If 2^(2006)-2006 divided by 7, the remainder is -Turito

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If $2 to the power of 2006 end exponent minus 2006$ divided by 7, the remainder is

Maths-General

2
0
4
1

Answer:The correct answer is: 0

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I The no of distinct terms in the expansion of $left parenthesis x subscript 1 end subscript plus x subscript 2 end subscript plus horizontal ellipsis. plus x subscript n end subscript right parenthesis to the power of 3 end exponent$ is $n plus 2 c subscript 3 end subscript$
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I) Formula
II) False

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II The no of irrational terms in the expansion $left parenthesis 2 to the power of 1 divided by 5 end exponent plus 3 to the power of 1 divided by 10 end exponent right parenthesis to the power of 55 end exponent$ is 55

I) Formula
II) False

I Three consecutive binomial coefficients cannot be in GP.
II Three consecutive binomial coefficients cannot be in A.P.
Which of the above statement is correct?

Standard Results

I Three consecutive binomial coefficients cannot be in GP.
II Three consecutive binomial coefficients cannot be in A.P.
Which of the above statement is correct?

Standard Results

S1: If the coefficients of $x to the power of 6 end exponent$ and $x to the power of 7 end exponent$ in the expansion of $left parenthesis fraction numerator x over denominator 4 end fraction plus 3 right parenthesis to the power of n end exponent$ are equal, then the number ofdivisors ofn is 12.
S2: If the expansion of $left parenthesis x to the power of 2 end exponent plus fraction numerator 2 over denominator x end fraction right parenthesis to the power of n end exponent$ for positive integer n has 13 ^th term independent of x Then the sum of divisors of $n$ is 39.

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$S subscript 2 end subscript$ :In the expansion of $left parenthesis x to the power of 2 end exponent plus fraction numerator a over denominator x to the power of 3 end exponent end fraction right parenthesis to the power of 10 end exponent$ , the coefficients of $x to the power of 5 end exponent$ and $x to the power of 15 end exponent$ are equal, then the positive value of a is 8

S subscript 1 end subscript right parenthesis

Find 4^th and second term

S subscript 2 end subscript right parenthesis

x to the power of 5 end exponent

x to the power of 15 end exponent

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$S subscript 2 end subscript$ :In the expansion of $left parenthesis x to the power of 2 end exponent plus fraction numerator a over denominator x to the power of 3 end exponent end fraction right parenthesis to the power of 10 end exponent$ , the coefficients of $x to the power of 5 end exponent$ and $x to the power of 15 end exponent$ are equal, then the positive value of a is 8

S subscript 1 end subscript right parenthesis

Find 4^th and second term

S subscript 2 end subscript right parenthesis

x to the power of 5 end exponent

x to the power of 15 end exponent

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II The term independent of x in the expansion of $open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses$ is $0$ when is even.
Which of the above statements is correct?

I The sum of the binomial coefficients of the expansion $open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses$ is $2 to the power of n end exponent$
II The term independent of x in the expansion of $open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses$ is $0$ when is even.
Which of the above statements is correct?

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The arrangement of the following binomial expansions in the ascending order of their independent terms A $left parenthesis square root of x minus fraction numerator 3 over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 10 end exponent$ B $left parenthesis x plus fraction numerator 1 over denominator x end fraction right parenthesis to the power of 6 end exponent$ C $left parenthesis 1 plus x right parenthesis to the power of 32 end exponent$ D $left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent$