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

The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

0
1
$2^{n}$
${}^{2 n}C_{n}$

hint Hint:

The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
(a+b)ⁿ= ∑ⁿr=0ⁿCr a^n-rb^r,
where n is a positive integer and a, b are real numbers, and 0 < r ≤ n.

The correct answer is: 1

Given :
$left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$

Further simplify
$left parenthesis 1 plus x right parenthesis to the power of n open parentheses 1 plus 1 over x close parentheses to the power of n space equals left parenthesis 1 plus x right parenthesis to the power of n open parentheses fraction numerator x space plus 1 over denominator x end fraction close parentheses to the power of n space equals space left parenthesis 1 plus x right parenthesis to the power of 2 n end exponent space. space x to the power of negative n end exponent left parenthesis 1 plus x right parenthesis to the power of 2 n end exponent space equals space left parenthesis x space plus space a right parenthesis to the power of n$

Binomial formula
$left parenthesis 1 plus x right parenthesis to the power of 2 n end exponent space equals space C presuperscript 2 n end presuperscript subscript 0 space left parenthesis 1 right parenthesis to the power of n plus space C presuperscript 2 n end presuperscript subscript 1 space left parenthesis 1 right parenthesis to the power of n minus 1 end exponent left parenthesis x right parenthesis to the power of 1 space plus C presuperscript 2 n end presuperscript subscript 2 left parenthesis 1 right parenthesis to the power of n minus 2 end exponent space left parenthesis x right parenthesis squared space plus space... space... x to the power of negative n end exponent left parenthesis 1 plus x right parenthesis to the power of 2 n end exponent space equals space x to the power of negative n end exponent open square brackets C presuperscript 2 n end presuperscript subscript 0 space plus space C presuperscript 2 n end presuperscript subscript 1 space left parenthesis x right parenthesis to the power of blank space plus C presuperscript 2 n end presuperscript subscript 2 space left parenthesis x right parenthesis squared space plus space... space... close square brackets M u l t i p l y i n g space x to the power of negative n space end exponent i n s i d e space t h e space b r a c k e t s comma x to the power of negative n end exponent left parenthesis 1 plus x right parenthesis to the power of 2 n end exponent space equals space x to the power of negative n end exponent space. C presuperscript 2 n end presuperscript subscript 0 space plus space C presuperscript 2 n end presuperscript subscript 1 space left parenthesis x right parenthesis to the power of 1 minus n end exponent space plus C presuperscript 2 n end presuperscript subscript 2 space left parenthesis x right parenthesis to the power of 2 minus n end exponent space plus space... space... T h e r e f o r e space comma space C o e f f i c i e n t space o f space x to the power of negative n end exponent space i s space C presuperscript 2 n end presuperscript subscript 0 W e space k n o w space C presuperscript n subscript 0 space equals space 1 T h e r e f o r e space C presuperscript 2 n end presuperscript subscript 0 space equals space 1$

Related Questions to study

$open parentheses 1 plus x plus x squared plus horizontal ellipsis plus x to the power of p close parentheses to the power of n equals a subscript 0 plus a subscript 1 x plus a subscript 2 x squared plus horizontal ellipsis$ $plus a subscript n p end subscript x to the power of n p end exponent not stretchy rightwards double arrow a subscript 1 plus 2 a subscript 2 plus 3 a subscript 3 plus horizontal ellipsis plus n p$

$open parentheses 1 plus x plus x squared plus horizontal ellipsis plus x to the power of p close parentheses to the power of n equals a subscript 0 plus a subscript 1 x plus a subscript 2 x squared plus horizontal ellipsis$ $plus a subscript n p end subscript x to the power of n p end exponent not stretchy rightwards double arrow a subscript 1 plus 2 a subscript 2 plus 3 a subscript 3 plus horizontal ellipsis plus n p$

Compounds (A) and (B) are –

Compounds (A) and (B) are –

chemistry-General

$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

parallel

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

parallel

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 $m s to the power of negative 1 end exponent$ to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 $m s to the power of negative 1 end exponent$ to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

physics-General

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a $capital delta A B C open parentheses fraction numerator a to the power of 2 end exponent over denominator sin invisible function application A end fraction plus fraction numerator b to the power of 2 end exponent over denominator sin invisible function application B end fraction plus fraction numerator c to the power of 2 end exponent over denominator sin invisible function application C end fraction close parentheses times s i n invisible function application fraction numerator A over denominator 2 end fraction s i n invisible function application fraction numerator B over denominator 2 end fraction s i n invisible function application fraction numerator C over denominator 2 end fraction$ simplifies to

In a $capital delta A B C open parentheses fraction numerator a to the power of 2 end exponent over denominator sin invisible function application A end fraction plus fraction numerator b to the power of 2 end exponent over denominator sin invisible function application B end fraction plus fraction numerator c to the power of 2 end exponent over denominator sin invisible function application C end fraction close parentheses times s i n invisible function application fraction numerator A over denominator 2 end fraction s i n invisible function application fraction numerator B over denominator 2 end fraction s i n invisible function application fraction numerator C over denominator 2 end fraction$ simplifies to

parallel

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

A bullet of mass $m$ is fired with a velocity of 50 $m s to the power of negative 1 end exponent$ at an angle $theta$ with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length $l equals 10 divided by 3$ m and gets embedded in the bob. After the collision, the string moves to an angle of 120 $degree$ . What is the angle $theta ?$

A bullet of mass $m$ is fired with a velocity of 50 $m s to the power of negative 1 end exponent$ at an angle $theta$ with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length $l equals 10 divided by 3$ m and gets embedded in the bob. After the collision, the string moves to an angle of 120 $degree$ . What is the angle $theta ?$

physics-General

A spherical hollow is made in a lead sphere of radius $R$ such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?

A spherical hollow is made in a lead sphere of radius $R$ such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?

physics-General

parallel

On heating a mixture of $N H subscript 4 end subscript C l$ ans $K N O subscript 2 end subscript$ , we get –

On heating a mixture of $N H subscript 4 end subscript C l$ ans $K N O subscript 2 end subscript$ , we get –

chemistry-General

Three identical blocks $A comma B$ and $C$ are placed on horizontal frictionless surface. The blocks $A$ and $C$ are at rest. But $A$ is approaching towards $B$ with a speed 10 $m s to the power of negative 1 end exponent$ . The coefficient of restitution for all collisions is 0.5. The speed of the block $C$ just after collision is

Three identical blocks $A comma B$ and $C$ are placed on horizontal frictionless surface. The blocks $A$ and $C$ are at rest. But $A$ is approaching towards $B$ with a speed 10 $m s to the power of negative 1 end exponent$ . The coefficient of restitution for all collisions is 0.5. The speed of the block $C$ just after collision is

physics-General

Two identical masses $A$ and $B$ are hanging stationary by a light pulley (shown in the figure). A shell $C$ moving upwards with velocity $v$ collides with the block $B$ and gets stick to it. Then

Two identical masses $A$ and $B$ are hanging stationary by a light pulley (shown in the figure). A shell $C$ moving upwards with velocity $v$ collides with the block $B$ and gets stick to it. Then

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.