A binary number is made up to 8 digits. Suppose that the probability if an incorrect digit appearing is `p` and that the errors in different digits are independent of each other. Then find the probability of forming an incorrect number.
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The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are interchanged.
Correct option is: C. 18
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Five different digits from the set of numbers {1, 2, 3, 4, 5, 6, 7} are written in random order. Find the probability that five-digit number thus form
If the sum of the digits in a number is divisible by 9, then the number itself is divisible by 9. The least and the greatest sum of five digits...
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A `2n` digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime i
Correct Answer - B The prime digits are 2, 3, 5, 7. If we fix 2 at first place, then other 2n - 1 places are filled by all four digits....
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A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits
Correct Answer - D Three-digit numbers are 100, 101, …, 999. Total number of such numbers is 900. The three-digit numbers (which have all same digits) are 111, 222, 333, …,...
2 Answers 1 views
If the probability of a six digit number `N` whose six digit sare 1,2,3,4,5,6 written as random order is divisible by 6 is `p ,` then the value of `1/
Correct Answer - B Total number of cases = n(S) = 6! Now sum the given digits is 1 + 2 + 3 + 4 + 5 + 6 = 21,...
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The number of four-digit numbers that can be formed by using the digits `1,2,3,4,5,6,7,8` and `9` such that the least digit used is `4`, when repetiti
Correct Answer - B `(b)` Least digit used `=4` `:.` We can use `4,5,6,7,8,9`. So each of the four places can be filled in `6` ways So number of numbers is...
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Number of six-digit numbers such that any digit that appears in the number appears at least twice, where the digits of each number are from the set `{
Correct Answer - C `(c )` Case I : All six digits alike i.e. `111111`, `222222`……..etc. `=5` ways Case II : `2` alike `+2` other alike. Select any three in `"^(5)C_(3)`...
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The number of `n` digit number formed by using digits `{1,2,3}` such that if `1` appears, it appears even number of times, is
Correct Answer - B `(b)` Required number of numbers `="(n)C_(0)(2)^(n)+"(n)C_(2)(2)^(n-2)+…` We know that `(1+x)^(n)+(x-1)^(n)=2sum_(k=0)^(n)"(n)C_(k)x^(k)` Hence, put `x=2`, get the result `2["^(n)C_(0)(2)^(n)+^(n)C_(2)(2)^(n-2)+^(n)C_(2)(2)^(n-4)+^(n)C_(6)(2)^(n-6)+...]`
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Number of permutations of `1,2,3,4,5,6,7,8`, and `9` taken all at a time are such that digit `1` appearing somewhere to the left of `2` and digit `3`
Correct Answer - A `(a)` Number of digits are `9` Select `2` places for the digit `1` and `2` in `"^(9)C_(2)` ways from the remaining `7` places, select any two places...
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In a five digit number 1b6a3 a is the greatest single digit perfect cube and twice of it exceeds b by 7 .Then the sum of the number and it cube root i
Correct Answer - 19710
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