Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

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

8
9
10
11

The correct answer is: 9

We have, $T subscript r plus 1 end subscript equals blank to the power of 21 end exponent C subscript r end subscript open parentheses fraction numerator a to the power of 1 divided by 3 end exponent over denominator b to the power of 1 divided by 6 end exponent end fraction close parentheses to the power of 21 minus r end exponent open parentheses fraction numerator b to the power of 1 divided by 2 end exponent over denominator a to the power of 1 divided by 6 end exponent end fraction close parentheses to the power of r end exponent$
$equals blank to the power of 21 end exponent C subscript r end subscript fraction numerator a to the power of 7 minus left parenthesis r divided by 3 right parenthesis end exponent over denominator b to the power of 7 divided by 2 minus r divided by 6 end exponent end fraction. fraction numerator b to the power of r divided by 2 end exponent over denominator a to the power of r divided by 6 end exponent end fraction$
$equals blank to the power of 21 end exponent C subscript r end subscript a to the power of 7 minus left parenthesis r divided by 2 right parenthesis end exponent b to the power of 2 r divided by 3 minus 7 divided by 2 end exponent$
Since, exponents of $a$ and $b$ in the $left parenthesis r plus 1 right parenthesis$ th term are equal
$therefore blank 7 minus fraction numerator r over denominator 2 end fraction equals fraction numerator 2 r over denominator 3 end fraction minus fraction numerator 7 over denominator 2 end fraction$
$rightwards double arrow blank fraction numerator 21 over denominator 2 end fraction equals fraction numerator 7 over denominator 6 end fraction r blank rightwards double arrow r equals 9$

Related Questions to study

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

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

parallel

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

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

parallel

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 $left parenthesis for all n element of N right parenthesis$

The coefficient of $x to the power of 3 end exponent y to the power of 4 end exponent z to the power of 5 end exponent$ in the expansion of $left parenthesis x y plus y z plus x z right parenthesis to the power of 6 end exponent$ is

The coefficient of $x to the power of 3 end exponent y to the power of 4 end exponent z to the power of 5 end exponent$ in the expansion of $left parenthesis x y plus y z plus x z right parenthesis to the power of 6 end exponent$ is

parallel

Let $C subscript 1 end subscript comma blank C subscript 2 end subscript comma blank C subscript 3 end subscript$ are the usual binomial coefficients. Let $S equals C subscript 1 end subscript plus 2 C subscript 2 end subscript plus 3 C subscript 3 end subscript plus... plus n C subscript n end subscript$ , then $S$ equals

Let $C subscript 1 end subscript comma blank C subscript 2 end subscript comma blank C subscript 3 end subscript$ are the usual binomial coefficients. Let $S equals C subscript 1 end subscript plus 2 C subscript 2 end subscript plus 3 C subscript 3 end subscript plus... plus n C subscript n end subscript$ , then $S$ equals

The coefficient of $x$ in the expansion of $open parentheses 1 plus x close parentheses open parentheses 1 plus 2 x close parentheses open parentheses 1 plus 3 x close parentheses horizontal ellipsis horizontal ellipsis left parenthesis 1 plus 100 x right parenthesis$ is

The coefficient of $x$ in the expansion of $open parentheses 1 plus x close parentheses open parentheses 1 plus 2 x close parentheses open parentheses 1 plus 3 x close parentheses horizontal ellipsis horizontal ellipsis left parenthesis 1 plus 100 x right parenthesis$ is

$I f blank open vertical bar x close vertical bar less than fraction numerator 1 over denominator 2 end fraction comma blank t h e n blank t h e blank c o e f f i c i e n t blank o f blank x to the power of r end exponent blank i n blank t h e blank e x p a n s i o n blank o f fraction numerator 1 plus 2 x over denominator left parenthesis 1 minus 2 x right parenthesis to the power of 2 end exponent end fraction comma blank i s$

$I f blank open vertical bar x close vertical bar less than fraction numerator 1 over denominator 2 end fraction comma blank t h e n blank t h e blank c o e f f i c i e n t blank o f blank x to the power of r end exponent blank i n blank t h e blank e x p a n s i o n blank o f fraction numerator 1 plus 2 x over denominator left parenthesis 1 minus 2 x right parenthesis to the power of 2 end exponent end fraction comma blank i s$

parallel

In the expansion of $left parenthesis 1 plus x plus x to the power of 2 end exponent plus x to the power of 3 end exponent right parenthesis to the power of 6 end exponent comma$ then coefficient of $x to the power of 14 end exponent$ is

In the expansion of $left parenthesis 1 plus x plus x to the power of 2 end exponent plus x to the power of 3 end exponent right parenthesis to the power of 6 end exponent comma$ then coefficient of $x to the power of 14 end exponent$ is

A person can see clearly only upto 3m. What will be power of his spectacles lens, so that he can see clearly upto 12 m

A person can see clearly only upto 3m. What will be power of his spectacles lens, so that he can see clearly upto 12 m

Physics-General

The least distance of distinct vision for young adult with normal vision is about

The least distance of distinct vision for young adult with normal vision is about

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.