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Real Numbers — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsReal Numbers1 Mark
MCQ
Statement-1 $(A)$: If 11 divides 627264, then 11 divides 792.
Statement-2 $(R)$ : Let $p$ be a prime number and a be a positive integer, if $p$ divides $a^2$, then pdivides $a$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
✓

Answer

Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Using Theorem 2 (page 1.3 of main book), we find that the statement- 2 is true. We observe that 11 is prime and it divides 627264 . Therefore, by using statement-2, 11 divides $\sqrt{627264}=792$. So, statement-1 is also true. Also, statement-2 is a correct explanation for statement-1.

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