MCQ Questions

Q1: Probability — In a family, P(at least one parent ill) = 20%, P(father ill) = 12%, P(both ill) = 5%. What is P(mother ill)?

Answer: 13% Explanation: P(M) = P(A∪B) + P(A∩B) − P(F) = 20 + 5 − 12 = 13%.

Q2: Logic — Two rows of five students each face each other (Row-1, Row-2). Extremes are A/B/C/D; E is center of Row-1; F opposite E; J immediately right of A in Row-1; A and B in different rows and not opposite; I between F and B; H and C share a row. Which pair definitely shares a row?

Answer: G and D Explanation: Working through the seating constraints forces G and D into the same row as the only consistent assignment.

Q3: Vectors — Given vectors A and B, which statements are correct?

Answer: Dot product is 0 if orthogonal; cross product is 0 if collinear. Explanation: Orthogonality kills the dot product; collinearity (parallel or anti-parallel) kills the cross product.

Q4: Enrollment — 40 students; 12 in English, 27 in Chemistry, 9 in both. How many are in neither?

Answer: 10 Explanation: Either-class count = 12 + 27 − 9 = 30; neither = 40 − 30 = 10.

Q5: Charts — Over 1998-2002, how many of the 5 stocks (Warren Hays, Jackmail, Warren Bros, Brotherly Mail, Buffet Hastings) had a net overall price increase?

Answer: 3 Explanation: Compare 2002 vs 1998 per stock: Warren Hays 130 > 100, Warren Bros 175 > 100, Brotherly Mail 32 < 40, Jackmail 187 < 200, Buffet Hastings 129 < 132 — three net increases.