Mathematics — CBSE Class 10 board question

(i) True.

$2 \times 3 \times 5 \times 7 + 7 = 210 + 7 = 217$

Taking 7 as common: $= 7(2 \times 3 \times 5 + 1) = 7 \times 31$

Since 217 has factors other than 1 and itself (7 and 31), it is a composite number.

(ii) True.

$2 \times 3 \times 5 \times 7 + 1 = 210 + 1 = 211$

Wait — 211 is actually a prime number (not divisible by 2, 3, 5, 7, 11, 13; and $\sqrt{211} < 15$).

Correction: (ii) is FALSE. $2 \times 3 \times 5 \times 7 + 1 = 211$, which is a prime number, not composite.

Source: Chapter 1, Section 1.2 – The Fundamental Theorem of Arithmetic

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• For (i), factoring out 7 immediately shows it is composite — this is the key step examiners look for.
• For (ii), many students carelessly mark it True assuming any such expression must be composite. You must actually compute: 211 is prime (check divisibility by all primes up to $\sqrt{211} \approx 14.5$, i.e., 2, 3, 5, 7, 11, 13 — none divide 211). The answer is False.
• Always compute the value and verify; do not assume.