How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3, 4 if repetition is allowed? -Maths 9th

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Last Answer : Without repetition, a five -digit number can be formed using the five digits in 5! ways (5 4 3 2 1) Out of these 5! numbers, 4! numbers will be starting with digit 0. (0 (fixed) 4 3 2 1) ∴ Total ... + 6 + 6 + 4 + 4 + 4 = 30∴ Required probability = \(rac{30}{96}\) = \(rac{5}{16}.\)

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Last Answer : (a) \(rac{1}{2}\) Let S be the sample spaceThen n(S) = Number of four digit numbers that can be formed with out repetition1 of 4 digits1 of 3 digits1 of 2 digits1 of 1 digitThHTO= 4! = 4 3 2 1 ways = 24 ways. Let E : ... 1 = 12∴ P(E) = \(rac{n(E)}{n(S)}\) = \(rac{12}{24}\) = \(rac{1}{2}\).

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Description : What is the answer for the number of 3 letter words with or without meaning that can be formed out of the letters of the word LOGARITHMS if repetition of the letters is not allowed?

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Description : How many 3 letters words (with or without meaning) can be formed out of the letters of the word, "PLATINUM", if repetition of letters is not allowed? a) 742 b) 850 c) 990 d) 336 

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Description : Find sum of digits -Maths 9th

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Description : Determine the mean of first 10 natural numbers. -Maths 9th

Last Answer : Mean = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 / 10 = 55 / 10 = 5.5

Description : Determine the mean of first 10 natural numbers. -Maths 9th

Last Answer : Mean = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 / 10 = 55 / 10 = 5.5

Description : Find the arithmetic mean of first-five natural numbers. -Maths 9th

Last Answer : Mean = 1 + 2 + 3 + 4 + 5/5 = 15/5 = 3

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Description : On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

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Description : If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

Last Answer : (d) An equivalence relationWe can check the given properties as follows: Reflexive: Let (a, b) ∈ N x N. Then (a, b) ∈ N ⇒ a + b = b + a (Communtative law of Addition) ⇒ (a, b) R (b, a) ⇒ (a, b) R (a, ... , f) ⇒ (a, b) R (e, f) on N x N so R is transitive.Hence R is an equivalence relation on N N.

Description : The relation ‘is less than’ on a set of natural numbers is -Maths 9th

Last Answer : (c) Only transitiveLet N be the set of natural numbers. Then R = {(a, b) : a < b, a, b ∈N}A natural number is not less than itself ⇒ (a, a)∉R where a ∈N ⇒ R is not reflexive V a, b ∈N, (a, b) ∈R ⇒ a < b \( ot\ ... ∈N, (a, b) ∈R and (b, c) ∈R ⇒ a < b and b < c ⇒ a < c (a, c) ∈R ⇒ R is transitive.

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Description : Examine whether the following numbers are rational or irrational: -Maths 9th

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Description : Find three irrational numbers between 2 and 2.5 . -Maths 9th

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Description : There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be – 3.5. Find the mean of the given numbers. -Maths 9th

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Description : Write the following rational numbers in decimal form : -Maths 9th

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Description : Classify the following numbers as rational or irrational with justification . -Maths 9th

Last Answer : Classification of rational or irrational number with justification

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Description : How many rational numbers and irrational numbers can be inserted between 2 and 3 ? -Maths 9th

Last Answer : There are infinite number of rational and irrational numbers between 2 and 3 .

Description : Find three rational numbers lying between 0 and 0.1 . -Maths 9th

Last Answer : The three rational numbers lying between 0 and 0.1 are 001,005,009. The twenty rational numbers between 0 and 0.1 are 0.001 , 0.002, 0.003, 0.004,--- 0.011, 0.012,--- 0.099. To determine any ... 0 and 0.1 insert the square root of its product. i.e. The rational numbers between a and b is √a b .

Description : Which of the following rational numbers have the terminating decimal representation? -Maths 9th

Last Answer : (i) The prime factor of 5 is 5. Hence 3 / 5 has a terminating decimal representation. (ii) 20 = 4 x 5 = 22 x 5. The prime factors of 20 are both 2's and 5's. Hence 7 / 20 has a ... a terminating decimal. (vi) The prime factor of 7 is 7. Hence 23 / 7 has a non-terminating decimal representation.

Description : If a and b are two rational numbers, prove that a + b, a - b, ab are rational numbers. -Maths 9th

Last Answer : In this way a / b is also a rational number.