GPSC (Gujarat) - MCQ Practice Questions

Using Venn diagram: Students playing at least one game = 25 + 20 - 10 = 35. Students playing neither = 40 - 35 = 5.

Mother's brother = Uncle. Uncle's daughter = Cousin. So she is Rajesh's cousin.

From 1st to 25th, there are 24 days. 24 ÷ 7 = 3 weeks + 3 days. Monday + 3 days = Thursday.

From given conditions: A > B, D > C, B > C. Combining: A > B > C and D > C. So C is definitely the shortest.

From x + 2y = 8, x = 8 - 2y. Substitute in 3x + 5y = 21: 3(8-2y) + 5y = 21. 24 - 6y + 5y = 21. y = 3, x = 2.

Profit = 950 - 800 = 150. Profit % = ($\frac{150}{800}$) × 100 = 18.75%.

Each letter is replaced by the letter that is 9 positions back. M→N, O→L, B→D, I→B, L→J, E→D.

Pattern: 1×2, 2×3, 3×4, 4×5, 5×6, 6×7. So the next term is 6×7 = 42.

P(both red) = ($\frac{4}{10}$) × ($\frac{3}{9}$) = $\frac{12}{90}$ = $\frac{2}{15}$.

Defective units = 2% of 500 = 10. Good units = 500 - 10 = 490.

Differences: 5, 7, 9, 11, 13. Pattern: n(n+2). For n=6: 6×8 = 48.

The ratio of ages changes every year and will never be the same again as initially it was 24:18 or 4:3.

Using Pythagoras theorem: Displacement = √(15² + 12²) = √(225 + 144) = √369 ≈ 19.2 ≈ 19 km.

If 70% = 280, then 100% = (280 × 100)/70 = 400.

Each letter is shifted by +1 position in the alphabet. R→S, A→B, J→K, etc. Applying the same to GUJARAT: G→H, U→V, J→K, A→B, R→S, A→B, T→U = HVKBSBU

These are perfect squares in reverse: 12², 11², 10², 9², 8² = 64. The pattern decreases by 1 each time in the base.

This is a pure text question involving basic logic and set relationships.

We are given two premises:

1. All roses are flowers.

2. Some flowers are red.

We need to determine what must be true — that is, what is guaranteed to follow from these premises alone, regardless of any other assumptions.

Option A ("All roses are red") does not have to be true. The red flowers mentioned in premise 2 could be tulips or daisies — none of them need to be roses.

Option B ("Some roses are red") also does not have to be true, for the same reason: the red flowers could be entirely non-rose flowers, leaving all roses non-red.

Option C ("No roses are red") is not guaranteed either — it is possible that some roses are red, so this cannot be asserted as a necessary truth.

Option D ("Some flowers are not red") must be true. Here is why: premise 2 tells us only that *some* flowers are red, which means the statement does not cover all flowers. Since roses are flowers (by premise 1), and roses need not be red (as established above), there exists at least a logical possibility — in fact a necessity given the structure — that some flowers fall outside the "red" category. More precisely, "some flowers are red" is not the same as "all flowers are red," so it directly implies that the set of flowers is not entirely red, meaning some flowers are not red.

Therefore, the answer that must be true based solely on the given premises is D: Some flowers are not red.

8 km East and 8 km West cancel each other. Only 6 km North remains. Distance from starting point = 6 km

Using Venn diagram: Hindi only = 30-12 = 18, Gujarati only = 25-12 = 13, Both = 12. Total = 18+13+12 = 43. Neither = 50-43 = 7

The pattern becomes clear by examining the differences between consecutive terms:

The differences are consecutive odd numbers: $3,5,7,9,\dots$ The next difference must be $11$.

Alternatively, notice that each term equals one more than a perfect square:

So the $n$-th term is $n^2+1$. For $n=6$: