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Q. Which of the following numbers is not a perfect square ? প্ৰশ্ন: তলৰ কোনটো সংখ্যা বৰ্গ সংখ্যা (Perfect Square) নহয় ?

Options / বিকল্পসমূহ: A. 1225  B. 2025  C. 2525  D. 4225

Short Trick

A perfect square ending in 25 must have its first part multiplied consecutively.·         

• 1225 = 35² (3 × 4 = 12)


• 2025 = 45² (4 × 5 = 20)


• 4225 = 65² (6 × 7 = 42)


• 2525 For a square ending in 25, if last digit is 5, check: 5 × 6 = 30 ≠ 25

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Q. How many perfect squares are there between 100 and 200 ? (100 আৰু 200ৰ মাজত কিমানটা পূৰ্ণ বৰ্গ (Perfect Square) আছে ?)

Options / বিকল্পসমূহ: (a) 7 (b) 4 (c) 6 (d) 5

Tricks

√100 = 10,  √200 ≈ 14.14

Now count the integers between 10 and 14.14: (এতিয়া 10 আৰু 14.14ৰ মাজত থকা পূৰ্ণ সংখ্যাবোৰ গণনা কৰোঁ: 11, 12, 13, 14

Total integers = 4 (মুঠ পূৰ্ণ সংখ্যা = 4)

Therefore, the perfect squares are: সেয়ে পূৰ্ণ বৰ্গসমূহ হ'ল - 11² = 121, 12² = 144, 13² = 169, 14² = 196

Total / মুঠ = 4

Ans / উত্তৰ: (b) 4

Q. A, B, C, and D are four consecutive even numbers. If A + D = 120, then what is the sum of all four numbers ? (প্ৰশ্ন: A, B, C, D চাৰিটা ক্ৰমাগত জোৰ সংখ্যা। যদি A + D = 120, তেন্তে চাৰিওটা সংখ্যাৰ মুঠ যোগফল কিমান ?)

Trick: For four consecutive even numbers: A + D = B + C

Given: A + D = 120 

Therefore, B + C = 120 

So, A+B+C+D = (A+D) + (B+C) = 120 + 120 = $$240$$

Ans: B. 240

Shortcut: Sum = Average × Number of Terms

(A+D)/2 × 4 = 120/2 × 4 = 60 × 4 = 240