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Maths-

General

Easy

Question

The expression $open parentheses table row cell n end cell row cell k end cell end table close parentheses plus open parentheses table row cell n end cell row cell k plus 1 end cell end table close parentheses$ where $n greater or equal than k greater or equal than 1$ is the same as

$(\begin{matrix} n + 1 \\ k \end{matrix})$
$(\begin{matrix} n + 1 \\ k - 1 \end{matrix})$
$(\begin{matrix} n \\ k + 1 \end{matrix})$
$(\begin{matrix} n + 1 \\ k + 1 \end{matrix})$

The correct answer is: $open parentheses table row cell n plus 1 end cell row cell k plus 1 end cell end table close parentheses$

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The pairofcom pounds which cannot exist together in solution is:

The pairofcom pounds which cannot exist together in solution is:

Chemistry-General

If the greatest value of the term independent of x in expansion of $open parentheses x s i n invisible function application p plus x to the power of negative 1 end exponent c o s invisible function application p close parentheses to the power of 10 end exponent$ is achieved at $P equals theta$ Then the locus of point from which pair of tangents be drawn to $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ including an angle $theta$ is

If the greatest value of the term independent of x in expansion of $open parentheses x s i n invisible function application p plus x to the power of negative 1 end exponent c o s invisible function application p close parentheses to the power of 10 end exponent$ is achieved at $P equals theta$ Then the locus of point from which pair of tangents be drawn to $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ including an angle $theta$ is

parallel

The sum of the series $fraction numerator 5 over denominator 1.4 to the power of 2 end exponent end fraction plus fraction numerator 11 over denominator 4 to the power of 2 end exponent times 7 to the power of 2 end exponent end fraction plus fraction numerator 17 over denominator 7 to the power of 2 end exponent times 10 to the power of 2 end exponent end fraction plus horizontal ellipsis.. plus$ is equal to

The sum of the series $fraction numerator 5 over denominator 1.4 to the power of 2 end exponent end fraction plus fraction numerator 11 over denominator 4 to the power of 2 end exponent times 7 to the power of 2 end exponent end fraction plus fraction numerator 17 over denominator 7 to the power of 2 end exponent times 10 to the power of 2 end exponent end fraction plus horizontal ellipsis.. plus$ is equal to

In the expansion of $open parentheses x plus x to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis.. close parentheses open parentheses 1 plus x plus x to the power of 2 end exponent plus x to the power of 3 end exponent close parentheses open parentheses x to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis. plus x to the power of 10 end exponent close parentheses$ the coefficient of is

In the expansion of $open parentheses x plus x to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis.. close parentheses open parentheses 1 plus x plus x to the power of 2 end exponent plus x to the power of 3 end exponent close parentheses open parentheses x to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis. plus x to the power of 10 end exponent close parentheses$ the coefficient of is

Maths-General

Statement 1:The coefficient of $x to the power of n end exponent$ in the binomial expansion of $left parenthesis 1 minus x right parenthesis to the power of negative 2 end exponent$ is $left parenthesis n plus 1 right parenthesis$
Statement 2:The coefficient of $x to the power of r end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative n end exponent$ when $n element of N$ is $blank to the power of n plus r minus 1 end exponent C subscript r end subscript$

Statement 1:The coefficient of $x to the power of n end exponent$ in the binomial expansion of $left parenthesis 1 minus x right parenthesis to the power of negative 2 end exponent$ is $left parenthesis n plus 1 right parenthesis$
Statement 2:The coefficient of $x to the power of r end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative n end exponent$ when $n element of N$ is $blank to the power of n plus r minus 1 end exponent C subscript r end subscript$

parallel

If the $left parenthesis r plus 1 right parenthesis$ th term in the expansion of $open parentheses fraction numerator a to the power of 1 divided by 3 end exponent over denominator b to the power of 1 divided by 6 end exponent end fraction plus fraction numerator b to the power of 1 divided by 2 end exponent over denominator a to the power of 1 divided by 6 end exponent end fraction close parentheses to the power of 21 end exponent$ has equal exponents of both $a$ and $b$ , then value of $r$ is

If the $left parenthesis r plus 1 right parenthesis$ th term in the expansion of $open parentheses fraction numerator a to the power of 1 divided by 3 end exponent over denominator b to the power of 1 divided by 6 end exponent end fraction plus fraction numerator b to the power of 1 divided by 2 end exponent over denominator a to the power of 1 divided by 6 end exponent end fraction close parentheses to the power of 21 end exponent$ has equal exponents of both $a$ and $b$ , then value of $r$ is

If in the expansion of $left parenthesis 1 plus x right parenthesis to the power of n end exponent$ , the coefficient of $r$ th and $left parenthesis r plus 2 right parenthesis$ th term be equal, then $r$ is equal to

If in the expansion of $left parenthesis 1 plus x right parenthesis to the power of n end exponent$ , the coefficient of $r$ th and $left parenthesis r plus 2 right parenthesis$ th term be equal, then $r$ is equal to

The sum of the series $not stretchy sum from r equals 0 to n of left parenthesis negative 1 right parenthesis to the power of r end exponent blank to the power of n end exponent C subscript r end subscript open parentheses fraction numerator 1 over denominator 2 to the power of r end exponent end fraction plus fraction numerator 3 to the power of r end exponent over denominator 2 to the power of 2 r end exponent end fraction plus fraction numerator 7 to the power of r end exponent over denominator 2 to the power of 3 r end exponent end fraction plus fraction numerator 15 to the power of r end exponent over denominator 2 to the power of 4 r end exponent end fraction plus... plus m blank t e r m s close parentheses$ is

The sum of the series $not stretchy sum from r equals 0 to n of left parenthesis negative 1 right parenthesis to the power of r end exponent blank to the power of n end exponent C subscript r end subscript open parentheses fraction numerator 1 over denominator 2 to the power of r end exponent end fraction plus fraction numerator 3 to the power of r end exponent over denominator 2 to the power of 2 r end exponent end fraction plus fraction numerator 7 to the power of r end exponent over denominator 2 to the power of 3 r end exponent end fraction plus fraction numerator 15 to the power of r end exponent over denominator 2 to the power of 4 r end exponent end fraction plus... plus m blank t e r m s close parentheses$ is

parallel

The coefficient of $t to the power of 24 end exponent$ in the expansion of $open parentheses 1 plus t to the power of 2 end exponent close parentheses to the power of 12 end exponent open parentheses 1 plus t to the power of 12 end exponent close parentheses left parenthesis 1 plus t to the power of 24 end exponent right parenthesis$ is

The coefficient of $t to the power of 24 end exponent$ in the expansion of $open parentheses 1 plus t to the power of 2 end exponent close parentheses to the power of 12 end exponent open parentheses 1 plus t to the power of 12 end exponent close parentheses left parenthesis 1 plus t to the power of 24 end exponent right parenthesis$ is

The coefficient of $x to the power of 5 end exponent$ in the expansion of $open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent$ is

The coefficient of $x to the power of 5 end exponent$ in the expansion of $open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent$ is

Let $R equals left parenthesis 2 plus square root of 3 right parenthesis to the power of 2 n end exponent$ and $f equals R minus left square bracket R right square bracket$ where $left square bracket bullet right square bracket$ denotes the greatest integer function, then $R open parentheses 1 minus f close parentheses$ is equal to

Let $R equals left parenthesis 2 plus square root of 3 right parenthesis to the power of 2 n end exponent$ and $f equals R minus left square bracket R right square bracket$ where $left square bracket bullet right square bracket$ denotes the greatest integer function, then $R open parentheses 1 minus f close parentheses$ is equal to

parallel

If $left parenthesis 1 plus x plus x to the power of 2 end exponent right parenthesis to the power of n end exponent equals not stretchy sum from r equals 0 to 2 n of a subscript r end subscript x to the power of r end exponent comma blank t h e n blank a subscript 1 end subscript minus 2 a subscript 2 end subscript plus 3 a subscript 3 end subscript horizontal ellipsis minus 2 n a subscript 2 n end subscript$ is equal to

If $left parenthesis 1 plus x plus x to the power of 2 end exponent right parenthesis to the power of n end exponent equals not stretchy sum from r equals 0 to 2 n of a subscript r end subscript x to the power of r end exponent comma blank t h e n blank a subscript 1 end subscript minus 2 a subscript 2 end subscript plus 3 a subscript 3 end subscript horizontal ellipsis minus 2 n a subscript 2 n end subscript$ is equal to

Let $open square brackets x close square brackets$ denote the greatest integer less than or equal to $x$ . If $x equals open parentheses square root of 3 plus 1 close parentheses to the power of 5 end exponent$ , then $open square brackets x close square brackets$ is equal to

Let $open square brackets x close square brackets$ denote the greatest integer less than or equal to $x$ . If $x equals open parentheses square root of 3 plus 1 close parentheses to the power of 5 end exponent$ , then $open square brackets x close square brackets$ is equal to

$left parenthesis 2 to the power of 3 n end exponent minus 1 right parenthesis$ will be divisible by $left parenthesis for all n element of N right parenthesis$

$left parenthesis 2 to the power of 3 n end exponent minus 1 right parenthesis$ will be divisible by $left parenthesis for all n element of N right parenthesis$

parallel

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