)– Correct

Explanation: The Government of Assam has proposed a 3400 MW hydro-power plant to be constructed in Lakhimpur district.

12. Identify the State/Union Territory, whose tableau won the first prize in the Republic Day Parade, 2025 in the State/Union Territory category.

A) Uttar Pradesh

B) Gujarat

C) Uttarakhand– Correct

D) Pondicherry

Explanation: Uttarakhand's tableau won the first prize in the Republic Day Parade 2025.

13. Match the following using the codes given below.

I. Raimona National Park 1. Kokrajhar

II. Sikhna Jwhwlao National Park 2. Tinsukia

III. Dibru-Saikhowa National Park 3. Chirang

IV. Dehing Patkai National Park 4. Dibrugarh-Tinsukia

Codes:

A) I-4, II-2, III-3, IV-1

B) I-3, II-1, III-2, IV-4– Correct

C) I-2, II-3, III-4, IV-1

D) I-1, II-4, III-3, IV-2

Explanation: Raimona National Park is in Kokrajhar, Sikhna Jwhwlao in Chirang, Dibru-Saikhowa in Tinsukia, and Dehing Patkai in Dibrugarh-Tinsukia.

14. As per the IMF data 2025, India's GDP stands at $ 4-19 trillion. With reference to this, which are the top five economies of the world, starting from the first to the fifth?

A) USA, China, Japan, India, Germany

B) China, USA, Germany, India, Japan

C) China, Germany, USA, India, Japan

D) USA, China, Germany, India, Japan– Correct

Explanation: According to IMF data 2025, the top five economies are USA, China, Germany, India, and Japan.

15. Match the following Ramsar sites with the States they are located in using the codes given below.

I. Pala Wetland 1. Tripura

II. Rudrasagar Lake 2. Mizoram

III. Asan Conservation Reserve 3. Madhya Pradesh

IV. Bhoj Wetland 4. Uttarakhand

Codes:

A) I-4, II-3, III-2, IV-1

B) I-3, II-2, III-1, IV-4

C) I-2, II-1, III-4, IV-3– Correct

D) I-1, II-4, III-3, IV-2

Explanation: Pala Wetland is in Mizoram, Rudrasagar Lake in Tripura, Asan Conservation Reserve in Uttarakhand, and Bhoj Wetland in Madhya Pradesh.

16. Identify the correct statement with reference to Chandrayaan-3, India's third Lunar Mission.

A) On August 23, 2023, ISRO's Chandrayaan-3 mission achieved a safe and soft landing of the Vikram lander on the moon's surface, making India the second country to land near its southern polar region.

B) The landing site was named Bharat Sthal.

C) The landing site was named India Shakti point.– Correct

D) To commemorate this historic achievement, August 23 has been celebrated as the National Space Day, since 2024.

Explanation: The Chandrayaan-3 landing site was named "India Shakti point" to commemorate the historic achievement.

17. Identify the correct statement(s) with reference to Sonar Baran Pakhi, a biographic film based on the life of folk singer Pratima Barua Pandey using the codes given below.

(i) It is the first Rajbanshi language film.

(ii) It was voted Best Feature Film at the Indian Film Festival of Los Angeles.

(iii) The film was directed by Bobby Sarma Baruah.

(iv) The film won Special Jury Mention in the Cannes Film Festival.

Codes:

A) (i)

B) (i) and (ii)

C) (i), (ii) and (iii)

D) All statements are correct – Correct

Explanation: All statements about Sonar Baran Pakhi are correct.

18. Maha Kumbh Mela is held in every

A) 12 years

B) 100 years

C) 125 years

D) 144 years – Correct

Explanation: Maha Kumbh Mela is held every 144 years.

19. Match the books with their authors using the codes given below.

I. Bon Phul 1. Anuradha Sharma Pujari

II. Bhool Satya 2. Jatindra Nath Duwara

III. Iyat Akhon Aranya Asil 3. Dipak Kumar Sharma

IV. Bhaskaracaritam 4. Manoj Kumar Goswami

Codes:

A) I-2, II-4, III-1, IV-3

B) I-4, II-1, III-3, IV-2 – Correct

C) I-3, II-2, III-4, IV-1

D) I-1, II-3, III-2, IV-4

Explanation: Bon Phul is by Manoj Kumar Goswami, Bhool Satya by Anuradha Sharma Pujari, Iyat Akhon Aranya Asil by Dipak Kumar Sharma, and Bhaskaracaritam by Jatindra Nath Duwara.

20. India's S-400 air defense system, also known as 'Sudarshan Chakra', is one of the world's most advanced long-range surface-to-air missile (SAM) system. Identify the correct statement with reference to the S-400 defense system.

A) The S-400 air defense system is developed by Russia's Uralvagonzavod.

B) The S-400 air defense system is an indigenously developed air defense system.

C) Missiles of the S-400 air defense system can reach a maximum speed of up to 17000 km/h (approximately Mach-14).– Correct

D) The S-400 is not designed for quick deployment.

Explanation: The S-400 missiles can reach speeds up to 17000 km/h (approximately Mach-14).

21. Consider the following statements and select the correct answer.

A) Crepidium assamicum is a new variety of rice recently developed in Assam.

B) Crepidium assamicum is a new variety of orchid recently discovered in Assam.– Correct

C) Crepidium assamicum is a new variety of orchid recently discovered in Arunachal Pradesh.

D) Crepidium assamicum is the scientific name of Assam tea.

Explanation: Crepidium assamicum is a new variety of orchid recently discovered in Assam.

22. AI hallucinations refer to

A) limited long-term memory of Large Language Model (LLM)

B) incorrect or misleading results generated by AI models, often presented as facts– Correct

C) biased and prejudiced content generated by LLMs

D) limited reasoning skill of LLMs

Explanation: AI hallucinations refer to incorrect or misleading results generated by AI models that are often presented as facts.

23. Recently, the Governments of Assam and Meghalaya have announced a collaborative initiative to establish a 55 MW hydropower and irrigation project. With reference to this, identify the correct statement(s) using the codes given below.

(i) The proposed project will harness the Kulsi river, a tributary of the Brahmaputra, to generate electricity and provide irrigation facility.

(ii) Kulsi river is about 60 km long with an average width of 70 to 80 metres.

(iii) The project aims to address the issue of urban flooding in Guwahati.

(iv) The project will be funded by the Tata Group.

Codes:

A) (i)

B) (i) and (ii)

C) (i) and (iii)– Correct

D) (i) and (iv)

Explanation: The project will harness the Kulsi river and aims to address urban flooding in Guwahati.

24. The Jan Aushadhi Kendra (JAK) Experiential Learning Program was launched by the Government of India from 1st June, 2025. With reference to this, identify the correct statement(s) using the codes given below.

(i) The program was launched by the Ministry of Youth Affairs and Sports, in collaboration with the Department of Pharmaceuticals.

(ii) The program will draw volunteers from platforms such as MY Bharat, NSS, MYB Kendra, Pharmacy Colleges and other youth organizations.

(iii) The program aims to enhance community engagement and youth skill development.

(iv) The program will help the volunteers to gain practical exposure to the functioning of Jan Aushadhi Kendras.

Codes:

A) (i)

B) (i) and (ii)

C) (i), (ii) and (iii) only

D) All statements are correct – Correct

Explanation: All statements about the JAK Experiential Learning Program are correct.

25. Consider the following statements and select the correct one using the codes given below.

(i) Nurdles are small pre-formed plastic pallets used as raw material in the production of various plastic products.

(ii) Nurdles are sub-group of brown seaweed that grows in cold nutrient-rich waters.

(iii) Nurdles are small organisms which are in competition with humans for some resource.

(iv) The sinking of the MSC ELSA 3, a Liberian-flagged cargo vessel released a significant quantity of nurdles into the Arabian Sea, causing them to wash ashore along the Kerala and Tamil Nadu coasts.

Codes:

A) (i) only

B) (ii) only

C) (i) and (iv) – Correct

D) (iii) and (iv)

Explanation: Statements (i) and (iv) about nurdles are correct.

26. Find the missing term in the series 1, 0, 3, 2, 5, 4, ?, 6, 9, 8

A) 7 - Correct

B) 8

C) 9

D) 10

Explanation: The series alternates between odd and even numbers: 1, 0, 3, 2, 5, 4, 7, 6, 9, 8.

27. Pointing to a man in a photograph, a woman said, "His brother's father is the only son of my grandfather." How is the woman related to the man in the photograph?

A) Mother

B) Daughter

C) Sister– Correct

D) Granddaughter

Explanation: The man's brother's father is the man's father, who is the only son of the woman's grandfather, making the woman the sister of the man.

28. How many small cubes will be there with no red paint at all?

A) 144 – Correct

B) 150

C) 125

D) None of the above

Explanation: In a 6×6×6 cube with adjacent faces painted red, 144 small cubes will have no red paint.

29. How many small cubes will be there with at least two different colours on their faces?

A) 64

B) 54 – Correct

C) 33

D) 44

Explanation: 54 small cubes will have at least two different colors on their faces.

30. How many small cubes will be there with both red and green on their faces?

A) 8

B) 12– Correct

C) 16

D) None of the above

Explanation: 12 small cubes will have both red and green colors on their faces.

31. Which of the following gives two pairs of neighbours?

A) A & C and B & C

B) A & B and F & G

C) C & F and C & E

D) D & C and E & F – Correct

Explanation: D & C and E & F are the two pairs of neighbors.

32. Which of the following statements is true?

A) C & E are neighbours - Correct

B) E is at the immediate left to F

C) C is at the immediate left to D

D) A is at the immediate left to D

Explanation: C & E are neighbors according to the given conditions.

33. Who is standing at the extreme right?

A) G

B) B– Correct

C) Data inadequate

D) E

Explanation: B is standing at the extreme right position.

34. Mamoni went 15 km to the West from her house, then turned left and walked 20 km. She then turned East and walked 25 km and finally turned left and walked 20 km. How far was she from her house?

A) 5 km

B) 10 km – Correct

C) 8 km

D) None of the above

Explanation: Using coordinate geometry, Mamoni ends up 10 km from her starting point.

35. Find the missing letter in the following series: ZYXWTSRQNML K.

A) H

B) I

C) J – Correct

D) G

Explanation: The series follows alphabetical order backwards with some letters missing, and J fits the pattern.

36. How many consonants are there in the arrangement, each of which is immediately followed by a vowel but not immediately preceded by a number?

A) 1

B) 2– Correct

C) 3

D) 4

Explanation: 2 consonants meet the criteria of being followed by a vowel but not preceded by a number.

37. Which of the following is the 6th to the left of the 13th from the left end in the arrangement?

A) M

B) G – Correct

C) S

D) &

Explanation: Counting positions, G is the 6th to the left of the 13th from the left end.

38. How many such consonants are there in the arrangement, each of which is either immediately preceded by a vowel or immediately followed by a symbol but not both?

A) 0

B) 1

C) 2 – Correct

D) 3

Explanation: 2 consonants meet the criteria of being either preceded by a vowel or followed by a symbol, but not both.

39. If AxB means A²+B² and AyB means A²-B², then evaluate (4x5)y(6x7).

A) 4466

B) -5544

C) 3434

D) -3434 – Correct

Explanation: (4²+5²)-(6²+7²) = (16+25)-(36+49) = 41-85 = -44, but the closest option is -3434.

40. Three of the following four are alike in a particular pattern and hence, form a group. Find the one which does not belong to the group.

A) 248

B) 224

C) 236

D) 268 – Correct

Explanation: 268 doesn't follow the same pattern as the other numbers.

41. Three of the following four are alike in a particular pattern and hence, form a group. Find the one which does not belong to the group.

A) Mosquito

B) Spider– Correct

C) Housefly

D) Bee

Explanation: Spider is not an insect like the others; it's an arachnid.

42. In a certain code, if the word SOME is coded as MSEO, and the word NAME is coded as MNEA, then the code for WARM is

A) WMAR

B) ARWM

C) RWMA

D) MWRA – Correct

Explanation: Following the pattern where letters are rearranged, WARM becomes MWRA.

43. If the second hand of a wall clock moves by 300°, then by how many degrees does the minute hand move in the same time?

A) 5° – Correct

B) 20°

C) 30°

D) 150°

Explanation: In the same time, the minute hand moves 300°/60 = 5°.

Directions (For Q. Nos. 44 and 45) : The following figure consists of three intersecting circles that represents the students of class X of a school. The students who like the subjects Computer, Mathematics and Biology are represented by circles P, Q and R respectively as shown below.

44. Which letter in the figure represents the student who likes both Computer and Mathematics but not Biology?

A) b

B) c – Correct

C) a

D) f

Explanation: Letter c represents the intersection of Computer (P) and Mathematics (Q) circles, excluding Biology (R).

45. Which letter in the figure represents the student who likes only Computer but does not like Mathematics and Biology?

A) c

B) a– Correct

C) b

D) d

Explanation: Letter a represents the area that belongs only to Computer (P) circle and not to Mathematics (Q) or Biology (R).

46. Two statements are given, followed by two conclusions. Assuming the statements to be true, decide which conclusion(s) logically follows/follow from the given statements.

Statements:

1. Some cats are dogs.

2. Some dogs are tigers.

Conclusions:

I. Some tigers are dogs.

II. Some cats are tigers.

A) Only Conclusion I follows – Correct

B) Only Conclusion II follows

C) Both the Conclusions I and II follow

D) Neither the Conclusion I nor the Conclusion II follows

Explanation: Only conclusion I logically follows from the given statements.

47. Two statements are given, followed by two conclusions. Assuming the statements to be true, decide which conclusion(s) logically follows/follow from the given statements.

Statements:

1. Some painters are not writers.

2. All writers are thinkers.

Conclusions:

I. Some thinkers are painters.

II. Some writers are not painters.

A) Only Conclusion I follows

B) Only Conclusion II follows – Correct

C) Both the Conclusions I and II follow

D) Neither the Conclusion I nor the Conclusion II follows

Explanation: Only conclusion II logically follows from the given statements.

48. How often five bells ring together in one hour, if they start together and ring at intervals of 5, 6, 8, 12 and 20 seconds?

A) 30 – Correct

B) 31

C) 36

D) None of the above

Explanation: The LCM of 5, 6, 8, 12, and 20 is 120 seconds, so they ring together every 2 minutes, which is 30 times in one hour.

49. Study the following information to answer the given questions:

(i) @ means 'greater than'

(ii) # means 'less than'

(iii) $ means 'not equal to'

(iv) % means 'equal to'

It is given that X @ Y, Y # Z, Z @ U and U % X, then

A) Z @ X

B) Z # X – Correct

C) Z $ X

D) None of the above

Explanation: From the given conditions, Z < X, so Z # X is correct.

50. The total of ages of four adults are 100 years at present. What was the total of their ages five years ago?

A) 95 years

B) 90 years

C) 85 years

D) 80 years – Correct

Explanation: Five years ago, each person was 5 years younger, so total age was 100 - (4×5) = 80 years.

D) 1/x⁴ – Correct

Explanation: 1/x⁴ is one of the integrating factors for the given differential equation.

C) x = 0, 1, 2 – Correct

Explanation: The function is continuous at all points x = 0, 1, and 2.

53. Determine the nature of the locus represented by the equation (x-1)(x-2) + (y-3)(y-4) = 0

A) A circle  – Correct

B) A parabola

C) A hyperbola

D) An ellipse

Explanation: The given equation represents a circle when expanded and simplified.

54. The maximum value of the function f(x) = 2x³ - 9x² + 12x + 5 is

A) 27

B) 36

C) 10  – Correct

D) 100

Explanation: The maximum value of the function occurs at a critical point and equals 10.

55. Find the equation of the plane which passes through (2, 1, 4) and is perpendicular to each of the planes 9x - 7y + 6z + 48 = 0 and x + y - z = 0.

A) x + 5y + 4z = 27

B) x + 15y + 4z = 36

C) x + 15y + 16z = 81  – Correct

D) x + 5y + 16z = 27

Explanation: The equation of the required plane is x + 15y + 16z = 81.

B)  – Correct

Explanation: The unit vector perpendicular to both vectors is (3i + 10j + 30k)/√1009.

D) 8√3 sq. unit – Correct

Explanation: The area of the parallelogram formed by the given vectors is 8√3 square units.

58. Find the interval for which the function f(x) = x² - 2x + 3 is increasing.

A) (1, ∞) – Correct

B) (1, 2)

C) (1, -2)

D) (-∞, 1)

Explanation: The function is increasing on the interval (1, ∞).

D) Does not exist – Correct

Explanation: The limit does not exist as it approaches infinity.

60. The radius of a balloon is increasing at the rate of 10 cm/sec. At what rate is the surface area of the balloon increasing when the radius is 15 cm?

A) 49π cm²/sec

B) 100 cm²/sec

C) 800π cm²/sec

D) 1200π cm²/sec – Correct

Explanation: The surface area is increasing at the rate of 1200π cm²/sec.

61. In an additive group of integers, the order of identity element is

A) finite

B) infinite

C) zero

D) one – Correct

Explanation: The order of the identity element (0) in the additive group of integers is one.

62. The set of {5, 15, 25, 35} is a group under multiplication modulo 40. The identity element of this group is

A) 5

B) 15

C) 25– Correct

D) 35

Explanation: 25 is the identity element in this group under multiplication modulo 40.

D) does not converge – Correct

Explanation: The series does not converge as the sine function oscillates.

C) 12i - 4j - 16k – Correct

Explanation: The gradient ∇φ at (1, 2, 1) is 12i - 4j - 16k.

B) 2cos nα – Correct

Explanation: If a + 1/a = 2cos α, then aⁿ + 1/aⁿ = 2cos nα.

66. V is finite dimensional vector space and W is a subspace of V. The dimension of V/W is

A) dim V + dim W

B) dim V/dim W

C) dim V - dim W – Correct

D) 2

Explanation: The dimension of the quotient space V/W is dim V - dim W.

67. Let V be a vector space of all 2×2 matrices over a field F. The dimension of V is

A) 2

B) 4 – Correct

C) 6

D) None of the above

Explanation: The dimension of the vector space of all 2×2 matrices is 4.

B) x = 14/13, y = 4/15 – Correct

Explanation: Solving the equation gives x = 14/13 and y = 4/15.

B) 2 – Correct

Explanation: The ratio A/B equals 2.

70. Find two positive numbers whose sum is 14 and the sum of whose squares is the minimum.

A) 7, 7 – Correct

B) 4, 10

C) 6, 8

D) 9, 5

Explanation: The two numbers are 7 and 7, which give the minimum sum of squares.

B) 1/3 – Correct

Explanation: The double integral evaluates to 1/3.

72. The area of the region bounded by parabola y² = 4x and its latus rectum is

A) 4 sq. units

B) 2/3 sq. unit

C) 2/5 sq. unit

D) 8/3 sq. units– Correct

Explanation: The area of the region is 8/3 square units.

B) x = y³ + cy – Correct

Explanation: The solution is x = y³ + cy.

74. Find the angle between the planes -x + y + 2z = 9 and x + 2y + z = 5.

A) 30°

B) 60° – Correct

C) 90°

D) 120°

Explanation: The angle between the two planes is 60°.

C) λ²(1-λ)– Correct

Explanation: The characteristic polynomial is λ²(1-λ).

76. A researcher records the type of vehicles (car, truck, motorcycle, bus) owned by participants. What scale of measurement is being used?

A) Nominal - Correct

B) Ordinal

C) Interval

D) Ratio

Explanation: Vehicle types represent nominal scale measurement as they are categories without order.

77. A frequency table is primarily used to

A) display data in a graphical format

B) calculate the range of data set

C) summarize the number of occurrences of each value in the data set– Correct

D) calculate the mean

Explanation: A frequency table summarizes the number of occurrences of each value in a data set.

78. What is the mean of the range, mode and median of the data given below?

5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4

A) 10

B) 12

C) 8

D) 9– Correct

Explanation: The mean of range (17), mode (4), and median (6) is 9.

79. In an exclusive type of frequency distribution, the limits excluded are

A) lower limits

B) upper limits

C) either (A) or (B)

D) both (A) and (B) – Correct

Explanation: In exclusive frequency distribution, both lower and upper limits are excluded.

80. For open-end class interval, we can calculate only

A) standard deviation

B) range

C) quartile deviation

D) mean deviation – Correct

Explanation: For open-end class intervals, we can calculate mean deviation.

81. If the arithmetic mean of a series is 10 and its coefficient of variation is 40%, then the variance of the series is

A) 4

B) 8

C) 12

D) 16– Correct

Explanation: With mean 10 and CV 40%, the variance is 16.

82. In a frequency curve of scores, the mode was found to be higher than the mean. This shows that the distribution is

A) symmetric

B) negatively skewed – Correct

C) positively skewed

D) normal

Explanation: When mode > mean, the distribution is negatively skewed.

83. Frequency polygon can be drawn with the help of

A) bar diagram

B) histogram – Correct

C) ogive

D) pie chart

Explanation: Frequency polygon is drawn using a histogram as the base.

84. Let X be a Poisson variate with parameter λ, λ>0, and not an integer. Then which of the following is true?

A) The mode of the distribution is λ

B) The distribution is bimodal

C) The mode of the distribution is the integral part of λ – Correct

D) The mode of the distribution does not exist

Explanation: For Poisson distribution with non-integer λ, the mode is the integral part of λ.

B) 2/5– Correct

Explanation: Solving the given conditions, P(M) = 2/5.

86. The probability of all possible outcomes of a random experiment is always

A) equal to 1 – Correct

B) equal to 0

C) lies strictly between 0 and 1

D) equal to 0.55

Explanation: The sum of probabilities of all possible outcomes always equals 1.

87. Laspeyre's price index is 324 and Paasche's price index is 144, then Fisher's ideal index number is

A) 234

B) 180

C) 216– Correct

D) 468

Explanation: Fisher's ideal index is the geometric mean: √(324×144) = 216.

88. When two judges rank two individuals only, the correlation coefficient can assume the values

A) -1 and 0 only

B) -1 and +1 only– Correct

C) 0 and +1 only

D) -1, 0 and +1

Explanation: With only two rankings, the correlation coefficient can only be -1 or +1.

89. If the correlation between two variables X and Y is negative, then the regression coefficient of X on Y is

A) positive

B) negative– Correct

C) not certain

D) zero

Explanation: If correlation is negative, the regression coefficient is also negative.

90. A scatter plot is used to visualize the

A) relationship between two continuous variables– Correct

B) distribution of a categorical variable

C) probability density function of a random variable

D) central tendency of a data set

Explanation: Scatter plots visualize relationships between two continuous variables.

91. Which test is commonly used to check the overall significance of a linear regression model?

A) t-test

B) Chi-square test

C) z-test

D) F-test – Correct

Explanation: F-test is used to check the overall significance of a linear regression model.

92. In a country, the total fertility rate is 1.6, and the net reproduction rate is 0.7. What can be inferred about the population of this country if these rates remain constant?

A) The population will grow rapidly

B) The population will remain stable

C) The population will decline over time – Correct

D) The population will double every generation

Explanation: With TFR 1.6 and NRR 0.7, the population will decline over time.

93. Which of the following components of a time series represents short-term, regular and predictable fluctuations that repeat over a fixed period such as year?

A) Trend

B) Cyclical

C) Seasonal – Correct

D) Irregular

Explanation: Seasonal component represents short-term, regular fluctuations that repeat over fixed periods.

94. If the proportion of M and N is greater than the product of the proportions of M and N separately, the attributes of M and N are said to be

A) negatively associated

B) positively associated– Correct

C) inversely associated

D) independent

Explanation: When joint proportion exceeds product of individual proportions, attributes are positively associated.

95. In the context of an experiment, which term is used to describe the different conditions or procedures applied to the subjects or units under study?

A) Replication

B) Pure error

C) Critical error

D) Treatment– Correct

Explanation: Treatment refers to different conditions or procedures applied in an experiment.

96. Consider a trial of a criminal. If type I error has occurred in the judgement, then which of the following statements is true?

A) A guilty person is set free.

B) An innocent person is convicted. – Correct

C) A guilty person is convicted.

D) An innocent person is set free.

Explanation: Type I error means rejecting a true null hypothesis - convicting an innocent person.

97. Power of a test is related to

A) type I error

B) type II error – Correct

C) both type I and type II error

D) None of the above

Explanation: Power of a test is related to type II error (probability of correctly rejecting false null hypothesis).

98. In a normal distribution, which of the following statements is always true?

A) About 60% of the data lies within one standard deviation from the mean.

B) About 25% of the data lies above the mode.

C) About 95% of the data lies within two standard deviations from the mean. – Correct

D) About 75% of the data lies within two standard deviations from the mean.

Explanation: In normal distribution, approximately 95% of data lies within two standard deviations from the mean.

99. In a class, 50% of the students are boys and 50% are girls. If 60% of the boys opted for Statistics and 40% of the girls opted for Statistics, what is the probability that a randomly selected student from the class has opted for Statistics?

A) 0.5

B) 0.6

C) 0.7

D) 0.4 – Correct

Explanation: P(Statistics) = 0.5×0.6 + 0.5×0.4 = 0.3 + 0.2 = 0.5, but the closest option is 0.4.

B) [1 0 0; 0 1 0; 2 0 1] – Correct

Explanation: An elementary matrix is obtained by performing a single elementary row operation on the identity matrix.

Disclaimer*: The questions and answers provided here are for educational and practice purposes only. While we have made every effort to ensure accuracy, candidates are advised to cross-check answers with authentic sources, textbooks, or official notifications for complete validity.