a) Original research studies b) Publicly available databases c) Personal interviews d) Laboratory experiments

Answer: B

Secondary data = data already collected by someone else, for another purpose — published reports, government databases, journals, census records. Options (a), (c), (d) all describe you generating fresh data → that is primary data.

a) Surveying existing research papers b) Reviewing census data c) Analyzing historical records d) Conducting interviews and surveys

Answer: D

Only (d) generates new, first-hand data. The other three all re-use data that already exists → secondary. ⭐ The rule: if you go out and get it yourself → primary. If you look it up → secondary.

a. Questionnaires collect data by asking people to respond to a set of questions b. Validity, reliability and response rate depend largely on the design of your questions c. Collect the data without a pilot test of all questionnaires d. Consider the wording of individual questions prior to the order in which they appear

a) a and b b) b and c c) a and d d) b and d

Answer: A

✅ (a) — the definition of a questionnaire. ✅ (b) — design drives validity, reliability and response rate. ❌ (c) — a pilot test is essential, never skipped. This is the giveaway wrong statement. ❌ (d) — reversed. Best practice is to settle the ORDER/flow first, then refine individual wording. Since (c) is clearly wrong, any option containing it dies — that leaves A and C, and (d) being wrong settles it.

a) Tabulation allows presentation of complicated data b) Tabulation is a prerequisite for diagrammatic representation c) Statistical analysis necessarily involves tabulation d) Tabulation facilitates comparison between rows and not columns

Answer: D

A table has both rows and columns, and its whole purpose is comparison in both directions. Saying "rows and not columns" is plainly false. The other three are true: tables simplify complex data, you must tabulate before you can draw a diagram, and analysis presupposes tabulated data. ⚠️ Read the stem carefully — it asks for the FALSE one.

a) a, b, c, d b) a, d, b, c c) d, c, b, a d) c, b, d, a

Answer: C

Step 1 — Mean = (4+8+7+5+3+7+7+3) ÷ 8 = 44 ÷ 8 = 5.5 Step 2 — Sort: 3, 3, 4, 5, 7, 7, 7, 8 → n is even, so Median = (5+7)/2 = 6 Step 3 — Mode = the most frequent value = 7 (appears 3 times) Step 4 — n = 8

Decreasing → d, c, b, a ✓

P: Probabilities can never add up to more than one Q: Probabilities of mutually exclusive events always add up to one R: Probabilities can never be zero S: Probabilities are always positive

a) P and S b) S only c) P, R and S d) P, Q, R and S

Answer: A

✅ P — the total probability of a sample space is exactly 1; it cannot exceed it. ✅ S — probability is never negative; 0 ≤ P(A) ≤ 1. ❌ Q — mutually exclusive events sum to 1 only if they are also EXHAUSTIVE. Two mutually exclusive events can easily sum to less than 1. ❌ R — an impossible event has probability exactly 0. (e.g. rolling a 7 on a die.)

Core rules to carry: 0 ≤ P(A) ≤ 1 · impossible = 0 · certain = 1 · P(A∪B) = P(A) + P(B) − P(A∩B) · mutually exclusive → P(A∩B) = 0

a. Boys who play Kho-Kho · b. Girls who play cricket · c. Boys who play cricket · d. Total number of boys (1 = 2 · 2 = 10 · 3 = 14 · 4 = 40 · 5 = 60)

a) a-1, b-2, c-3, d-5 b) a-3, b-1, c-2, d-4 c) a-3, b-1, c-4, d-5 d) a-3, b-1, c-2, d-5

Answer: D

Step 1 — Total boys = 100 − 40 girls = 60 → d-5 ✓ Step 2 — Boys in Kho-Kho = 27 total − 13 girls = 14 → a-3 ✓ Step 3 — Girls' places: Kho-Kho 13 + Volleyball (33 − 13 boys = 20) + Football (28 − 23 boys = 5) = 38 → remaining girls = 40 − 38 = 2 girls play cricket → b-1 ✓ Step 4 — Boys in cricket = 12 − 2 = 10 → c-2 ✓

⚠️ The printed paper reads "23 boys play cricket" — that is an OCR/print error; only 12 students picked cricket at all. It must be football, and the answer key confirms it: the grid balances perfectly to 60/40/100.

a) 5 b) 10.5 c) 20 d) 15

Answer: C — 20

Step 1 — Flip the quantity index to the right base. It is given as 1990 with base 1993; you need 1993 with base 1990, so take the reciprocal: Q(1993/1990) = 1 ÷ 0.5 = 2 Step 2 — Value Index = Price Index × Quantity Index = 10 × 2 = 20 ✓

Formulas to know:

Fisher's is called "ideal" because it satisfies BOTH the time-reversal and factor-reversal tests.

a) Defining boundaries b) Simultaneity c) Employment of census-workers d) Homogeneity

Answer: B

⭐ Simultaneity = the count refers to one single reference moment for the whole country, so nobody is counted twice or missed. The others describe administrative activities involved in running a census, not defining features of it.

The features of a census: ⭐ Simultaneity · Universality (everyone counted) · Periodicity (every 10 years in India) · Government sponsorship · Individual enumeration · Defined territory

a. Gross Reproduction Rate · b. Age-Specific Fertility Rate · c. Net Reproduction Rate · d. Maternal Mortality Rate (1 = reduces the reproduction rates · 2 = affected by mortality rates · 3 = has modal value between 20 and 25 · 4 = measured per 1000 live births · 5 = measures the number of daughters over a lifetime)

a) a-5, b-3, c-2, d-1 b) a-5, b-3, c-4, d-2 c) a-5, b-3, c-2, d-4 d) a-3, b-5, c-2, d-1

Answer: C

• a → 5 — GRR = average number of daughters a woman would bear over her reproductive life, assuming no mortality
• b → 3 — ASFR peaks in the 20–25 age group (the modal childbearing age)
• c → 2 — ⭐ NRR is GRR adjusted for mortality, so it is affected by mortality rates. NRR ≤ GRR always
• d → 4 — MMR is expressed per 1,000 (or 1,00,000) live births

⭐ The one distinction that matters: GRR ignores mortality · NRR accounts for it.

a) It decreases as sample size increases b) It does not depend on population size c) It cannot be reduced by an appropriate sampling plan d) It cannot be measured and controlled in a probability sample survey

Answer: A

Sampling error = the difference between the sample result and the true population value, caused by studying only a part of the population. ⭐ Larger sample → smaller sampling error (it approaches zero as the sample approaches the whole population). (b), (c), (d) are all false — it does relate to the population, it can be reduced by good design, and in a probability sample it can be measured. ⚠️ Note: a census has no sampling error (but may still have non-sampling error).

a) Experiments b) Personal Interview c) Questionnaire d) Government Publications

Answer: D

Experiments, interviews and questionnaires all generate fresh, first-hand data → primary. Government publications already exist → secondary.

a) {1,2,3,4,5,6,7} b) {5,6,7} c) {1,2,3,4} d) {1,2,5,6,7}

Answer: D

Symmetric difference A △ B = (A − B) ∪ (B − A) = elements in exactly one set, excluding the common ones. A − B = {1, 2} · B − A = {5, 6, 7} → A △ B = {1, 2, 5, 6, 7} ✓ (Common elements {3,4} are removed — that is the whole point.)

a) 300 b) 350 c) 400 d) 450

Answer: A

A 3-month moving average for January uses the three months immediately before it — Oct, Nov, Dec: (200 + 300 + 400) ÷ 3 = 900 ÷ 3 = 300 ✓ (September is dropped — it falls outside the 3-month window.)

a) 1/2 b) 1½ c) 2½ d) 3½

Answer: A

Addition rule: P(M ∪ P) = P(M) + P(P) − P(M ∩ P) Count first: 30 + 20 − 10 = 40 students take at least one. P = 40 / 80 = 1/2 ✓ ⚠️ Options (b), (c), (d) all exceed 1 — impossible for a probability. You could eliminate three options without any calculation.

a) 9.4 b) 11.4 c) 13.4 d) 15.4

Answer: B

Distance = √[(x₂−x₁)² + (y₂−y₁)²] = √[(9−2)² + (11−2)²] = √[49 + 81] = √130 ≈ 11.40 ✓

a) Tends to become jagged b) Remains the same c) Tends to become increasingly smooth d) Varies if data becomes more reliable

Answer: C

As classes become more numerous and narrower, the polygon's line segments shorten and the outline smooths into a frequency CURVE. This is the conceptual bridge from a histogram to a continuous distribution.

a) 60 b) 70 c) 80 d) 90

Answer: B

⭐ For two INDEPENDENT attributes: (AB) = (A) × (B) ÷ N = (100 × 140) ÷ 200 = 14,000 ÷ 200 = 70 ✓

Also worth knowing:

• If (AB) > (A)(B)/N → the attributes are positively associated
• If (AB) < (A)(B)/N → negatively associated
• If equal → independent

a) 97.6 b) 96.7 c) 98.2 d) 95.3

Answer: B

As computed by this paper: (men ÷ women) × 100 = (151,781,326 ÷ 156,964,212) × 100 = 96.70 ✓ ⚠️ Caution: India's official sex ratio is stated as females per 1,000 males (Census 2011 = 943). This question used the inverse convention — read the options to see which convention is intended.

a) Kerala b) Goa c) Nagaland d) Tamil Nadu

Answer: C

Nagaland was the only state with negative decadal growth (−0.58%) in Census 2011 — the standout fact from that census.

Census 2011 numbers worth memorising: population 121.09 crore · decadal growth 17.7% · density 382/km² · sex ratio 943 · literacy 74.04% · most populous state UP · least populous Sikkim · highest literacy Kerala · lowest Bihar