Solve Problem : Which one among the following is the greatest ? A) √201- √199  B) √101 - √99  C) √301 - √299  D) √401 - √399

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Q. Which one among the following is the greatest ? A) √201- √199  B) √101 - √99  C) √301 - √299  D) √401 - √399

Solⁿ

Trick: If the difference (gap) is the same, smaller numbers give a larger value. (Gap same থাকিলে, যিটো জোৰা সংখ্যা সৰু, সেইটোৰ মান ডাঙৰ।)​

Smaller n ⇒ smaller denominator ⇒ larger value.

Therefore, Option B is the greatest.

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MCQ

1. a¹⁷+b¹⁷ is divisible by which of the following ? (১. a¹⁷+b¹⁷ তলৰ কোনটোৰে বিভাজ্য ?)

(a) a + b   (b) a − b   (c) a² + b²    (d) None

Ans / উত্তৰ: (a) a + b

Explanation / ব্যাখ্যা: 17 is an odd number. Therefore, a¹⁷+b¹⁷ is divisible by a+b.

2. a²⁵ + b²⁵ is divisible by which of the following ? (২. a²⁵ + b²⁵ তলৰ কোনটোৰে বিভাজ্য ?)

(a) a+b   (b) a−b   (c) ab   (d) None

Ans / উত্তৰ: (a) a+b

Explanation / ব্যাখ্যা: 25 is odd. Hence, a²⁵ + b²⁵ is divisible by a + b.

3. a³¹ − b³¹ is divisible by which of the following ? (৩. a³¹ − b³¹ তলৰ কোনটোৰে বিভাজ্য ?)

(a) a + b   (b) a − b   (c) a² + b²   (d) None

Ans / উত্তৰ: (b) a − b

Explanation / ব্যাখ্যা: For any positive integer n, aⁿ - bⁿ is always divisible by a − b.

4. a⁵¹ + b⁵¹ is divisible by which of the following ? (৪. a⁵¹ + b⁵¹ তলৰ কোনটোৰে বিভাজ্য ?)

(a) a + b   (b) a − b  (c) a² - b²   (d) None

Ans / উত্তৰ: (a) a + b

Explanation / ব্যাখ্যা: 51 is an odd number. So, a⁵¹ + b⁵¹ is divisible by a + b.

5. a⁹⁹ − b⁹⁹ is divisible by which of the following ? (৫. a⁹⁹ − b⁹⁹ তলৰ কোনটোৰে বিভাজ্য ?)

(a) a + b  (b) a − b   (c) ab   (d) None

Ans / উত্তৰ: (b) a − b

Explanation / ব্যাখ্যা: aⁿ−bⁿ is always divisible by a − b, regardless of whether $n$ is odd or even.

Quick Rule / দ্ৰুত নিয়ম

• aⁿ + bⁿ → Divisible by (a+b) when $n$ is odd. (বিজোড় ঘাত + যোগ ⇒ (a+b) ৰে বিভাজ্য।)


• aⁿ - bⁿ → Always divisible by (a − b). (বিয়োগ থাকিলে সদায় $(a-b)$-ৰে বিভাজ্য।)