If the coefficients of pth, (p+1)th and (p+2)th terms in the expansion of (1+x

Sail E0 Webinar

Question

If the coefficients of $p^{t h}$ , $(p + 1)^{t h}$ and $(p + 2)^{t h}$ terms in the expansion of $(1 + x)^{n}$ are in A.P., then

Options:

A .

n^{2} - 2 n p + 4 p^{2}

= 0

B .

n^{2} - n (4 p + 1) + 4 p^{2} - 2

= 0

C .

n^{2} - n (4 p + 1) + 4 p^{2}

= 0

D . None of these

Answer: Option B
:
B

2 $^{n} c_{p} = n_{c_{p - 1}} + p_{c_{p + 1}} \Rightarrow \frac{2}{(n - p)! P!} = \frac{1}{(n - p + 1)! (p - 1)!} + \frac{1}{(n - p - 1)! (p + 1)!} \Rightarrow \frac{2}{(n - p) p} = \frac{1}{(n - p + 1) (n - p)} + \frac{1}{(p + 1) p} o n s i m p l i f i n g w e g e t n^{2} - n (4 p + 1) + 4 p^{2} - 2 = 0$

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The sum of coefficients of the last six terms in the expansion of (1+x)11 is ....

Question 2. The value of (√2+1)6 + (√2−1)6 will be ....

Question 3. The middle term in the expansion of (1+x)2n is ....

Question 4. If the coefficient of (2r+3)th and (r−3)th terms in the expansion of (1+x)18 are equal, then r = ....

Question 5. If the coefficient of x in the expansion of (x2+kx)5 is 270, then k = ....

Question 6. If the coefficient of x7 in (ax2+1bx)11 is equal to the coefficient of x−7 in (ax−1bx2)11, then ab....to the coefficient of x−7 in (ax−1bx2)11, then ab =

Question 7. If the coefficient of the middle term in the expansion of (1+x)2n+2 is p and the coefficients of middle term....in the expansion of (1+x)2n+1 are q and r, then

Question 8. If (1+ax)n = 1 + 8x + 24 x2 + ......, then the value of a and n is ....

Question 9. C0−C1+C2−C3+........+(−1)nCn is equal to ....

Question 10. In the polynomial (x - 1)(x - 2)(x - 3)............... .........(x - 100), the coefficient of x99 is ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

GPOE / GPA Combined 1 Free Mock Test SAIL JO E-0 2024

ICA Combined 1 Free Revision Test SAIL JO E-0

RDIC Review Test SAIL JO E-0

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

RSP Combined 1 Free Revision Test SAIL JO E-0