The middle term in the expansion of ( 1 + x ) 2 n is Options: A . &nbsp1.3.5.......(5n−1)n!xn B . &nbsp2.4.6.......2nn!x2n+1 C . &nbsp1.3.5.......(2n−1)n!xn D . &nbsp1.3.5.......(2n−1)n!2nxn

Answer: Option D : D Middle term of ( 1 + 2 x ) 2 n is T n + 1 = 2 n C n x n = ( 2 n ) ! n ! n ! x n = 1.3.5....... ( 2 n − 1 ) n ! 2 n x n .

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

Question

The middle term in the expansion of

(1 + x)^{2 n}

Options:

A . 1.3.5.......(5n−1)n!xn

B . 2.4.6.......2nn!x2n+1

C . 1.3.5.......(2n−1)n!xn

D . 1.3.5.......(2n−1)n!2nxn

Answer: Option D
:
D
Middle term of

(1 + 2 x)^{2 n}

T_{n + 1}

^{2 n} C_{n}

x^{n}

\frac{(2 n)!}{n! n!}

x^{n}

\frac{1.3.5....... (2 n - 1)}{n!}

2^{n}

x^{n}

Was this answer helpful ?

Next Question

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

Question 2. If the coefficient of x in the expansion of (x2+kx)5 is 270, then k = ....

Question 3. In the expansion of ( ax+bx)12, the coefficient of x−10 will be ....

Question 4. 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 5. If the coefficients of x3 and x4 in the expansion of (1+ax+bx2) (1–2x)18 in powers of x are both zero, then (a,b)....of x are both zero, then (a,b) is equal to

Question 6. The value of (21C1−10C1)+(21C2−10C2)+(21C3−10C3)+(21C4−10C4)+...+(21C10−10C10) is....

Question 7. The coefficient of x7 in the expansion of (1−x−x2+x3)6. is?....

Question 8. Coefficient of t24 in (1+t2)12(1+t12)(1+t24) is ?....

Question 9. The number of integral terms in the expansion of (√3+8√5)256 is ?....

Question 10. The term independent of x expansion of (x+1x23−x13+1−x−1x−x12)10 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

DSP Combined 1 Free Revision Test SAIL JO E-0

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

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0