Find the cube roots of the following by finding the digits in the units and tens places
A. 110592
B. 32768
C. 2744
D. n/a
1 Answers
Find (i) the last digit, (ii) the last two digits, and (iii) the last three digits of `17^(256)dot`
We have `17^(256) = (17^(2))^(128) = (289)^(128) = (290-1)^(128)` `:. 17^(256) = .^(128)C_(0)(290)^(128)-.^(128)C_(1)(290)^(127)+.^(128)C_(2)(290)^(126)-"....."` `- .^(128)C_(125)(290)^(3)+.^(128)C_(126)(290)^(2)-.^(128)C_(127)(290)+1` `=[.^(128)C_(0)(290)^(128) - .^(128)C_(1)(290)^(127)+.^(128)C_(2)(290)^(126)-"....."` `-.^(128)C_(125)(290)^(3)]+.^(128)C_(126)(290)^(2) -.^(128)C_(127)(290)+1` `=1000m+((128)(127))/(2)(290)^(2)-128xx290+1` `= 1000 m + (128)(127)(290)(145)-128xx290-1` `= 1000m+(128)(290)(127xx145-1)+1` `=1000m+(128)(290)(18414)+1` `=1000m+683527680+1`...
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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 ar
Correct Answer - `1-(1-p)^(8)` Probability for an incorrec digit is p. hence, probability for 8 correct digit is `1-p)^(8).` Hence, required probability is `1-(1-p)^(8).`
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In a `DeltaABC, b = 12` units, c = 5 units and `Delta = 30`sq. units. If d is the distance between vertex A and incentre of the triangle then the valu
Correct Answer - 8 `AI = r "cosec" (A)/(2) = (Delta)/(s) "cosec" (A)/(2)` Also, `Delta = (1)/(2) bc sin A` `rArr 30 = (1)/(2) xx 12 xx 5 xx sin A`...
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Find number of seven-digit number in the form of `a b c d efg(g,f,e ,` tc. Are digits at units, tens hundreds place etc.) `where a<< b<< c<< d>>e>>f>>
Correct Answer - C `(c )` Case (i) : zero not taken. Now we have to select seven digits from `1,2,3,4,5,6,7,8,9` so ways are `"^(9)C_(7)` From `7` digit select the largest...
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Find the smallest number which must be subtracted from the following to make them perfect cubes .What are the corresponding cube roots?
Correct Answer - (a) 7(b)104 (c )69 (d)104
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Find the cube roots of the following using prime factorisation method
Correct Answer - (a)18 (b)27 (c )21 (d)74
2 Answers 1 views
Find the cube roots of the following numbers by successive subtraction of numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 64 (ii) 512 (ii
Correct Answer - (a)5 (b)7 (c )13 13
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A square is drawn with the length of side equal to the diagonal of a cube. If the area of the square is `72075 cm^(2)`, then find the side of the cube
Correct Answer - 155 cm
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Round off each of the following to the number of significant digits indicated : i. 1.223 to two digits ii. 12.56 to three digits
i. 1.223 to two digits = 1.2 This is because the third digit is less than 5, so we drop it and all the other digits to its right. ii. 12.56 to...
2 Answers 3 views
Write each of the following as decimals : (a) Seven-tenths (b) Two tens and nine-tenths (c) Fourteen point six (d) One hundred and two ones (e) Six hu
Correct Answer - `{:((a)0.7,(b)20.9,(c)14.6,(d)102.0,(e)600.8):}`
2 Answers 1 views