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गणित: संख्या क्रम और संभावना

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Questions and Answers

किस कथन में संतुलन राशि (common difference) का वर्णन सही रूप में किया गया है?

यह एक निश्चित मात्रा है जो किसी दो निरंतर अनुक्रमों के बीच की भिन्नता है। (correct)

यह एक अनुपात है जो किसी दो निरंतर बिंदुओं के बीच होता है।

यह संख्याओं के अनुक्रम में सबसे बड़ा अंतर होता है।

यह वह मान होता है जो केवल पहले तत्व के समीप होता है।

संख्याओं के अनुक्रम में n वां तत्व खोजने का सही सूत्र क्या है?

an = n(a + d)

an = a + (n - 1)d (correct)

an = a + (n + 1)d

an = a + d(n - 1)

प्रायिकता का मान 0 का क्या अर्थ है?

घटना निश्चित रूप से होगी।

घटना संभव है।

घटना असंभव है। (correct)

घटना लगभग निश्चित है।

किसी घटना के संयोजन की प्रायिकता को सीखने के दौरान हमें क्या महत्व रखना चाहिए?

संयोजन और क्रम दोनों को समझना आवश्यक है। Signup and view all the answers

अनुपात में पहले n तत्वों का योग निकालने का सूत्र क्या है?

Sn = n/2[2a + (n-1)d] Signup and view all the answers

स्वतंत्र घटनाओं की प्रायिकता का अर्थ क्या है?

एक घटना की प्रायिकता दूसरी घटना को प्रभावित नहीं करती। Signup and view all the answers

यदि एक घटना की प्रायिकता 0.7 है, तो उसके विपरीत घटना की प्रायिकता क्या होगी?

0.3 Signup and view all the answers

कौन से घटक संयुक्त घटनाओं के लिए सही प्रायिकता नियम का अनुसरण करते हैं?

P(A या B) = P(A) + P(B) - P(A और B) Signup and view all the answers

Study Notes

Arithmetic Progressions

An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is constant. This constant difference is called the common difference.
The general form of an arithmetic progression is: a, a + d, a + 2d, a + 3d, ..., where 'a' is the first term and 'd' is the common difference.
The nth term of an arithmetic progression can be calculated using the formula: a_n = a + (n-1)d
The sum of the first n terms of an arithmetic progression can be calculated using the formula: S_n = n/2[2a + (n-1)d] or S_n = n/2(a + a_n)

Probability

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, inclusive.
A probability of 0 indicates that the event is impossible.
A probability of 1 indicates that the event is certain.
An event is a collection of possible outcomes of a particular experiment or observation.
Sample space is the set of all possible outcomes of a given experiment.
Mutually exclusive events are events that cannot occur simultaneously. The probability of the union of mutually exclusive events is the sum of their probabilities.
Independent events: The outcome of one event does not affect the outcome of the other event. The probability of two independent events occurring is the product of their individual probabilities.
Conditional probability is the probability of an event occurring, given that another event has already occurred. It is calculated as P(A|B) = P(A and B) / P(B).
Probability distributions assign probabilities to possible outcomes. Common examples include binomial distributions (for events with a fixed number of trials and a constant probability of success) and normal distributions (a bell-shaped curve used to model many natural phenomena).
Basic probability rules include: P(A or B) = P(A) + P(B) - P(A and B), if not mutually exclusive
Calculating probabilities often involves understanding combinations and permutations

Relationship between Arithmetic Progressions and Probability

While arithmetic progressions are about sequences of numbers, and probability is about likelihood and chance, there's no direct, inherent relationship between them. There aren't specific probability problems that rely on the properties of arithmetic progressions, other than the idea that a sequence of events could be assigned probabilities.
Arithmetic progressions might be used in modeling scenarios where data points are evenly spaced, but the probability aspect would come from the actual outcomes or events associated with those points.

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यह परीक्षा गणित में अंकगणितीय प्रगति और संभावना की समझ को मापती है। इसमें आप संख्या क्रम के सामान्य रूप और संभावना के सिद्धांतिक पहलुओं की जांच करेंगे। सटीक उत्तर देने के लिए फार्मुलों का प्रयोग करें।