Mathematics — Standard (041) — CBSE Class 10 board question

(A) $\dfrac{7}{50}$

Total cards = 55 – 6 + 1 = 50. Perfect squares between 6 and 55: 9, 16, 25, 36, 49 = 5 numbers... wait — also check: $\sqrt{9}=3$, $\sqrt{16}=4$, $\sqrt{25}=5$, $\sqrt{36}=6$, $\sqrt{49}=7$ → 5 values. Hmm, but option (A) has 7 in numerator.

Re-check: cards numbered 6 to 55, perfect squares are 9, 16, 25, 36, 49 — that is 5 cards. None of the options match $\dfrac{5}{50}=\dfrac{1}{10}$... Option (C) $\dfrac{1}{10}$ = $\dfrac{5}{50}$.

Answer: (C) $\dfrac{1}{10}$

Total outcomes = 50; Perfect squares from 6–55: 9, 16, 25, 36, 49 → 5 favourable outcomes.

$$P = \frac{5}{50} = \frac{1}{10}$$

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• Cards range from 6 to 55 → total = 55 − 6 + 1 = 50.
• Perfect squares in this range: 9 (3²), 16 (4²), 25 (5²), 36 (6²), 49 (7²) → 5 values (8² = 64 > 55, so excluded).
• P = 5/50 = 1/10.
• Option (A) with 7 in the numerator would be correct only if the range were 1–50 (giving seven perfect squares: 1,4,9,16,25,36,49), a common distractor — don't confuse the range.