Free mock test · APPSC Paper I
APPSC ASO Paper II Mock 1 with answers
- 150 questions
- 150 minutes
- +1 right · −0.33 wrong
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Topics in this test (10)
Questions and answers
- Q1 Economic Concepts
Consider the following statements about arc elasticity of demand:
1. It measures elasticity between two points on a demand curve and is suited to large changes in price.
2. When the averages of the old and new prices and quantities are used as the base, it gives the same value whether price rises or falls.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Arc elasticity is the average elasticity over a segment of the curve, used for discrete or large price changes. Using mid-point bases makes the formula symmetric, so the direction of the change does not matter.
Source: Telugu Akademi B.A. Economics, Micro Economics (Elasticity of Demand); Ahuja, Advanced Economic Theory
- Q2 Economic Concepts
Consider the following statements about the kinked demand curve model of oligopoly:
1. It assumes that rivals follow a price cut but do not follow a price rise.
2. The marginal revenue curve has a discontinuous (vertical) gap at the kink.
3. It explains how the initial price at the kink is determined.
Which of the statements given above is/are correct?
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Answer C. 1 and 2 only
Demand is elastic above the kink (rivals do not follow a rise) and inelastic below it (rivals match a cut), giving a gap in MR. MC can shift within the gap without changing price, explaining price rigidity. The model does not explain how the kink price is reached.
Source: Koutsoyiannis, Modern Microeconomics; Telugu Akademi B.A. Economics, Market Structures and Price Determination
- Q3 Economic Concepts
Consider the following statements:
1. Hicks and Hansen criticised the classical, loanable funds and Keynesian theories of interest as indeterminate.
2. The criticism arises because saving (and liquidity preference) depend on the level of income, which itself depends on the rate of interest.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Hicks and Hansen showed that none of these theories can fix the interest rate unless income is known, while income depends on the rate of interest; the IS-LM model resolves this by determining both together.
Source: Jhingan, Macro Economic Theory (Theories of Interest)
- Q4 Economic Concepts
Consider the following statements:
I. Real GDP values the output of a year at constant (base-year) prices.
II. GDP deflator is the ratio of real GDP to nominal GDP.
III. A GDP deflator of 150 means the price level is 50% higher than in the base year.
Which of the statements given above is/are correct?
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Answer D. I and III only
I and III are correct. The GDP deflator is nominal GDP divided by real GDP, not the other way round.
Source: NCERT Class 12 Introductory Macroeconomics ch.2 (p.39); PW Indian Economy (ref) ch.2 (p.20)
- Q5 Economic Concepts
Consider the following statements about the CPI (Combined) series with base year 2012:
I. Food and beverages carry the largest weight.
II. Housing carries a larger weight than the miscellaneous group.
III. Fuel and light carry a weight of less than 10%.
Which of the statements given above is/are correct?
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Answer C. I and III only
I and III are correct. Housing (about 10%) carries much less weight than the miscellaneous group (about 28%).
Source: PW Indian Economy, ch.2 National Income Accounting (CPI, WPI, PPI, IIP) (Components of CPI)
- Q6 Economic Concepts
Which of the following taxes were NOT subsumed in GST?
I. Basic Customs Duty
II. Stamp duty
III. Entry tax (all forms)
IV. Electricity duty
Select the correct answer using the codes given below.
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Answer B. I, II and IV only
Basic Customs Duty, stamp duty and electricity duty remain outside GST. Entry tax in all forms was subsumed in GST.
Source: Indian Economy reference ch.5 (Government Budgeting and Fiscal Policy) (p.57-58); NCERT Class 12 Introductory Macroeconomics ch.5 (p.93)
- Q7 Economic Concepts
Consider the following statements about the budget line of a consumer buying goods X and Y:
1. Its slope equals −Px/Py.
2. A rise in money income, with prices unchanged, shifts it outward parallel to itself.
3. A fall in the price of X alone makes it pivot outward along the X-axis, with its Y-intercept unchanged.
4. Doubling both prices and money income shifts it outward.
Which of the statements given above are correct?
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Answer D. 1, 2 and 3 only
The budget line PxX + PyY = M has slope −Px/Py and intercepts M/Px and M/Py. A higher M with fixed prices gives a parallel outward shift; a lower Px raises only M/Px. Doubling M, Px and Py leaves both intercepts unchanged, so the line does not move.
Source: Telugu Akademi B.A. Economics, Micro Economics (Theory of Consumer Behaviour); Koutsoyiannis, Modern Microeconomics
- Q8 Economic Concepts
A monopolist faces the demand curve P = 100 − Q and has a constant marginal and average cost of ₹20. What is its maximum profit?
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Answer C. ₹1,600
Profit is maximised where MR = MC: 100 − 2Q = 20, so Q = 40 and P = 100 − 40 = 60. Profit = (P − AC) × Q = 40 × 40 = ₹1,600.
Source: Standard method; answer and every option computed and checked in Python
- Q9 Economic Concepts
Under perfect competition, the marginal physical product of the last worker hired is 6 units and the product sells at ₹25 per unit. According to the marginal productivity theory, the wage paid to each worker is:
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Answer D. ₹150
Wage = VMP = MPP × price = 6 × 25 = ₹150.
Source: Standard method; answer and every option computed and checked in Python
- Q10 Economic Concepts
From the following (₹ crore), find domestic income (NDP at factor cost) by the income method: compensation of employees 4,200; rent 600; interest 500; profits 1,300; mixed income of the self-employed 900; old-age pensions paid by government 250; sale of a second-hand car 80.
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Answer A. ₹7,500 crore
Only factor incomes count: 4,200 + 600 + 500 + 1,300 + 900 = 7,500. Pensions are transfers; a second-hand sale is not current production.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q11 Economic Concepts
Consider the following statements about the Liquidity Adjustment Facility (LAF) corridor:
I. The SDF rate is the floor of the LAF corridor.
II. The MSF rate is the ceiling of the LAF corridor.
III. After April 2022 the fixed-rate reverse repo continued to be the floor of the corridor.
Which of the statements given above is/are correct?
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Answer B. I and II only
I and II are correct. From April 2022 the SDF rate replaced the fixed-rate reverse repo as the floor.
Source: PW Indian Economy, ch.4 Monetary Policy and Inflation (LAF corridor)
- Q12 Economic Concepts
Consider the following statements about taxes in India:
I. Personal income tax is progressive: the tax rate rises as income rises.
II. Excise duties are levied on goods produced within the country, while customs duties are levied on goods imported into or exported out of India.
Which of the statements given above is/are correct?
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Answer C. Both I and II
Both statements are correct. Personal income tax is progressive, and excise duty falls on domestic production while customs duty falls on imports and exports.
Source: NCERT Class 12 Introductory Macroeconomics ch.5 (p.78)
- Q13 Economic Concepts
A consumer is willing to pay ₹50, ₹40, ₹30, ₹20 and ₹10 for the 1st, 2nd, 3rd, 4th and 5th units of a good. If the market price is ₹20 per unit, what is the Marshallian consumer's surplus?
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Answer B. ₹60
At ₹20 the consumer buys 4 units (willingness to pay ≥ price). Consumer's surplus = total willingness to pay − actual payment = 140 − 80 = ₹60, i.e. 30 + 20 + 10 + 0.
Source: Marshall's consumer's surplus; answer and every option computed and checked in Python
- Q14 Economic Concepts
At a certain output the average revenue of a firm is ₹60 and the price elasticity of demand is 3. What is the marginal revenue?
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Answer A. ₹40
The relation between AR, MR and elasticity is MR = AR × (e − 1)/e = 60 × 2/3 = ₹40.
Source: Standard method; answer and every option computed and checked in Python
- Q15 Economic Concepts
According to J.B. Clark's dynamic theory of profit, which of the following are dynamic changes that give rise to profit?
1. Increase in population
2. Increase in capital
3. Improvement in methods of production
4. Multiplication of consumers' wants
Select the correct answer using the code given below:
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Answer D. 1, 2, 3 and 4
Clark listed five dynamic changes: growth of population, growth of capital, improved methods of production, changes in the forms of industrial organisation and multiplication of consumers' wants. In a static economy profit disappears.
Source: Jhingan, Micro Economic Theory (Theories of Profit)
- Q16 Economic Concepts
Consider the following statements:
I. Gross value added of a firm is the value of its output minus the value of intermediate goods used.
II. Net value added is gross value added plus depreciation.
III. GDP is the sum of gross value added of all producing units in the economy.
Which of the statements given above is/are correct?
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Answer C. I and III only
I and III are correct. Net value added is gross value added minus (not plus) depreciation.
Source: NCERT Class 12 Introductory Macroeconomics ch.2 (p.30)
- Q17 Economic Concepts
Match the measures of money supply with their components:
List I
a. M1
b. M2
c. M3
d. M4
List II
I. M1 + net time deposits of commercial banks
II. M3 + total post office deposits (excluding NSCs)
III. Currency with the public + demand deposits + other deposits with RBI
IV. M1 + savings deposits with post office savings banks
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Answer D. a-III, b-IV, c-I, d-II
M1 = currency with the public + demand deposits + other deposits with RBI; M2 = M1 + post office savings deposits; M3 = M1 + net time deposits of banks; M4 = M3 + total post office deposits excluding NSCs.
Source: NCERT Class 12 Introductory Macroeconomics ch.3 Money and Banking (p.58); PW Indian Economy, ch.3 Money and Banking
- Q18 Economic Concepts
Consider the following statements:
I. Tax evasion is the illegal non-payment of tax by concealing or misreporting income.
II. Tax avoidance is the legal use of exemptions and loopholes in the law to reduce tax liability.
Which of the statements given above is/are correct?
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Answer C. Both I and II
Both statements are correct. Evasion is illegal and punishable; avoidance is legal, though anti-avoidance rules such as GAAR target aggressive cases.
Source: Indian Economy reference ch.5 (Government Budgeting and Fiscal Policy) (p.59)
- Q19 Economic Concepts
The demand function for a good is Q = 100 − 4P. What is the (numerical) point price elasticity of demand at P = 10?
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Answer B. 0.67
At P = 10, Q = 60. Point elasticity = (dQ/dP) × (P/Q) = 4 × 10/60 = 0.67.
Source: Standard method; answer and every option computed and checked in Python
- Q20 International Economics
India imports 50 units of a machine, each valued at ₹3,000. The compound duty is ₹200 per unit plus 10% ad valorem. What is the total duty payable?
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Answer D. ₹25,000
Specific part = 50 × ₹200 = ₹10,000. Ad valorem part = 10% of (50 × ₹3,000 = ₹1,50,000) = ₹15,000. Compound duty = ₹10,000 + ₹15,000 = ₹25,000.
Source: Standard method; answer and every option computed and checked in Python
- Q21 International Economics
Consider the following statements:
I. Devaluation is a reduction in the value of a currency by government action under a fixed exchange rate system.
II. Depreciation is a fall in the value of a currency caused by market forces under a flexible exchange rate system.
III. Revaluation makes the domestic currency cheaper for foreigners.
Which of the statements given above is/are correct?
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Answer C. I and II only
Statements I and II are correct. Revaluation makes the domestic currency costlier, not cheaper.
Source: NCERT Class 12 Introductory Macroeconomics ch.6 (Open Economy)
- Q22 International Economics
Which of the following pairs of report and publishing institution is NOT correctly matched?
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Answer C. Global Economic Prospects : IMF
The World Economic Outlook and the Global Financial Stability Report are IMF flagships; the World Development Report and Global Economic Prospects are World Bank publications.
Source: IMF and World Bank publication pages (imf.org, worldbank.org)
- Q23 International Economics
Match List I (economist) with List II (contribution):
List I:
A. Ragnar Nurkse
B. W. Arthur Lewis
C. Robert Solow
D. T.W. Schultz
List II:
1. Human capital
2. Vicious circle of poverty
3. Development with unlimited supplies of labour
4. Neoclassical growth model
Select the correct answer using the code given below.
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Answer D. A-2, B-3, C-4, D-1
Nurkse (1953) explained low capital formation by the vicious circle of poverty; Lewis (1954) the dual economy with unlimited labour; Solow (1956) the neoclassical model; Schultz (1961) human capital.
Source: M.L. Jhingan, The Economics of Development and Planning
- Q24 International Economics
If the import volume index is 130 and the export volume index is 104 (base = 100), the gross barter terms of trade (Taussig) are
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Answer D. 125
Gross barter terms of trade = (Qm / Qx) × 100 = (130 / 104) × 100 = 125.
Source: Standard method; answer and every option computed and checked in Python
- Q25 International Economics
Assertion (A): The SDR is a currency used by member countries to pay for goods in international markets.
Reason (R): The SDR is an international reserve asset created by the IMF to supplement member countries' official reserves.
Choose the correct answer using the codes below.
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Answer D. A is false, but R is true
A is false and R is true. The SDR is not a currency for buying goods; it is a reserve asset (a book-keeping entry) that can be exchanged among official holders for usable currencies.
Source: PW Indian Economy, BoP & Foreign Exchange chapter
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Start free - Q26 International Economics
Consider the following statements about the New Development Bank (NDB):
1. The agreement to set up the NDB was signed at the BRICS summit held at Fortaleza, Brazil, in 2014.
2. The five founding members hold equal shares in the NDB's initial subscribed capital.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
The NDB agreement was signed at the 6th BRICS summit in Fortaleza (July 2014); the bank is headquartered in Shanghai and its first president was India's K.V. Kamath. Brazil, Russia, India, China and South Africa each subscribed an equal share (US$10 billion each of the initial US$50 billion).
Source: New Development Bank, 'About us' (ndb.int)
- Q27 International Economics
Which of the following pairs of concept and economist is NOT correctly matched?
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Answer C. Low-level equilibrium trap : Ragnar Nurkse
Nelson's low-level equilibrium trap links population growth and per capita income; Nurkse is associated with the vicious circle of poverty and balanced growth.
Source: M.L. Jhingan, The Economics of Development and Planning; R.R. Nelson (1956); K.J. Arrow (1962); P. Romer (1990)
- Q28 International Economics
Which one of the following has NOT been offered as an explanation of the Leontief paradox?
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Answer C. US tariffs mainly protected the capital-intensive industries of the US
The usual explanations are human capital (Kravis, Kenen), natural resources (Vanek), factor-intensity reversal and US trade barriers. The trade-barrier argument is that US tariffs protected labour-intensive industries, which reduced labour-intensive imports; the reverse statement is not an explanation.
Source: Salvatore, International Economics, Ch. 2–5 (trade theory); B.A. Economics, International Economics
- Q29 International Economics
Consider the following statements about instruments of foreign capital:
I. Foreign Currency Convertible Bonds are rupee-denominated bonds issued abroad.
II. External commercial borrowings are loans raised by Indian entities from non-resident lenders.
III. ECBs are regulated by the Reserve Bank of India.
Which of the statements given above is/are INCORRECT?
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Answer D. I only
Statement I is incorrect: FCCBs are issued in a foreign currency and can be converted into equity; rupee-denominated bonds issued abroad are masala bonds. Statements II and III are correct.
Source: PW Indian Economy, BoP & Foreign Exchange chapter
- Q30 International Economics
Consider the following statements about the Bretton Woods system:
1. Member currencies had par values against the US dollar and were to be kept within a band of ±1% around them.
2. The Jamaica Accords of 1976 restored fixed par values after the breakdown of 1971.
Which of the statements given above is/are correct?
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Answer A. 1 only
Bretton Woods was an adjustable-peg system with ±1% bands around dollar parities. The Jamaica Accords (1976) did the opposite of restoring parities: they legalised floating exchange rates and demonetised gold (Second Amendment, 1978).
Source: Salvatore, International Economics; M.L. Jhingan, International Economics
- Q31 International Economics
A country invests 30% of its GDP and its GDP grows at 7.5% a year. What is its incremental capital-output ratio (ICOR)?
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Answer D. 4
ICOR = (I / Y) / (ΔY / Y) = 30% / 7.5% = 4: four units of investment are needed per unit of extra output.
Source: Standard method; answer and every option computed and checked in Python
- Q32 Indian Economics
Match the measures with what they capture:
List I
a. Gini coefficient
b. Headcount ratio
c. Poverty gap index
d. Multidimensional Poverty Index
List II
I. Product of headcount and intensity of deprivation
II. Inequality on a scale from 0 to 1
III. Shortfall of the incomes of the poor from the poverty line
IV. Share of the population below the poverty line
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Answer C. a-II, b-IV, c-III, d-I
Gini - inequality from 0 to 1; headcount ratio - share below the line; poverty gap - shortfall from the line; MPI - H x A.
Source: PW Indian Economy
- Q33 Indian Economics
Consider the following statements about tax reforms after 1991:
Statement I: Income tax rates were reduced, since high rates were seen as a reason for tax evasion.
Statement II: GST was introduced in 1991 as part of the New Economic Policy.
Which of the statements given above is/are correct?
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Answer A. I only
Only Statement I is correct. GST came much later, after the 2016 constitutional amendment.
Source: NCERT Class 11 Indian Economic Development ch.3 (p.58)
- Q34 Indian Economics
Holders of mining leases granted on or after 12 January 2015 must pay to the District Mineral Foundation an amount equal to what share of the royalty?
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Answer A. 10 per cent
DMF contribution is 10 per cent of royalty for leases from 12 January 2015 and 30 per cent for earlier leases.
Source: PW Indian Economy, ch.9 Industry, Manufacturing and Infrastructure, p.134
- Q35 Indian Economics
As per the Union Budget 2025-26, the Central Government's debt-to-GDP ratio in 2025-26 (Budget Estimates) is estimated at
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Answer B. 56.1%
The Budget estimated the Central Government debt-to-GDP ratio at 56.1% in 2025-26 (BE), down from 57.1% in 2024-25 (RE).
Source: Union Budget 2025-26, Fiscal Policy Strategy Statement; PW Indian Economy (p.52 printed)
- Q36 Indian Economics
Consider the following statements about measures of inequality:
I. A Gini coefficient of zero means perfect equality.
II. A Lorenz curve that coincides with the 45-degree line of equality means perfect inequality.
Which of the statements given above is/are correct?
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Answer A. I only
Only I is correct. A Lorenz curve on the line of equality means perfect equality; the more it bows away, the greater the inequality.
Source: PW Indian Economy (Human Capital, Unemployment and Poverty chapter)
- Q37 Indian Economics
Consider the following statements about the Aspirational Districts Programme:
I. It was launched in January 2018.
II. NITI Aayog anchors the programme at the central level.
III. Districts are ranked only on the basis of their per capita income.
Which of the statements given above is/are correct?
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Answer C. I and II only
Statements I and II are correct. The programme, launched in January 2018 and anchored by NITI Aayog, ranks districts on many indicators such as health and nutrition, education, agriculture, financial inclusion and infrastructure.
Source: NITI Aayog, Aspirational Districts Programme
- Q38 Indian Economics
Consider the following statements about negotiable warehouse receipts in India:
I. The Warehousing Development and Regulatory Authority was set up under the Warehousing (Development and Regulation) Act, 2007.
II. These receipts are regulated by the Securities and Exchange Board of India.
III. Farmers can obtain bank loans against receipts issued by registered warehouses.
Which of the statements given above is/are correct?
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Answer B. I and III only
Statements I and III are correct. I is true; II is false (they are regulated by WDRA); III is true.
Source: PW Indian Economy, ch.8 Agriculture and Allied Sector, p.118
- Q39 Indian Economics
Consider the following statements about agriculture announcements in the Union Budget 2025-26:
I. A five-year Mission for Cotton Productivity was announced.
II. A National Mission on High Yielding Seeds was announced.
Which of the statements given above is/are correct?
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Answer C. Both I and II
The Budget announced a five-year Mission for Cotton Productivity and a National Mission on High Yielding Seeds, among other agriculture measures.
Source: Union Budget 2025-26, Budget Speech (1 Feb 2025)
- Q40 Indian Economics
Consider the following statements about Multidimensional Poverty Indices:
I. The Global MPI was introduced in 2010 by UNDP and OPHI.
II. The Global MPI uses 10 indicators.
III. India's National MPI uses 14 indicators.
Which of the statements given above is/are correct?
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Answer B. I and II only
I and II are correct. India's National MPI uses 12 indicators.
Source: PW Indian Economy; NITI Aayog National MPI Baseline Report
- Q41 Indian Economics
Consider the following statements about the Indian rupee:
Statement I: It is fully convertible on the current account.
Statement II: It is fully convertible on the capital account.
Which of the statements given above is/are correct?
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Answer A. I only
Only Statement I is correct. Current account convertibility was achieved in 1994; capital account convertibility is still partial.
Source: PW Indian Economy (ref) p.143
- Q42 Indian Economics
Consider the following statements about organic farming in India:
I. Kerala was the first State in India to be declared fully organic.
II. Paramparagat Krishi Vikas Yojana promotes cluster-based organic farming.
III. MOVCDNER is meant only for the North-Eastern States.
Which of the statements given above is/are correct?
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Answer C. II and III only
Statements II and III are correct. I is false (Sikkim was first, in 2016); II is true; III is true.
Source: PW Indian Economy, ch.8 Agriculture and Allied Sector, p.115
- Q43 Indian Economics
Consider the following statements about regulatory reform measures in the Union Budget 2025-26:
I. A High-Level Committee for Regulatory Reforms will review all non-financial sector regulations, certifications, licences and permissions.
II. The High-Level Committee is expected to give its recommendations within five years.
III. An Investment Friendliness Index of States will be launched in 2025.
Which of the statements given above is/are INCORRECT?
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Answer D. II only
Statement II is incorrect: the High-Level Committee for Regulatory Reforms is expected to make recommendations within a year. It covers non-financial sector regulations, and an Investment Friendliness Index of States was to be launched in 2025.
Source: Union Budget 2025-26, Budget Speech (1 Feb 2025)
- Q44 Indian Economics
According to the Human Development Report 2025, India's HDI rank among 193 countries was
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Answer A. 130
HDR 2025 placed India at rank 130 of 193, with life expectancy of 72 years.
Source: NCERT Class 10 Understanding Economic Development, Table 1.6 (HDR 2025)
- Q45 Indian Economics
Consider the following statements about the National Manufacturing Policy, 2011:
Statement I: It aimed to raise the share of manufacturing in India's GDP to at least 35 per cent by 2022.
Statement II: It aimed to create 100 million additional jobs by 2022.
Which of the statements given above is/are correct?
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Answer B. II only
Only statement II is correct. The target share of manufacturing in GDP was 25 per cent, not 35 per cent. The National Manufacturing Policy, 2011 targeted 12-14 per cent manufacturing growth, a 25 per cent share of GDP and 100 million additional jobs by 2022; it also proposed National Investment and Manufacturing Zones.
Source: Indian Economy (reference) ch.9 p.133; National Manufacturing Policy 2011 (DIPP)
- Q46 Indian Economics
Consider the following statements about AGMARK:
I. It is issued under the Agricultural Produce (Grading and Marking) Act, 1937.
II. It is administered by the Bureau of Indian Standards.
III. It is a quality certification mark for agricultural products.
Which of the statements given above is/are NOT correct?
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Answer C. II only
Statement II is NOT correct. I is true; II is false (it is administered by the Directorate of Marketing and Inspection); III is true.
Source: PW Indian Economy, ch.8 Agriculture and Allied Sector, p.117
- Q47 Financial Accounting
Consider the following statements about the matching concept:
1. Expenses of a period are set against the revenues earned in that period to find profit.
2. Under the matching concept, an expense is recorded only in the period in which cash is paid.
Which of the statements given above is/are correct?
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Answer A. 1 only
The matching concept matches the revenues of a period with the expenses incurred to earn them; this needs outstanding and prepaid adjustments, so recording expenses only when paid (cash basis) is contrary to it.
Source: Telugu Akademi / APSCHE B.Com Financial Accounting, Accounting Concepts and Conventions
- Q48 Financial Accounting
Consider the following statements:
1. Trade discount is recorded in the books of account by debiting Discount Allowed A/c.
2. Cash discount allowed to a customer is a loss and is debited to Discount Allowed A/c.
Which of the statements given above is/are correct?
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Answer B. 2 only
Trade discount is a reduction from list price given at the time of sale; the transaction is recorded at the net amount, so no discount account is opened. Cash discount for prompt payment is recorded: allowed is a loss (debit), received is a gain (credit).
Source: Standard B.Com Financial Accounting (Telugu Akademi / T.S. Grewal), Journal (discounts)
- Q49 Financial Accounting
Which of the following pairs of error and its effect on the trial balance is NOT correctly matched?
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Answer B. Complete omission of a credit purchase : Disclosed by the trial balance
An error of complete omission records neither the debit nor the credit, so the trial balance still agrees; it is not disclosed. The other pairs are correct.
Source: Standard B.Com Financial Accounting text (Telugu Akademi / APSCHE), Trial Balance and Rectification of Errors
- Q50 Financial Accounting
Consider the following statements:
1. Carriage inwards is debited to the trading account.
2. Carriage outwards is debited to the trading account.
Which of the statements given above is/are correct?
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Answer A. 1 only
Carriage inwards adds to the cost of goods and is debited to the trading account; carriage outwards is a selling and distribution expense debited to the P&L account.
Source: Standard B.Com Financial Accounting text (Telugu Akademi / S.N. Maheshwari), Final Accounts with Adjustments
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Start free - Q51 Financial Accounting
From the following, find the subscriptions to be credited to the Income and Expenditure Account of a club for 2025-26: subscriptions received during the year ₹80,000; subscriptions outstanding on 1 April 2025 ₹6,000 and on 31 March 2026 ₹9,000; subscriptions received in advance on 1 April 2025 (for 2025-26) ₹4,000 and on 31 March 2026 (for 2026-27) ₹5,000.
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Answer D. ₹82,000
Income = received − opening outstanding (received now, but income of last year) + closing outstanding + opening advance (received last year, income of this year) − closing advance = 80,000 − 6,000 + 9,000 + 4,000 − 5,000 = ₹82,000.
Source: Standard method; answer and every option computed and checked in Python
- Q52 Financial Accounting
Lakshmi started business with cash ₹2,00,000. She borrowed ₹50,000 from a bank, bought furniture for ₹30,000 in cash and bought goods worth ₹40,000 on credit. What are the total assets of the business after these transactions?
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Answer B. ₹2,90,000
Cash = ₹2,00,000 + ₹50,000 − ₹30,000 = ₹2,20,000; furniture ₹30,000; stock ₹40,000. Total = ₹2,90,000.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q53 Financial Accounting
A trader keeps a three-column cash book. Transactions: received ₹4,900 from A in full settlement of ₹5,000; received ₹2,940 from B in full settlement of ₹3,000; paid ₹1,960 to C in full settlement of ₹2,000. What is the total of the discount column on the debit side?
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Answer D. ₹160
The debit-side discount column records discount allowed on receipts: A ₹100 + B ₹60 = ₹160. The ₹40 discount on payment to C is discount received, recorded on the credit side.
Source: Standard method; answer and every option computed and checked in Python
- Q54 Financial Accounting
On 31 December the cash book shows a bank balance of ₹15,000 (debit). During December, cheques of ₹6,000 were issued, of which only ₹4,500 were presented for payment; cheques of ₹5,000 were deposited, of which only ₹3,200 were credited by the bank by that date. What is the balance as per the pass book?
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Answer B. ₹14,700
Cheques not presented = ₹6,000 − ₹4,500 = ₹1,500 (add); cheques not cleared = ₹5,000 − ₹3,200 = ₹1,800 (deduct). ₹15,000 + ₹1,500 − ₹1,800 = ₹14,700.
Source: Standard method; answer and every option computed and checked in Python
- Q55 Financial Accounting
A firm holds 8% investments of ₹50,000 throughout the year. Interest received during the year was ₹3,000; the rest is accrued. What amount of interest is credited to the profit and loss account?
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Answer D. ₹4,000
Income for the full year is credited: 50,000 × 8% = ₹4,000, of which ₹1,000 accrued interest is also shown as an asset.
Source: Standard method; answer and every option computed and checked in Python
- Q56 Financial Accounting
A machine is bought for ₹1,00,000 and ₹10,000 is spent on its installation. Its estimated scrap value is ₹20,000 at the end of its useful life of 6 years. What is the annual depreciation under the straight line method?
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Answer B. ₹15,000
Depreciable amount = cost including installation − scrap value = ₹1,10,000 − ₹20,000 = ₹90,000. Spread equally over 6 years: ₹90,000 / 6 = ₹15,000 a year.
Source: Standard method; answer and every option computed and checked in Python
- Q57 Financial Accounting
Ravi started business with cash ₹1,00,000. He bought goods on credit for ₹40,000 and sold goods costing ₹20,000 for ₹28,000 in cash. What are his total assets after these transactions?
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Answer A. ₹1,48,000
Cash = ₹1,00,000 + ₹28,000 = ₹1,28,000; stock = ₹40,000 − ₹20,000 = ₹20,000; total assets = ₹1,48,000. Check: creditors ₹40,000 + capital (₹1,00,000 + profit ₹8,000) = ₹1,48,000.
Source: Standard method; answer and every option computed and checked in Python
- Q58 Financial Accounting
A business's sales book total for the year is ₹48,000, cash sales are ₹5,000 and the sales returns book total is ₹3,200. What is the figure of net sales shown in the Trading Account?
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Answer A. ₹49,800
Total sales = credit sales 48,000 + cash sales 5,000 = ₹53,000; less sales returns 3,200 gives net sales ₹49,800.
Source: Standard method; answer and every option computed and checked in Python
- Q59 Financial Accounting
Which of the following balances appear on the credit side of a trial balance?
1. Sales returns
2. Purchases returns
3. Outstanding expenses
4. Prepaid expenses
5. Provision for doubtful debts
Select the correct answer using the code given below.
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Answer B. 2, 3 and 5 only
Sales returns (reduction of income) and prepaid expenses (asset) are debit balances. Purchases returns, outstanding expenses (liability) and provision for doubtful debts are credit balances.
Source: Standard B.Com Financial Accounting text (Telugu Akademi / APSCHE), Trial Balance and Rectification of Errors
- Q60 Financial Accounting
Match List I (item) with List II (treatment in final accounts):
List I:
A. Carriage inwards
B. Bad debts
C. Goodwill
D. Drawings
List II:
1. Debit side of the profit and loss account
2. Debit side of the trading account
3. Deducted from capital on the liabilities side
4. Assets side of the balance sheet
Select the correct answer using the code given below.
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Answer D. A-2, B-1, C-4, D-3
Direct expenses go to the trading account, losses such as bad debts to the P&L account, intangible assets to the balance sheet, and drawings reduce capital.
Source: Standard B.Com Financial Accounting text (Telugu Akademi / S.N. Maheshwari), Final Accounts with Adjustments
- Q61 Financial Accounting
The annuity method of depreciation is most suitable for which of the following assets?
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Answer B. Leasehold property acquired on a long lease
The annuity method takes into account interest on the capital invested in the asset; it is used for leases and similar assets with a long, fixed life and heavy initial cost.
Source: Telugu Akademi / APSCHE B.Com Financial Accounting, Depreciation, Provisions and Reserves
- Q62 Basics of Computers
What is the decimal equivalent of the binary number (101101)₂?
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Answer A. 45
(101101)₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32 + 8 + 4 + 1 = 45.
Source: Standard method; answer and every option computed and checked in Python
- Q63 Basics of Computers
Match List I (code) with List II (description):
List I:
A. ASCII
B. EBCDIC
C. Unicode
D. Gray code
List II:
1. Universal character set covering the scripts of the world's languages
2. 7-bit code for 128 characters
3. Unit-distance code in which successive values differ in one bit
4. 8-bit code used on IBM mainframes
Select the correct answer using the code given below.
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Answer A. A-2, B-4, C-1, D-3
ASCII is a 7-bit code (128 characters); EBCDIC is IBM's 8-bit code; Unicode gives a code point to the characters of nearly all writing systems; Gray code changes one bit between successive values.
Source: Standard computer fundamentals texts; The Unicode Standard (unicode.org)
- Q64 Basics of Computers
Trace the flowchart: Start → S = 0, I = 1 → [Is I ≤ 5?] — Yes → S = S + I × I → I = I + 1 → back to the decision; No → Print S → Stop. What value is printed?
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Answer C. 55
The loop runs for I = 1 to 5 and adds I²: S = 1 + 4 + 9 + 16 + 25 = 55, which is printed when I becomes 6.
Source: Standard method; answer and every option computed and checked in Python
- Q65 Basics of Computers
Cell E1 contains =A1*2. Consider the following statements about MS Excel 2019:
1. If E1 is cut and pasted into G5, G5 contains =A1*2.
2. If E1 is copied and pasted into G5, G5 contains =C5*2.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Moving a formula (cut and paste) keeps its references unchanged. Copying shifts relative references by the same offset: E1 → G5 is +2 columns, +4 rows, so A1 → C5.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q66 Basics of Computers
Consider the following statements about converting decimal numbers to binary:
1. A decimal integer is converted by repeated division by 2, and the remainders are read from the last to the first.
2. A decimal fraction is converted by repeated multiplication by 2, and the integer parts are read from the last to the first.
Which of the statements given above is/are correct?
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Answer A. 1 only
For the integer part, divide by 2 repeatedly and read the remainders from the last to the first (bottom to top). For the fractional part, multiply by 2 repeatedly and read the integer parts in the order they are obtained (top to bottom), e.g. 0.625 → 1, 0, 1 → 0.101.
Source: Standard B.Com/B.Sc. Computer Fundamentals textbook (Telugu Akademi), Number Systems
- Q67 Basics of Computers
Consider the following statements:
1. Static RAM stores each bit as a charge on a capacitor and must be refreshed periodically.
2. Cache memory is usually built from static RAM.
Which of the statements given above is/are correct?
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Answer B. 2 only
DRAM stores bits as capacitor charge and needs periodic refreshing; SRAM uses flip-flops, needs no refresh, is faster and costlier, and is used for cache memory.
Source: Standard computer organisation texts (M. Morris Mano, Computer System Architecture), Memory organisation
- Q68 Basics of Computers
Consider the following statements about the XNOR gate:
1. Its output is 1 when both inputs are equal.
2. It is the complement of the XOR gate.
3. For inputs A and B its output is A·B + A'·B'.
Which of the statements given above are correct?
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Answer D. 1, 2 and 3
XNOR (equivalence gate) gives 1 for inputs 00 and 11; it is NOT of XOR, and its expression is A·B + A'·B'.
Source: Standard computer fundamentals textbook (e.g., P. K. Sinha, Computer Fundamentals), Logic Gates
- Q69 Basics of Computers
What does =(5>3)+1 return in MS Excel?
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Answer B. 2
A comparison returns a logical value. When TRUE or FALSE is used in an arithmetic formula, Excel converts it to 1 or 0. Here (5>3) = TRUE = 1, so the result is 2.
Source: Standard spreadsheet method; answer and every option computed and checked in Python
- Q70 Basics of Computers
Consider the following statements:
1. Each octal digit can be written as a group of exactly three binary digits.
2. Each hexadecimal digit can be written as a group of exactly four binary digits.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Because 8 = 2³, each octal digit 0–7 matches a 3-bit group 000–111; because 16 = 2⁴, each hexadecimal digit 0–F matches a 4-bit group 0000–1111.
Source: Standard B.Com/B.Sc. Computer Fundamentals textbook (Telugu Akademi), Number Systems
- Q71 Basics of Computers
The Gray code 1101 is converted to binary. What is the result?
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Answer B. 1001
Copy the MSB, then each binary bit = previous binary bit ⊕ current Gray bit: 1, 1⊕1 = 0, 0⊕0 = 0, 0⊕1 = 1, so binary = 1001 (decimal 9). Check: 1001 → Gray 1101.
Source: Standard method; answer and every option computed and checked in Python
- Q72 Basics of Computers
How is −45 represented in 8-bit 2's complement form?
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Answer D. 11010011
+45 = 00101101. Inverting gives 11010010 (1's complement), and adding 1 gives 11010011, the 2's complement form of −45.
Source: Standard method; answer and every option computed and checked in Python
- Q73 Basics of Computers
Match List I (error value) with List II (usual cause):
List I:
A. #DIV/0!
B. #NAME?
C. #REF!
D. #N/A
List II:
1. A formula refers to a cell that has been deleted
2. A lookup value is not available
3. A number is divided by zero or by an empty cell
4. A function name is misspelt
Select the correct answer using the code given below.
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Answer D. A-3, B-4, C-1, D-2
#DIV/0! = division by zero; #NAME? = unrecognised text such as a misspelt function; #REF! = invalid (deleted) reference; #N/A = value not available, typically from a failed lookup.
Source: Microsoft Support, How to correct errors in formulas
- Q74 Basics of Computers
What is the decimal equivalent of the octal number (157)₈?
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Answer B. 111
(157)₈ = 1×8² + 5×8¹ + 7×8⁰ = 64 + 40 + 7 = 111.
Source: Standard method; answer and every option computed and checked in Python
- Q75 Basics of Computers
The bit pattern of the 7-bit ASCII code of the letter 'C' is 1000011. If an even-parity bit is added to make 8 bits, what is the parity bit?
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Answer B. 1
1000011 contains three 1s. For even parity the total number of 1s including the parity bit must be even, so the parity bit is 1.
Source: Standard method; answer and every option computed and checked in Python
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75 questions to go. Take the rest with a timer and see your score.
Start free - Q76 Basics of Computers
A sequence of instructions is written as: Step 1: Read A, B. Step 2: If A > B then Max = A else Max = B. Step 3: Print Max. Step 4: Go to Step 1. Which property of an algorithm does this procedure violate?
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Answer D. Finiteness
With an unconditional 'Go to Step 1' and no stopping condition, the procedure never ends; an algorithm must terminate after a finite number of steps.
Source: D. E. Knuth, The Art of Computer Programming, Vol. 1, §1.1 (properties of an algorithm)
- Q77 Statistics: Data, Sampling & Presentation
Consider the following statements:
1. Non-sampling errors can arise in both census and sample surveys.
2. Non-sampling errors are usually larger in a census than in a sample survey.
3. Sampling error can be reduced by increasing the sample size.
4. Non-response is a sampling error.
Which of the statements given above are correct?
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Answer B. 1, 2 and 3 only
Non-sampling errors (from faulty measurement, non-response, processing mistakes, bias) occur in both methods and tend to be larger in a census because of its scale and the many untrained staff. Sampling error falls with sample size. Non-response is a non-sampling error.
Source: S.P. Gupta, Statistical Methods, Sampling; Telugu Akademi B.A. Statistics
- Q78 Statistics: Data, Sampling & Presentation
What is the probability that a leap year, selected at random, contains 53 Sundays?
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Answer B. 2/7
A leap year has 366 days = 52 weeks + 2 days. The two extra days form one of 7 equally likely pairs (Sun–Mon, Mon–Tue, …, Sat–Sun); two of them contain a Sunday, so P = 2/7.
Source: Standard method; answer and every option computed and checked in Python
- Q79 Statistics: Data, Sampling & Presentation
The class marks of a continuous frequency distribution with equal classes are 15, 25, 35 and 45. What are the limits of the class whose class mark is 35?
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Answer C. 30 – 40
Class width = difference between consecutive class marks = 10. Lower limit = 35 − 10/2 = 30 and upper limit = 35 + 10/2 = 40.
Source: Standard method; answer and every option computed and checked in Python
- Q80 Statistics: Data, Sampling & Presentation
The standard deviation of the weights of school children is 12 kg. What is the minimum simple random sample size needed to estimate the mean weight within ±2 kg with 95% confidence (z = 1.96)?
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Answer C. 139
n = (zσ/E)² = (1.96 × 12/2)² = 138.30; round up to 139, since 138 would give an error slightly above 2 kg.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q81 Statistics: Data, Sampling & Presentation
Consider the following statements about two events A and B:
1. If A and B are independent, then A and B' (complement of B) are also independent.
2. If A and B are independent, then P(A ∩ B) = P(A) + P(B).
Which of the statements given above is/are correct?
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Answer A. 1 only
P(A ∩ B') = P(A) − P(A ∩ B) = P(A) − P(A)P(B) = P(A)P(B'), so A and B' are independent. For independent events P(A ∩ B) = P(A)P(B), a product, not a sum.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
- Q82 Statistics: Data, Sampling & Presentation
A frequency distribution uses the inclusive classes 10–19, 20–29, 30–39. What are the true class limits (class boundaries) of the class 20–29?
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Answer B. 19.5 – 29.5
Gap between the upper limit of one class and the lower limit of the next is 1, so the correction factor is 0.5. Class 20–29 becomes 19.5–29.5.
Source: Standard method; answer and every option computed and checked in Python
- Q83 Statistics: Data, Sampling & Presentation
A sample of 200 households is to be selected from a list of 4,000 households by systematic sampling. The sampling fraction and the sampling interval are, respectively,
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Answer A. 5% and 20
Sampling fraction f = n/N = 200/4000 = 0.05 = 5%. Interval k = N/n = 4000/200 = 20.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q84 Statistics: Data, Sampling & Presentation
Which of the following are axioms in the axiomatic definition of probability?
1. P(A) ≥ 0 for every event A
2. P(S) = 1, where S is the sample space
3. P(A ∪ B) = P(A) + P(B) for mutually exclusive events A and B
4. P(A ∩ B) = P(A) P(B) for any two events A and B
Select the correct answer using the code given below.
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Answer B. 1, 2 and 3 only
The axioms are non-negativity, certainty (P(S) = 1) and additivity for mutually exclusive (disjoint) events. P(A ∩ B) = P(A)P(B) holds only for independent events and is not an axiom.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
- Q85 Statistics: Data, Sampling & Presentation
The class 40–60 of a frequency distribution has frequency 50. What is its frequency density?
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Answer A. 2.5
Frequency density = frequency ÷ class width = 50 ÷ 20 = 2.5.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q86 Statistics: Data, Sampling & Presentation
Nothing is known in advance about the proportion of households using LPG in a town. What is the minimum sample size needed to estimate this proportion within ±0.03 with 95% confidence (z = 1.96)?
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Answer C. 1,068
With P unknown take P = 0.5 (largest PQ = 0.25). n = z²PQ/E² = 1.96² × 0.25/0.03² = 1067.11, rounded up to 1,068.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q87 Statistics: Data, Sampling & Presentation
A problem is given to three students whose chances of solving it independently are 1/2, 1/3 and 1/4. What is the probability that the problem is solved?
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Answer D. 3/4
P(no one solves) = (1/2)(2/3)(3/4) = 1/4, so P(solved by at least one) = 1 − 1/4 = 3/4.
Source: Standard method; answer and every option computed and checked in Python
- Q88 Statistics: Data, Sampling & Presentation
A histogram is drawn for the classes 0–10 (f = 8), 10–20 (f = 14), 20–40 (f = 30) and 40–50 (f = 6). Taking the class width 10 as standard, what should be the height (adjusted frequency) of the rectangle over 20–40?
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Answer D. 15
In a histogram with unequal classes the area of each rectangle is proportional to the frequency. For a class twice the standard width, height = 30 / 2 = 15.
Source: Standard method; answer and every option computed and checked in Python
- Q89 Statistics: Data, Sampling & Presentation
A question in a household survey reads: "Does your household have a ration card? (Yes / No)". Such a question is called
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Answer C. a dichotomous question
A closed question with only two possible answers (yes/no, true/false) is a dichotomous question.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q90 Statistics: Data, Sampling & Presentation
Which definition of probability is also known as 'a priori' probability?
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Answer B. Classical definition
The classical definition is called a priori because the probability is found by reasoning before the experiment is performed, assuming equally likely outcomes.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
- Q91 Statistics: Data, Sampling & Presentation
Which of the following is a continuous variable?
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Answer D. Weight of students in a class
A continuous variable can take every value in an interval (weight, height, time). Counts such as rooms, accidents or shareholders are discrete.
Source: NCERT Class 11 Statistics for Economics, Organisation and Presentation of Data
- Q92 Statistics: Data, Sampling & Presentation
Which one of the following is NOT a probability (random) sampling method?
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Answer D. Snowball sampling
Simple random, stratified, systematic, cluster and multistage sampling give each unit a known chance of selection. Snowball sampling, where existing respondents recruit further respondents, is a non-probability method.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q93 Measures of Central Tendency
A shop sold three grades of tea priced at ₹200, ₹250 and ₹300 per kg. The quantities sold were 50 kg, 30 kg and 20 kg respectively. What is the weighted average price per kg?
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Answer B. ₹235
Weighted mean = Σwx / Σw = (10,000 + 7,500 + 6,000) / 100 = ₹235.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q94 Measures of Central Tendency
The weights (in grams) of 100 fruits are grouped below. Find the 65th percentile (P65).
Weight: 100–120, 120–140, 140–160, 160–180, 180–200
No. of fruits: 12, 20, 30, 26, 12
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Answer D. 162.31
65N/100 = 65; c.f.: 12, 32, 62, 88, 100, so the P65 class is 160–180. P65 = 160 + (65 − 62)/26 × 20 = 162.31 g.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q95 Measures of Central Tendency
The mean of 10 observations is 20. Match the change made to every observation (List I) with the new mean (List II):
List I:
A. Each increased by 5
B. Each multiplied by 3
C. Each divided by 4
D. Each decreased by 20
List II:
1. 0
2. 5
3. 25
4. 60
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Answer C. A-3, B-4, C-2, D-1
A: 20 + 5 = 25; B: 3 × 20 = 60; C: 20 / 4 = 5; D: 20 − 20 = 0.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q96 Measures of Central Tendency
Find the median of the following distribution.
Class: 10–20, 20–30, 30–40, 40–50, 50–60
Frequency: 5, 7, 12, 10, 6
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Answer A. 36.67
N = 40, so N/2 = 20. Cumulative frequencies are 5, 12, 24, 34, 40, so the median class is 30–40 with L = 30, cf = 12, f = 12, h = 10. Median = L + (N/2 − cf)/f × h = 30 + (8/12) × 10 = 36.67.
Source: Standard method; answer and every option computed and checked in Python
- Q97 Measures of Central Tendency
The arithmetic mean of two positive numbers is 10 and their harmonic mean is 6.4. What are the two numbers?
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Answer B. 4 and 16
For two numbers GM² = AM × HM = 10 × 6.4 = 64, so GM = 8 and the product is 64. The sum is 2 × 10 = 20. Numbers with sum 20 and product 64 are 4 and 16 (check: HM = 2 × 64 / 20 = 6.4).
Source: Standard method; answer and every option computed and checked in Python
- Q98 Measures of Central Tendency
Find the median of the following distribution.
Class: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60
Frequency: 7, 11, 18, 24, 13, 7
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Answer A. 31.67
N = 80, N/2 = 40; c.f.: 7, 18, 36, 60, 73, 80, so the median class is 30–40. Median = L + (N/2 − c)/f × h = 30 + (40 − 36)/24 × 10 = 31.67.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q99 Measures of Central Tendency
The mean of 20 observations was found to be 15. Later it was found that one observation, 52, had been recorded as 25, and that another observation, 30, should not have been included at all. What is the correct mean of the remaining observations?
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Answer B. 15.63
Correct total = 300 − 25 + 52 − 30 = 297 for 19 observations, so the mean = 297 / 19 ≈ 15.63.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q100 Measures of Central Tendency
In the distribution below, which class contains the third quartile?
Class: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 10, 15, 25, 20, 10
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Answer B. 30–40
N = 80, so Q3 is at 3N/4 = 60. Cumulative frequencies are 10, 25, 50, 70, 80; the first one that is at least 60 is 70, for the class 30–40.
Source: Standard method; answer and every option computed and checked in Python
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50 questions to go. Take the rest with a timer and see your score.
Start free - Q101 Measures of Central Tendency
Consider the following statements for positive observations:
1. If the observations are not all equal, AM > GM > HM.
2. For any two positive numbers, GM² = AM × HM.
3. For any three positive numbers, GM² = AM × HM.
Which of the statements given above is/are correct?
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Answer B. 1 and 2 only
AM ≥ GM ≥ HM with equality only when all values are equal. For two numbers a, b: AM × HM = ((a + b)/2) × (2ab/(a + b)) = ab = GM². This does not hold in general for three numbers: for 1, 2, 3, AM × HM = 2 × 18/11 ≈ 3.273 while GM² = 6^(2/3) ≈ 3.302.
Source: Standard method; answer and every option computed and checked in Python
- Q102 Measures of Central Tendency
Find the fourth decile (D4) of the following distribution.
Class: 0–8, 8–16, 16–24, 24–32, 32–40, 40–48
Frequency: 9, 15, 26, 22, 18, 10
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Answer D. 20.92
N = 100, 4N/10 = 40; c.f.: 9, 24, 50, 72, 90, 100, so the D4 class is 16–24. D4 = 16 + (40 − 24)/26 × 8 = 20.92.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q103 Measures of Central Tendency
The harmonic mean of a group of 20 observations is 8 and that of another group of 30 observations is 15. What is the harmonic mean of all 50 observations?
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Answer D. 11.11
Σ(1/x) for the groups = 20/8 + 30/15 = 2.5 + 2 = 4.5, so the combined HM = 50 / 4.5 ≈ 11.11.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q104 Measures of Central Tendency
Find the mode of the following distribution of marks.
Marks: 10–19, 20–29, 30–39, 40–49, 50–59
No. of students: 6, 15, 28, 19, 7
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Answer A. 35.41
Convert to class boundaries (subtract 0.5): modal class 29.5–39.5, f1 = 28, f0 = 15, f2 = 19, h = 10. Mode = 29.5 + 13/22 × 10 = 35.41.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q105 Measures of Central Tendency
For two positive numbers, the arithmetic mean is 25 and the harmonic mean is 16. What is their geometric mean?
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Answer B. 20
For two positive numbers GM² = AM × HM = 25 × 16 = 400, so GM = 20.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q106 Measures of Central Tendency
Which average is most appropriate for a frequency distribution with open-end classes such as 'below 10' and '60 and above'?
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Answer C. Median
Open-end classes have no definite mid-points, so the mean, GM and HM cannot be computed without assumptions. The median can be calculated as long as the median class is not open-ended.
Source: Telugu Akademi / APSCHE B.Com Business Statistics, Measures of Central Tendency
- Q107 Measures of Central Tendency
If every weight in a weighted arithmetic mean is multiplied by 5, the weighted mean:
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Answer A. remains unchanged
x̄w = Σwx / Σw; multiplying every w by 5 multiplies both numerator and denominator by 5, which cancel.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q108 Dispersion & Skewness
Of 10 observations, five are equal to 4 and five are equal to −4. What is their standard deviation?
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Answer B. 4
Mean = 0; every squared deviation is 16; σ² = 16, σ = 4.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q109 Dispersion & Skewness
The first four moments of a distribution about the value 10 are −1, 10, −20 and 300. The value of β₂ and the nature of the curve are
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Answer B. 3.42, leptokurtic
μ₂ = 10 − (−1)² = 9; μ₄ = 300 − 4(−20)(−1) + 6(10)(−1)² − 3(−1)⁴ = 300 − 80 + 60 − 3 = 277; β₂ = 277/81 = 3.42 > 3, leptokurtic.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q110 Dispersion & Skewness
What is the variance of the first ten even numbers 2, 4, …, 20?
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Answer D. 33
They are 2 × (1, 2, …, 10). Variance of 1 … 10 = (100 − 1)/12 = 8.25; multiply by 2² = 4: 33.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q111 Dispersion & Skewness
Match List I with List II:
List I:
A. Mesokurtic
B. Leptokurtic
C. Platykurtic
D. γ₂ (excess kurtosis)
List II:
1. β₂ < 3
2. β₂ − 3
3. β₂ = 3
4. β₂ > 3
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Answer B. A-3, B-4, C-1, D-2
Mesokurtic (normal) β₂ = 3; leptokurtic, more peaked, β₂ > 3; platykurtic, flatter, β₂ < 3; γ₂ = β₂ − 3.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q112 Dispersion & Skewness
The coefficient of variation of a distribution is 25% and its mean is 48. What is its variance?
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Answer D. 144
σ = CV × mean/100 = 0.25 × 48 = 12; variance = 12² = 144.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q113 Dispersion & Skewness
Consider the following statements about normal variables:
1. If X is normal, aX + b (a ≠ 0) is also normal.
2. The sum of two independent normal variables is normal.
3. For independent normal X and Y, the variance of X − Y is σ₁² − σ₂².
4. The normal curve is unimodal.
Select the correct answer:
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Answer A. 1, 2 and 4 only
A linear function of a normal variable and the sum or difference of independent normal variables are normal; variances add for both X + Y and X − Y, so Var(X − Y) = σ₁² + σ₂². The curve has a single peak at μ.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q114 Dispersion & Skewness
The coefficient of standard deviation of a series is 0.15 and its standard deviation is 6. What is the mean?
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Answer D. 40
Coefficient of SD = σ/x̄ ⇒ x̄ = 6/0.15 = 40.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q115 Dispersion & Skewness
The second and fourth central moments of a distribution are μ2 = 2 and μ4 = 18. What is β2 and how is the distribution described?
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Answer A. 4.5; leptokurtic
β2 = μ4 / μ2² = 18 / 2² = 4.5. Since β2 > 3 (the normal value), the distribution is leptokurtic (more peaked than normal).
Source: S.C. Gupta & V.K. Kapoor, Fundamentals of Mathematical Statistics, Moments, Skewness and Kurtosis
- Q116 Dispersion & Skewness
What is the standard deviation of 6, 8, 10, 12 and 14?
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Answer A. 2.83
Mean = 10; squared deviations 16, 4, 0, 4, 16, sum 40; variance = 40/5 = 8; SD = √8 = 2.83.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q117 Dispersion & Skewness
Marks are normally distributed with mean 70 and standard deviation 8. The standard normal variate Z for a score of 82 is
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Answer B. 1.5
Z = (X − μ)/σ = (82 − 70)/8 = 1.5.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q118 Dispersion & Skewness
A series has mean 40 and SD 6. What is the root mean square deviation of the observations about the value 48?
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Answer B. 10
s² = σ² + (x̄ − A)² = 36 + 64 = 100, so s = 10. It is least (= σ) when A is the mean.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q119 Dispersion & Skewness
The first four moments of a distribution about the value 5 are 1, 4, 10 and 46. What are β2 and the nature of kurtosis?
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Answer C. 3.0; mesokurtic
Convert to central moments: μ2 = μ2′ − μ1′² = 4 − 1 = 3; μ4 = μ4′ − 4μ3′μ1′ + 6μ2′μ1′² − 3μ1′⁴ = 46 − 40 + 24 − 3 = 27. β2 = μ4 / μ2² = 27 / 9 = 3, so the distribution is mesokurtic.
Source: S.C. Gupta & V.K. Kapoor, Fundamentals of Mathematical Statistics, Moments, Skewness and Kurtosis
- Q120 Dispersion & Skewness
If y = a + bx, where a and b are constants (b ≠ 0), consider the following:
1. ȳ = a + b x̄
2. σᵧ = |b| σₓ
3. The coefficient of variation of y is always equal to that of x
4. Range of y = |b| × range of x
Which of the above are correct?
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Answer B. 1, 2 and 4 only
The mean follows both origin and scale (ȳ = a + bx̄); SD and range change only with scale (|b|). CVᵧ = |b|σₓ/|a + bx̄| × 100, which differs from CVₓ whenever a ≠ 0 (or b < 0 with a positive mean), so statement 3 is not always true.
Source: Gupta, S.C. & Kapoor, V.K., Fundamentals of Mathematical Statistics, Measures of Dispersion
- Q121 Dispersion & Skewness
In a positively skewed distribution, the usual relationship among the three averages is
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Answer B. Mean > Median > Mode
With positive skew the tail extends to the right; extreme high values raise the mean most, so Mean > Median > Mode.
Source: S.P. Gupta, Statistical Methods, Skewness, Moments and Kurtosis
- Q122 Dispersion & Skewness
The standard deviation of a set of observations is zero if and only if:
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Answer A. all the observations are equal
σ² = Σ(x − x̄)²/n is a sum of squares; it is zero only when every x equals x̄, i.e. all observations are equal.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q123 Correlation
While ranking a series, three items tie for the 4th place. What rank is given to each of them?
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Answer D. 5
The three items occupy ranks 4, 5 and 6, so each gets their mean, (4 + 5 + 6)/3 = 5. The next item gets rank 7.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q124 Correlation
If r = 0.9 for 25 pairs of observations, what is the probable error of r?
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Answer B. 0.0256
PE = 0.6745 (1 − r²)/√n = 0.6745 × (1 − 0.81)/√25 = 0.6745 × 0.19/5 = 0.0256.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q125 Correlation
Assertion (A): If the ranks of n items in one series are exactly the reverse of the ranks in the other, Spearman's rank correlation coefficient is −1.
Reason (R): Spearman's rank correlation coefficient can be applied only to quantitative data.
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Answer C. (A) is true but (R) is false
Completely reversed ranks give Σd² = n(n² − 1)/3 and R = 1 − 2 = −1, so A is true. Rank correlation is meant precisely for qualities such as beauty or honesty that can be ranked but not measured, so R is false.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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25 questions to go. Take the rest with a timer and see your score.
Start free - Q126 Correlation
Consider the following statements about interpreting r with its probable error (PE):
1. If r is less than PE, the correlation is not significant.
2. If r is more than six times PE, the correlation is definitely significant.
3. r ± PE gives the limits within which the population correlation coefficient may be expected to lie.
Which of the statements given above are correct?
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Answer D. 1, 2 and 3
All three are the standard rules: r < PE means no evidence of correlation; r > 6 PE means correlation is certain; ρ = r ± PE gives the limits.
Source: S.P. Gupta, Statistical Methods, Correlation Analysis
- Q127 Correlation
The coefficient of correlation between heights in centimetres and weights in kilograms of a group is 0.72. If heights are converted to inches (1 inch = 2.54 cm) and weights to pounds (1 kg = 2.2 lb), the new coefficient is
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Answer B. 0.72
Converting units multiplies each variable by a positive constant. r is independent of change of scale, so it remains 0.72.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q128 Correlation
Which of the following statements about the probable error (PE) of r are correct?
1. PE = 0.6745 × standard error of r.
2. r ± PE gives the limits within which the population coefficient of correlation is expected to lie.
3. PE is a reliable guide even for very small samples such as n = 5.
Select the correct answer:
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Answer A. 1 and 2 only
PE = 0.6745 (1 − r²)/√n = 0.6745 × SE, and r ± PE are the usual limits for ρ. The rule assumes a fairly large sample from a normal population, so it misleads for tiny samples.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q129 Correlation
Find Spearman's rank correlation coefficient, with the correction for tied ranks (to three decimals), for:
X: 25, 30, 30, 42, 18, 35, 30
Y: 60, 54, 58, 70, 45, 58, 50
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Answer C. 0.536
Ranks X: 6, 4, 4, 1, 7, 2, 4; Y: 2, 5, 3.5, 1, 7, 3.5, 6. Σd² = 23.5. Correction: X has 30 three times, 3(3² − 1)/12 = 2; Y has 58 twice, 2(2² − 1)/12 = 0.5. R = 1 − 6(23.5 + 2.5)/(7 × 48) = 0.536.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q130 Correlation
Consider the following statements about correlation:
1. A high value of r proves that changes in X cause changes in Y.
2. Correlation between two variables may arise because both are influenced by a third variable.
Which of the statements given above is/are correct?
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Answer B. 2 only
Correlation measures association, not causation. Two variables may be correlated because both depend on a common third factor (e.g. sales of ice cream and cold drinks both depend on temperature).
Source: S.P. Gupta, Statistical Methods, Correlation Analysis
- Q131 Correlation
For 7 pairs of ranks, the sum of squares of the rank differences is 14. What is Spearman's rank correlation coefficient?
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Answer A. 0.75
R = 1 − 6Σd²/[n(n² − 1)] = 1 − (6 × 14)/(7 × 48) = 1 − 84/336 = 0.75.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q132 Correlation
Which of the following are limitations of Karl Pearson's coefficient of correlation?
1. It is strongly affected by extreme values.
2. It assumes a linear relationship between the variables.
3. It cannot be computed when the two variables are in different units.
4. A high value does not by itself show cause and effect.
Select the correct answer:
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Answer B. 1, 2 and 4 only
r is sensitive to extreme items, measures only linear association and cannot show causation. It is a pure number, so X and Y may be in any units.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q133 Correlation
Marks of 8 candidates in two papers are:
Paper I: 60, 54, 54, 60, 50, 83, 54, 44
Paper II: 55, 44, 38, 47, 36, 47, 54, 44
What is Spearman's rank correlation coefficient after correcting for tied ranks (to three decimals)?
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Answer B. 0.601
Ranks I: 2.5, 5, 5, 2.5, 7, 1, 5, 8; II: 1, 5.5, 7, 3.5, 8, 3.5, 2, 5.5. Σd² = 30. Ties: 60 twice (0.5), 54 three times (2), 47 twice (0.5), 44 twice (0.5); total 3.5. R = 1 − 6 × 33.5/(8 × 63) = 0.601.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q134 Correlation
A district planner has only the ranks of 13 districts on literacy and on infant mortality, not the actual figures. Which measure should be used to study their relationship?
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Answer D. Spearman's rank correlation coefficient
When only ranks are known (ordinal data), Spearman's rank correlation R = 1 − 6Σd²/[n(n² − 1)] is the right measure.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q135 Correlation
In the formula PE = 0.6745 (1 − r²)/√n for the probable error of r, the constant 0.6745 is used because
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Answer D. in a normal distribution, 50% of the values lie within ±0.6745 standard errors of the mean
PE = 0.6745 × SE of r. In a normal distribution the middle 50% lies within mean ± 0.6745 SE, so the population coefficient lies within r ± PE with an even (50 : 50) chance.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q136 Time Series & Index Numbers
The 3-yearly moving averages of a series for 2019 and 2020 are 40 and 42. If the value of the series in 2018 was 36, its value in 2021 was
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Answer C. 42
MA(2019) = (Y18 + Y19 + Y20)/3 = 40 → total 120; MA(2020) = (Y19 + Y20 + Y21)/3 = 42 → total 126. Subtracting: Y21 − Y18 = 6, so Y21 = 42.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q137 Time Series & Index Numbers
From the data below, what is Fisher's ideal price index?
Commodity Base-year price (₹) Base-year quantity Current-year price (₹) Current-year quantity X 10 8 12 5 Y 5 4 8 10 Show answerHide answer
Answer B. 133.87
Laspeyres = 128 / 100 × 100 = 128; Paasche = 140 / 100 × 100 = 140. Fisher = √(L × P) = √(17920) = 133.87.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q138 Time Series & Index Numbers
Match List I (method of seasonal index) with List II (what each season's figure is expressed as a percentage of):
List I:
A. Simple average method
B. Ratio-to-trend method
C. Ratio-to-moving-average method
D. Link relative method
List II:
1. The figure of the preceding season
2. The centred moving average for that season
3. The trend value obtained by least squares
4. The average of the season averages (grand average)
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Answer A. A-4, B-3, C-2, D-1
Simple average: season average ÷ grand average × 100. Ratio to trend: Y ÷ trend × 100. Ratio to moving average: Y ÷ centred MA × 100. Link relative: current season ÷ previous season × 100.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q139 Time Series & Index Numbers
Consider the following statements about chain base index numbers:
1. Items can be added or dropped, and weights revised, more easily than in a fixed base index.
2. They are better than fixed base indices for comparing prices over a long period, such as 2005 with 2025.
Which of the statements given above is/are correct?
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Answer A. 1 only
In the chain base method each year's base is the preceding year, so new items and weights can be brought in easily. But link-relative errors cumulate when chained, so for long-period comparisons a fixed base index is preferred.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q140 Time Series & Index Numbers
Consider the following statements about the method of least squares for measuring trend:
1. Trend values can be obtained for every year of the series, including the first and the last.
2. If one more year's figure is added to the data, the whole trend equation has to be worked out again.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
A fitted equation gives a trend value for any year (no values are lost as in moving averages), but it is rigid: adding a year means refitting the line.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q141 Time Series & Index Numbers
A clerk earned ₹24,000 a month when the cost of living index was 120. The index has now risen to 150. What additional monthly allowance does he need to maintain his former standard of living?
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Answer D. ₹6,000
Income needed = present income × new index / old index = 24,000 × 150 / 120 = ₹30,000. Additional allowance = 30,000 − 24,000 = ₹6,000.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q142 Time Series & Index Numbers
Match List I (method of measuring trend) with List II (feature):
List I:
A. Freehand method
B. Semi-averages
C. Moving averages
D. Least squares
List II:
1. Data are divided into two equal parts
2. Minimises the sum of squared deviations of actual values from trend values
3. Highly subjective
4. No trend values for some periods at the beginning and the end
Select the correct answer using the code given below.
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Answer A. A-3, B-1, C-4, D-2
Freehand is subjective; semi-averages split data into two halves; moving averages lose values at both ends; least squares minimises Σ(Y − Yc)².
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
- Q143 Time Series & Index Numbers
The prices (in ₹) of three commodities in the base year are 10, 20 and 30 and in the current year 12, 25 and 38 respectively. What is the simple aggregative price index for the current year?
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Answer B. 125
Simple aggregative index = Σp1 / Σp0 × 100 = 75 / 60 × 100 = 125.
Source: Standard method; answer and every option computed and checked in Python
- Q144 Time Series & Index Numbers
The monthly trend equation of a company's sales (₹ lakh) is Yc = 80 + 1.5X, with origin January 2024 and X in months. The seasonal index for December is 120. The forecast of sales for December 2025 is
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Answer C. 137.4
Months from January 2024 to December 2025 = 23, so trend = 80 + 1.5 × 23 = 114.5. Forecast = 114.5 × 120 ÷ 100 = 137.4.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q145 Time Series & Index Numbers
If Laspeyres' price index is 144 and Paasche's price index is 121, what is Fisher's ideal index?
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Answer C. 132
Fisher's index is the geometric mean of Laspeyres and Paasche: √(144 × 121) = 12 × 11 = 132.
Source: Standard method; answer and every option computed and checked in Python
- Q146 Time Series & Index Numbers
The average link relatives of the four quarters are Q1 = 98, Q2 = 106, Q3 = 112 and Q4 = 88. Taking the chain relative of Q1 as 100, the chain relative of Q3 (before trend correction) is
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Answer D. 118.72
Chain relative = link relative × previous chain relative ÷ 100. Q2: 106; Q3: 106 × 112 ÷ 100 = 118.72.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q147 Time Series & Index Numbers
Using the data below, what is Paasche's price index?
Commodity Base-year price (₹) Base-year quantity Current-year price (₹) Current-year quantity Rice 8 10 10 12 Dal 15 4 18 5 Milk 5 20 6 15 Show answerHide answer
Answer C. 121.95
Paasche P01 = Σp1q1 / Σp0q1 × 100 = (120 + 90 + 90) / (96 + 75 + 75) × 100 = 300 / 246 × 100 = 121.95.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q148 Time Series & Index Numbers
Which method of computing seasonal indices is the most widely used and is generally regarded as the most satisfactory?
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Answer B. Ratio-to-moving-average method
The ratio-to-moving-average method eliminates T × C by the centred moving average before averaging the S × I ratios, so it is the most widely used; its drawback is the loss of values at the ends.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q149 Time Series & Index Numbers
The time reversal test is satisfied when (P01 is the index for period 1 on base 0 and P10 the index for period 0 on base 1, both as ratios):
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Answer B. P01 × P10 = 1
Fisher's time reversal test requires that the index computed forward and the index computed backward be reciprocals: P01 × P10 = 1.
Source: S.C. Gupta & V.K. Kapoor, Fundamentals of Applied Statistics, Index Numbers
- Q150 Time Series & Index Numbers
The seasonal index of the second quarter for a product is 80. This means that sales in the second quarter are typically
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Answer A. 20% below the average quarterly level
Seasonal indices are measured around 100: 80 means the quarter's normal level is 80% of an average quarter, i.e. 20% below it.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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