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In Q.No. $6 comma not stretchy ⋂ from n equals 3 to 10 of A subscript n end subscript equals$

${3,5, 7,11,13,17,19}$
$\{2,3, 5\}$
${2,3, 5,7, 11,13,17}$
${3,5, 7}$

The correct answer is: $open curly brackets 23 comma 5 close curly brackets$

We have,
$A subscript 2 end subscript subset of A subscript 3 end subscript subset of A subscript 4 end subscript subset of horizontal ellipsis subset of A subscript 10 end subscript$
$therefore not stretchy ⋂ from n equals 3 to 10 of A subscript n end subscript equals A subscript 3 end subscript equals left curly bracket 23 comma 5 right curly bracket$

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Statement 1: $1 to the power of 99 end exponent plus 2 to the power of 99 end exponent plus horizontal ellipsis plus 100 to the power of 99 end exponent$ is divisible by 10100
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parallel

Statement 1:Let $F subscript 1 end subscript open parentheses n close parentheses equals 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction$ , then $not stretchy sum from r equals 1 to n of F subscript 1 end subscript open parentheses r close parentheses equals open parentheses n plus 1 close parentheses F subscript 1 end subscript open parentheses n close parentheses minus n.$
Statement 2: $fraction numerator 1 to the power of negative 1 end exponent plus 2 to the power of negative 1 end exponent plus 3 to the power of negative 1 end exponent plus... plus n to the power of negative 1 end exponent over denominator n end fraction greater than open parentheses fraction numerator 1 plus 2 plus 3 plus... plus n over denominator n end fraction close parentheses to the power of negative 1 end exponent$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus plus... fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator n to the power of 2 end exponent over denominator not stretchy sum n end fraction$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator 2 n over denominator left parenthesis n plus 1 right parenthesis end fraction$

Statement 1:Let $F subscript 1 end subscript open parentheses n close parentheses equals 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction$ , then $not stretchy sum from r equals 1 to n of F subscript 1 end subscript open parentheses r close parentheses equals open parentheses n plus 1 close parentheses F subscript 1 end subscript open parentheses n close parentheses minus n.$
Statement 2: $fraction numerator 1 to the power of negative 1 end exponent plus 2 to the power of negative 1 end exponent plus 3 to the power of negative 1 end exponent plus... plus n to the power of negative 1 end exponent over denominator n end fraction greater than open parentheses fraction numerator 1 plus 2 plus 3 plus... plus n over denominator n end fraction close parentheses to the power of negative 1 end exponent$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus plus... fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator n to the power of 2 end exponent over denominator not stretchy sum n end fraction$ or $open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus... plus fraction numerator 1 over denominator n end fraction close parentheses greater than fraction numerator 2 n over denominator left parenthesis n plus 1 right parenthesis end fraction$

Statement 1:If an infinite G.P. has 2^nd term $x$ and its sum is 4, then $x$ belongs to $left parenthesis negative 8 comma blank 1 right parenthesis$
Statement 2:Sum of an infinite G.P. is finite if for its common ratio $r comma blank 0 less than open vertical bar r close vertical bar less than 1$

Statement 1:If an infinite G.P. has 2^nd term $x$ and its sum is 4, then $x$ belongs to $left parenthesis negative 8 comma blank 1 right parenthesis$
Statement 2:Sum of an infinite G.P. is finite if for its common ratio $r comma blank 0 less than open vertical bar r close vertical bar less than 1$

Statement 1:Coefficient of $x to the power of 14 end exponent$ in $open parentheses 1 plus 2 x plus 3 x to the power of 2 end exponent plus horizontal ellipsis plus 16 x to the power of 15 end exponent close parentheses to the power of 2 end exponent$ is 560
Statement 2: $not stretchy sum from r equals 1 to n of r left parenthesis n minus r right parenthesis equals fraction numerator n left parenthesis n to the power of 2 end exponent minus 1 right parenthesis over denominator 6 end fraction$

Statement 1:Coefficient of $x to the power of 14 end exponent$ in $open parentheses 1 plus 2 x plus 3 x to the power of 2 end exponent plus horizontal ellipsis plus 16 x to the power of 15 end exponent close parentheses to the power of 2 end exponent$ is 560
Statement 2: $not stretchy sum from r equals 1 to n of r left parenthesis n minus r right parenthesis equals fraction numerator n left parenthesis n to the power of 2 end exponent minus 1 right parenthesis over denominator 6 end fraction$

parallel

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