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Science of Math in Psc

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পিএসসি-২০১৪ বিষয়ঃগনিত (লিখিত + ৪০টি MCQ)
যোগ্যতাভিত্তক বহুনির্বাচনি প্রশ্নের উত্তর
১. আদমশুমারি কত বছর পর পর হয়?
২. ৩/৪ এর বিপরীত ভগ্নাংশ কত?
৩. ৬০ এর ১৫ % কত?
৪. ১২, ০, ১৮ এর গড় কত?
৫. ল. স. গু কি?
৬. একজন শ্রমিক সাপ্তাহে ৪৯০ টাকা আয় করেন।
ক) ৩ সাপ্তাহে তিনি কত টাকা আয় করবেন?
খ) তার দৈনিক আয় কত?
গ) ৫দিনে কত টাকা আয় করবেন?
ঘ) ১০৫০ টাকা আয় করতে তার কত দিন লাগবে?
ঙ) ১ বছরে তিনি কত টাকা আয় করবেন?
৭. কোন ক্ষুদ্রতম সংখ্যাকে ১৬, ২৪, ৩২, ৪০ দ্বারা ভাগ করলে প্রতি ক্ষেত্রে ৬ অবশিষ্ট থাকবে?
৮. একটি বাশের ১/৫ অংশ কাদায়, ২/৫অংশ পানিতে এবং বাকি অংশ পানির উপরে আছে। পানির উপরে কত অংশ আছে?
৯. দুইটি সংখ্যার গুণফল ১২.৭৭৫। একটি সংখ্যা. ৭ । অপরটি কত?
১০. ৬০০ টাকার ৩ বছরের মুনাফা ১৪৪ টাকা। মুনাফার হার নির্ণয় কর।
১১. বিআরটিসি বাস সকাল ৮টা ১০ মিনিটে ঢাকা ছেড়ে ১০ টা ৩০ মিনিটে জয়দেবপুর পৌঁছে। আন্তর্জাতিক রীতিতে উক্ত সময়কে প্রকাশ কর।
১২.ক) ৩ সে; মি; ব্যাসার্ধের একটি বৃত্ত আক এবং এর ব্যাস, ব্যাসার্ধ ও জ্যা চিহ্নিত কর।
খ) চিত্র সহ সংঙ্গা লিখ সামান্তরিক, সুষম কোণ
১৩. ২৯ কিলোমিটার ৮৯ সেন্টিমিটার ৭ মিলিমিটার
ক) ৮৯ সেন্টিমিটারকে মিলিমিটারে প্রকাশ কর।
খ) ২৯ কিলোমিটারকে মিলিমিটারে প্রকাশ কর
গ) ২৯ কিলোমিটার ৮৯ সেন্টিমিটার ৭ মিলিমিটারকে মিলিমিটারে প্রকাশ কর।
বহুনির্বাচনি প্রশ্নের উত্তরঃ
১) যে সংখ্যা দ্বারা গুণ করা হয় তাকে কী বলে ?
(ক) গুণক (খ) গুণ্য (গ) গুণফল (ঘ) গুণনীয়ক
২) যে সংখ্যা দ্বারা ভাগকরা হয়তাকে কী বলে ?
ক) ভাজক (খ)ভাজ্য (গ) ভাগফল (ঘ)ভাগশেষ
৩) ৬টি চেয়ার ৩০০০ টাকায়এবং ৩টি টেবিল ২৪০০ টাকায়ক্রয়করা হলো। তাহলে মোট কতটাকার চেয়ার ও টেবিল ক্রয় করা হলো ?
(ক) ৪৪০০ (খ) ৫০০০ (গ) ৫৪০০ (ঘ) ৫৬০০
৪) একই জাতীয় একাধিক রাশির গড় নির্ণেয়র জন্য রাশিগুলোর যোগফলকে রাশিগুলোর সংখ্যাদ্বারা কী করতে হয় ?
(ক) যোগ (খ) বিযোগ (গ) গুণ ঘ) ভাগ
5) ৪০, ৬০ ও ৭৫ এর গ.সা.গু.কোনটি ?
(ক) ৪ (খ) ৫ (গ) ১০ (ঘ) ১৫

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...A Solution Manual for: A First Course In Probability: Seventh Edition by Sheldon M. Ross. John L. Weatherwax∗ September 4, 2007 Introduction Acknowledgements Special thanks to Vincent Frost and Andrew Jones for helping find and correct various typos in these solutions. Miscellaneous Problems The Crazy Passenger Problem The following is known as the “crazy passenger problem” and is stated as follows. A line of 100 airline passengers is waiting to board the plane. They each hold a ticket to one of the 100 seats on that flight. (For convenience, let’s say that the k-th passenger in line has a ticket for the seat number k.) Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random. What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)? If one tries to solve this problem with conditional probability it becomes very difficult. We begin by considering the following cases if the first passenger sits in seat number 1, then all ∗ wax@alum.mit.edu 1 the remaining passengers will be in their correct seats and certainly the #100’th will also. If he sits in the last seat #100, then certainly the last passenger cannot sit there (in fact he will end up in seat #1). If he sits in any of the 98...

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