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নিচে পুরোটা copy-paste করার মতো code দিলাম। LaTeX-এর শুরুতে 

*** QuickLaTeX cannot compile formula:
</code> এবং শেষে <code>

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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রাখা হয়েছে। অন্য লেখাগুলো পরিবর্তন করিনি।

*** QuickLaTeX cannot compile formula:

# রাজশাহী বোর্ড-২০২৫
### বিষয়: গণিত (বহুনির্বাচনি অভীক্ষা)
**বিষয় কোড: ১০৯** | সময়: ৩০ মিনিট | পূর্ণমান: ৩০

১. বৃত্তে অন্তর্লিখিত সামান্তরিক একটি —
(ক) রম্বস (খ) আয়ত (গ) বর্গ (ঘ) ট্রাপিজিয়াম

২. কোনো ত্রিভুজের কয়টি বহিঃবৃত্ত অঙ্কন করা যায়?
(ক) ১টি (খ) ২টি (গ) ৩টি (ঘ) ৪টি

**নিচের তথ্যের আলোকে ৩ ও ৪নং প্রশ্নের উত্তর দাও :**

| শ্রেণিব্যাপ্তি | ২১ - ৩০ | ৩১ - ৪০ | ৪১ - ৫০ | ৫১ - ৬০ |
| :--- | :--- | :--- | :--- | :--- |
| গণসংখ্যা | ৬ | ১৬ | ২০ | ১৪ |

৩. মধ্যক নির্ণয়ের জন্য [latex]F_c

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 এর মান নিচের কোনটি?

(ক) ১৬ (খ) ২০ (গ) ২২ (ঘ) ৪২


৪. প্রদত্ত উপাত্তের প্রচুরক কত?

(ক) ৪৭ (খ) ৪৫ (গ) ৩৭ (ঘ) ৩৫


৫. বর্গক্ষেত্রের প্রতিসাম্য রেখা কয়টি?

(ক) ২ (খ) ৪ (গ) ৬ (ঘ) ৮


৬. কোনো ধারার ১ম পদ ৮, সাধারণ অন্তর ২ হলে—

i. ধারাটি = ৮ + ১০ + ১২ + ........

ii. ধারাটির দশম পদ = ২৬

iii. ধারাটির ১ম ১৫টি পদের সমষ্টি = ৩০০

নিচের কোনটি সঠিক?

(ক) i ও ii (খ) i ও iii (গ) ii ও iii (ঘ) i, ii ও iii


৭. 


*** QuickLaTeX cannot compile formula:
\log_3(3\sqrt{3})

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 = কত?

(ক) \frac{1}{3} (খ) \frac{2}{3} (গ) \frac{4}{3} (ঘ) \frac{3}{2}


৮. নিচের কোনটি বিচ্ছিন্ন চলক?

(ক) বয়স (খ) উচ্চতা (গ) ওজন (ঘ) জনসংখ্যা


৯. নিচের কোনটি স্বাভাবিক সংখ্যা?

(ক) 


*** QuickLaTeX cannot compile formula:
-3

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 (খ) \sqrt{3} (গ) \frac{5}{2} (ঘ) 3


১০. 


*** QuickLaTeX cannot compile formula:
\{4, 5, 6, 7, 8\}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 সেটটির প্রকৃত উপসেট কয়টি?

(ক) ১০ (খ) ৩১ (গ) ৩২ (ঘ) ৩৩


১১. 


*** QuickLaTeX cannot compile formula:
a^2 + \frac{1}{a^2} = 18

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 হলে—

i. 


*** QuickLaTeX cannot compile formula:
a - \frac{1}{a} = 4

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10005 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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ii. 


*** QuickLaTeX cannot compile formula:
(a + \frac{1}{a})^2 = 20

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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iii. 


*** QuickLaTeX cannot compile formula:
a^3 - \frac{1}{a^3} = 76

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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নিচের কোনটি সঠিক?

(ক) i ও ii (খ) i ও iii (গ) ii ও iii (ঘ) i, ii ও iii


১২. 


*** QuickLaTeX cannot compile formula:
\tan \theta = \sqrt{3}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 হলে 


*** QuickLaTeX cannot compile formula:
\sec \theta =

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 কত?

(ক) \frac{1}{2} (খ) \frac{2}{\sqrt{3}} (গ) 


*** QuickLaTeX cannot compile formula:
\sqrt{2}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 (ঘ) ২


১৩. ৩০ সে.মি. ব্যাসবিশিষ্ট বৃত্তের কেন্দ্র হতে ৯ সে.মি. দূরে অবস্থিত জ্যা এর দৈর্ঘ্য কত সে.মি.?

(ক) ১২ (খ) ২১ (গ) ২৪ (ঘ) ৪২


১৪. 


*** QuickLaTeX cannot compile formula:
x = -5

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 হলে 


*** QuickLaTeX cannot compile formula:
3x - 2y = 5

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 সমীকরণ হতে প্রাপ্ত বিন্দুটি কোন চতুর্ভাগে অবস্থিত?

(ক) প্রথম (খ) দ্বিতীয় (গ) তৃতীয় (ঘ) চতুর্থ


১৫. দুইটি সংখ্যার অনুপাত ২ : ৩ এবং তাদের ল.সা.গু ২৪ হলে সংখ্যা দুইটির গ.সা.গু কত?

(ক) ৪ (খ) ২ (গ) ৪ (ঘ) ১


১৬. একটি নির্দিষ্ট চতুর্ভুজ অঙ্কনের জন্য কয়টি স্বতন্ত্র উপাত্তের প্রয়োজন?

(ক) ২ (খ) ৩ (গ) ৪ (ঘ) ৫


১৭. সমকোণী ত্রিভুজের সূক্ষ্মকোণদ্বয়ের পার্থক্য ১০° হলে উক্ত কোণদ্বয়ের বৃহত্তম কোণটির মান কত?

(ক) ৪০° (খ) ৫০° (গ) ৫৫° (ঘ) ৮০°


১৮. 


*** QuickLaTeX cannot compile formula:
2.8^{x-1} = 1

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 হলে x এর মান কত?

(ক) \frac{2}{3} (খ) \frac{3}{4} (গ) \frac{4}{3} (ঘ) \frac{3}{2}


১৯. 


*** QuickLaTeX cannot compile formula:
f(x) = x^2 - 5x - 6

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 হলে x এর কোন মানের জন্য 


*** QuickLaTeX cannot compile formula:
f(x) = 0

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10004 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 হবে?

(ক) ২, -৩ (খ) ১, -৬ (গ) -১, ৬ (ঘ) -২, ৩


২০. ABC সমবাহু ত্রিভুজে 


*** QuickLaTeX cannot compile formula:
BD = 2

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10003 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 সে.মি. হলে AD এর দৈর্ঘ্য কত সে.মি.?

(ক) ৪\sqrt{3} (খ) ৪\sqrt{3} (গ) ২\sqrt{3} (ঘ) \sqrt{3}


২১. সুষম ষড়ভুজের শীর্ষবিন্দুতে উৎপন্ন শীর্ষকোণের পরিমাণ কত?

(ক) ১৩৫° (খ) ১২০° (গ) ১০৮° (ঘ) ৯০°


২২. ০.০০০০০৭৮৬ এর সাধারণ লগারিদমের পূর্ণক কত?

(ক) ৬ (খ) ৫ (গ) ৫ (ঘ) ৬


২৩. ৮ সে.মি. ও ৬ সে.মি. ব্যাস বিশিষ্ট দুইটি বৃত্ত পরস্পরকে অন্তঃস্পর্শ করলে, এদের কেন্দ্রদ্বয়ের মধ্যবর্তী দূরত্ব কত?

(ক) ১৪ সে.মি. (খ) ৭ সে.মি. (গ) ২ সে.মি. (ঘ) ১ সে.মি.


২৪. 


*** QuickLaTeX cannot compile formula:
\sin(90^\circ - \theta) = \frac{\sqrt{3}}{2}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 হলে 


*** QuickLaTeX cannot compile formula:
\theta =

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 কত?

(ক) ৩০° (খ) ৪৫° (গ) ৬০° (ঘ) ৯০°


২৫. পরিসীমা ও একটি কোণ দেওয়া থাকলে নিচের কোনটি আঁকা সম্ভব?

(ক) রম্বস (খ) আয়ত (গ) সামান্তরিক (ঘ) ট্রাপিজিয়াম


২৬. 


*** QuickLaTeX cannot compile formula:
\Delta LMN

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 ও 


*** QuickLaTeX cannot compile formula:
\Delta PQR

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
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 সদৃশ এবং 


*** QuickLaTeX cannot compile formula:
MN : QR = 4 : 5

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 হলে 


*** QuickLaTeX cannot compile formula:
\Delta PQR : \Delta LMN =

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 কত?

(ক) ১৬ : ২৫ (খ) ৪ : ৫ (গ) ৫ : ৪ (ঘ) ২৫ : ১৬


২৭. একটি সমবৃত্তভূমিক বেলনের ভূমির ব্যাসার্ধ ৫ সে.মি. এবং উচ্চতা ৬ সে.মি. হলে বেলনটির—

i. ভূমির ক্ষেত্রফল = 


*** QuickLaTeX cannot compile formula:
25\pi

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 বর্গ সে.মি.

ii. আয়তন = 


*** QuickLaTeX cannot compile formula:
150\pi

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 ঘন সে.মি.

iii. বক্রতলের ক্ষেত্রফল = 


*** QuickLaTeX cannot compile formula:
60\pi

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 বর্গ সে.মি.

নিচের কোনটি সঠিক?

(ক) i ও ii (খ) i ও iii (গ) ii ও iii (ঘ) i, ii ও iii


২৮. 


*** QuickLaTeX cannot compile formula:
\sqrt{4x-7} + 1 = 0

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10004 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 সমীকরণটির সমাধান সেট নিচের কোনটি?

(ক) 


*** QuickLaTeX cannot compile formula:
\emptyset

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
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 (খ) 


*** QuickLaTeX cannot compile formula:
\{\frac{1}{2}\}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 (গ) 


*** QuickLaTeX cannot compile formula:
\{\emptyset\}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10005 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 (ঘ) 


*** QuickLaTeX cannot compile formula:
\{2\}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10007 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


২৯. 


*** QuickLaTeX cannot compile formula:
\frac{1 + \cot^2 A}{1 - \cos^2 A} =

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 কোনটি?

(ক) 


*** QuickLaTeX cannot compile formula:
\text{cosec}^4 A

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 (খ) 


*** QuickLaTeX cannot compile formula:
\sin^4 A

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 (গ) 


*** QuickLaTeX cannot compile formula:
\cot^4 A

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 (ঘ) 


*** QuickLaTeX cannot compile formula:
\cos^4 A

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


৩০. সমকোণী ত্রিভুজের ৫০° কোণ অঙ্কনের ক্ষেত্রে নিচের কোনটি সঠিক?

(ক) ভূমি > লম্ব (খ) ভূমি < লম্ব (গ) ভূমি = লম্ব (ঘ) লম্ব = অতিভুজ


---


---


# রাজশাহী বোর্ড-২০২৫

### বিষয়: গণিত (সৃজনশীল)

**সময়: ২ ঘণ্টা ৩০ মিনিট | পূর্ণমান: ৭০**


#### ক বিভাগ—বীজগণিত


১। 


*** QuickLaTeX cannot compile formula:
x^4 + x^{-4} = 119

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এবং 


*** QuickLaTeX cannot compile formula:
y = \sqrt{5} - \sqrt{2}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10004 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


.


(ক) যদি 


*** QuickLaTeX cannot compile formula:
(2p + q, 5) = (7, q)

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 হয়, তবে 


*** QuickLaTeX cannot compile formula:
(p, q)

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এর মান নির্ণয় কর। [২]


(খ) প্রমাণ কর যে, 


*** QuickLaTeX cannot compile formula:
x^2 - 3x - 1 = 0

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 যখন 


*** QuickLaTeX cannot compile formula:
x > 0

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [৪]


(গ) 


*** QuickLaTeX cannot compile formula:
\frac{y^6 + 27}{y^3}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এর মান নির্ণয় কর। [৪]


২। (i) 


*** QuickLaTeX cannot compile formula:
A = \frac{4^{a+1}}{(2^{a+1})^{a-1}} \div \frac{2^{a+1}}{(2^a)^{a-1}}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


, 


*** QuickLaTeX cannot compile formula:
B = \log_{\sqrt{3}} 9

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10003 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


.


(ii) 


*** QuickLaTeX cannot compile formula:
\frac{p^2 + q^2}{q^2 + r^2} = \frac{(p - q)^2}{(q - r)^2}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


.


(ক) সরল কর: 


*** QuickLaTeX cannot compile formula:
(3c^{-1} + 2d^{-1})^{-1}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [২]


(খ) দেখাও যে, 


*** QuickLaTeX cannot compile formula:
A = B

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [৪]


(গ) প্রমাণ কর যে, 


*** QuickLaTeX cannot compile formula:
p, q, r

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 ক্রমিক সমানুপাতী। [৪]


৩। 


*** QuickLaTeX cannot compile formula:
7 + f + g + 448 + h

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10002 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 একটি গুণোত্তর ধারা।


(ক) 


*** QuickLaTeX cannot compile formula:
125 + 25 + 5 + ..........

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 ধারাটির কোন পদ 


*** QuickLaTeX cannot compile formula:
\frac{1}{125}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


? [২]


(খ) 


*** QuickLaTeX cannot compile formula:
g

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এবং 


*** QuickLaTeX cannot compile formula:
h

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এর মান নির্ণয় কর। [৪]


(গ) প্রদত্ত ধারাটির প্রথম পদকে ১ম পদ এবং সাধারণ অনুপাতকে সাধারণ অন্তর ধরে একটি সমান্তর ধারা গঠন কর এবং তার প্রথম 


*** QuickLaTeX cannot compile formula:
n

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 সংখ্যক পদের সমষ্টি ৯৮৭ হলে, 


*** QuickLaTeX cannot compile formula:
n

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


-এর মান নির্ণয় কর। [৪]


#### খ বিভাগ—জ্যামিতি


৪। 


*** QuickLaTeX cannot compile formula:
\Delta ABC

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


-এ AB, AC ও BC বাহুর মধ্যবিন্দু যথাক্রমে P, Q, R.


(ক) একটি বৃত্তের ক্ষেত্রফল 


*** QuickLaTeX cannot compile formula:
12\pi

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 বর্গ সে.মি. হলে, এর ব্যাস নির্ণয় কর। [২]


(খ) প্রমাণ কর যে, 


*** QuickLaTeX cannot compile formula:
PQ \parallel BC

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এবং 


*** QuickLaTeX cannot compile formula:
PQ = \frac{1}{2} BC

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [৪]


(গ) প্রমাণ কর যে, 


*** QuickLaTeX cannot compile formula:
AB + AC > 2AR

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [৪]


৫। [চিত্র সম্পর্কিত প্রশ্ন: একটি বৃত্তের ভেতরে দুটি স্পর্শক ও জ্যা সংক্রান্ত জ্যামিতিক চিত্র দেওয়া আছে]


(ক) প্রমাণ কর যে, বৃত্তের ব্যাসই বৃহত্তম জ্যা। [২]


(খ) প্রমাণ কর যে, 


*** QuickLaTeX cannot compile formula:
\angle DOE = 2\angle DFE

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [৪]


(গ) প্রমাণ কর যে, CO রেখাংশ স্পর্শ জ্যা DE এর লম্ব সমদ্বিখণ্ডক। [৪]


৬। একটি ত্রিভুজের ভূমি 


*** QuickLaTeX cannot compile formula:
a = 4

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 সে.মি., ভূমি সংলগ্ন একটি কোণ 


*** QuickLaTeX cannot compile formula:
\angle x = 60^\circ

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এবং অপর দুই বাহুর সমষ্টি 


*** QuickLaTeX cannot compile formula:
S = 9

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 সে.মি.।


(ক) রম্বসের একটি বাহু a এবং একটি কোণ 


*** QuickLaTeX cannot compile formula:
\angle x

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 হলে, রম্বসটি আঁক। [২]


(খ) অঙ্কনের চিহ্ন ও বিবরণসহ ত্রিভুজটি অঙ্কন কর। [৪]


(গ) 


*** QuickLaTeX cannot compile formula:
\frac{S}{2}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 বাহুবিশিষ্ট সমবাহু ত্রিভুজের অন্তর্বৃত্ত অঙ্কন কর। [৪]


#### গ বিভাগ—ত্রিকোণমিতি ও পরিমিতি


৭। 


*** QuickLaTeX cannot compile formula:
a = \sec \theta, b = \text{cosec} \theta

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এবং 


*** QuickLaTeX cannot compile formula:
c = \tan \theta

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


।


(ক) দেখাও যে, 


*** QuickLaTeX cannot compile formula:
b\sqrt{a^2 - 1} = a

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [২]


(খ) 


*** QuickLaTeX cannot compile formula:
a + c = x

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10003 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 হলে, প্রমাণ কর যে, 


*** QuickLaTeX cannot compile formula:
\sin \theta = \frac{x^2 - 1}{x^2 + 1}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


. [৪]


(গ) 


*** QuickLaTeX cannot compile formula:
\frac{1}{a} + \frac{1}{b} = \sqrt{2}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 হলে, \theta এর মান নির্ণয় কর। [৪]


৮। (i) একটি গাছ ঝড়ে ভেঙে গিয়ে সম্পূর্ণ বিচ্ছিন্ন না হয়ে ভাঙা অংশ ভূমির সাথে ৩০° কোণ উৎপন্ন করে গাছের গোড়া থেকে 


*** QuickLaTeX cannot compile formula:
10\sqrt{3}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10001 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 মিটার দূরে ভূমিকে স্পর্শ করে।


(ii) P এবং Q দুইটি স্থানের মধ্যবর্তী কোনো স্থানে একটি উড়োজাহাজ উড়ছে। উড়োজাহাজের অবস্থানে P ও Q এর অবনতি কোণ যথাক্রমে ৬০° ও ৪৫°।


(ক) 


*** QuickLaTeX cannot compile formula:
A = 60^\circ

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10002 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 হলে, 


*** QuickLaTeX cannot compile formula:
3\sin A - 4\sin^3 A

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 এর মান নির্ণয় কর। [২]


(খ) সম্পূর্ণ গাছটির দৈর্ঘ্য নির্ণয় কর। [৪]


(গ) 


*** QuickLaTeX cannot compile formula:
PQ = 1200

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timed out after 10000 milliseconds
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37


 মিটার হলে, ভূমি থেকে উড়োজাহাজের উচ্চতা নির্ণয় কর। [৪]


৯। (i) একটি সমবাহু ত্রিভুজের বাহুর দৈর্ঘ্য ৪ মিটার বাড়ালে এর ক্ষেত্রফল 16\sqrt{3} বর্গমিটার বেড়ে যায়।


(ii) একটি লোহার পাইপের ভিতরের ও বাইরের ব্যাস যথাক্রমে ১৪ সে.মি. ও ১৬ সে.মি. এবং পাইপের উচ্চতা ৪.৫ মি.।


(ক) একটি ঘনকের সম্পূর্ণ পৃষ্ঠের ক্ষেত্রফল ৩০০ বর্গ সে.মি.। এর কর্ণের দৈর্ঘ্য নির্ণয় কর। [২]


(খ) সমবাহু ত্রিভুজটির পরিসীমা নির্ণয় কর। [৪]


(গ) ১ ঘন সে.মি. লোহার ওজন ৭.২ গ্রাম হলে, পাইপের লোহার ওজন নির্ণয় কর। [৪]


#### ঘ বিভাগ—পরিসংখ্যান


১০। ডি.এস উচ্চ বিদ্যালয়ের দশম শ্রেণির ৬০ জন শিক্ষার্থীর গণিতে প্রাপ্ত নম্বরের গণসংখ্যা নিবেশন সারণি নিম্নরূপ:


| প্রাপ্ত নম্বর | ৪৪-৪৮ | ৪৯-৫৩ | ৫৪-৫৮ | ৫৯-৬৩ | ৬৪-৬৮ | ৬৯-৭৩ |

| :--- | :--- | :--- | :--- | :--- | :--- | :--- |

| গণসংখ্যা | ৪ | ১১ | ১৩ | ১৯ | ৮ | ৫ |


(ক) প্রচুরক শ্রেণির পূর্ববর্তী শ্রেণির মধ্যমান নির্ণয় কর। [২]


(খ) সারণি থেকে সংক্ষিপ্ত পদ্ধতিতে গড় নির্ণয় কর। [৪]


(গ) বিবরণসহ প্রদত্ত উপাত্তের গণসংখ্যা বহুভুজ অঙ্কন কর। [৪]


১১। নিচে একটি গণসংখ্যা নিবেশন সারণি দেওয়া হলো:


| শ্রেণিব্যাপ্তি | ৩১-৪০ | ৪১-৫০ | ৫১-৬০ | ৬১-৭০ | ৭১-৮০ | ৮১-৯০ | ৯১-১০০ |

| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |

| গণসংখ্যা | ৪ | ৬ | ৮ | ১২ | ৯ | ৭ | ৪ |


(ক) ৬, ৯, ৮, ০, ৫, ২ সংখ্যাগুলোর গড় নির্ণয় কর। [২]


(খ) প্রদত্ত সারণির মধ্যক নির্ণয় কর। [৪]


(গ) বিবরণসহ প্রদত্ত উপাত্তের অজিভ রেখা অঙ্কন কর। [৪]

[/latex]



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