Home
Class 12
MATHS
The coefficient of t^4 in ((1-t^6)/(1-t)...

The coefficient of `t^4` in `((1-t^6)/(1-t))^3` (a) `18` (b) `12` (c) `9` (d) `15`

Text Solution

Verified by Experts

The correct Answer is:
5
`((1-t^(6))/(1-t))=(1-t^(6))^(3)(1-t)^(-3)=(1-3C_(1)t^(6)+……..)(sum_(r=0)^(oo).^(3+r-1)C_(r)x^(r ))`
Coefficient of `x^(4)=.^(3+4-1)C_(4)=.^(6)C_(4)=15`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 1 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS - SECTION 2|5 Videos

  • JEE MAIN REVISION TEST - 30 | JEE -2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISION TEST - 1 | JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS ( SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

The coefficient of t^50 in (1+t)^41 (1-t+t^2)^40 is equal to

Coefficient of t^(24) in (1+t^(2))^(12)(1+t^(12))(1+t^(24)) is :

Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9 .

Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9 .

The differential coefficient of sin^(-1)t/(sqrt(1+t^2))w.r.t cos^(-1)1/(sqrt(1+t^2)) is (a) 1 AAt >0 (b) -1AAt<0 (c) 1AAt in R (d) None of these

The coefficients of (r-1)^(t h),\ r t h\ a n d\ (r+1)^(t h) terms in the expansion of (x+1)^n are in the ratio 1:3:5. Find n\ a n d\ rdot

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If the coefficients of the (n+1)^(t h) term and the (n+3)^(t h) term in the expansion of (1+x)^(20) are equal , then the value of n is a. 10 b. 8 c. 9 d. none of these

If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expansion of (1+x)^(14) are in A.P., then r is/are a. 5 b. 11 c. 10 d. 9

The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^2+t+1; t in R , is (a) (1, 1) (b) (2, 2) (c) (1/2,1/2) (d) (3,3)