Practice question of Binomial Theorem for iitjee , nda and airforce (Set 2)

Progression

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Question no. 16

The coefficient of x^-9 in the expansion of is

looks_one 512

looks_two -512

looks_3 521

looks_4 251

Option looks_two -512

Solution :

Question no. 17

If the coefficients of x² and x³ in the expansion of (3 + ax)⁹ are the same , then the value of a is

looks_one -7/9

looks_two -9/7

looks_3 7/9

looks_4 9/7

Option looks_4 9/7

Solution :

Question no. 18

If the second , third and fourth term in the expansion of (x + a)ⁿ are 240, 720 and 1080 respectively, then the value of n is

looks_one 15

looks_two20

looks_3 10

looks_4 5

Option looks_4 5

very soon 3

Question no. 19

Coefficient of x² in the expansion of is

looks_one 1/7

looks_two -1/7

looks_3 7

looks_4 -7

Option looks_4 -7

Solution :

Question no. 20

The coefficient of x⁵ in the expansion of (x+3)⁶ is

looks_one 18

looks_two 6

looks_3 12

looks_4 10

Option looks_one 18

Solution :
T_r+1 = ⁶C_r(x)^6-r(3)^r
x⁵ = (x)^6-r
5 = 6-r
r = 1
coefficient of x⁵ = ⁶C₁(3)¹ = 6*3 = 18

Question no. 21

If in the expansion of (1+x)²¹, the coefficient of x^r and x^r+1 be equal , then r is equal to

looks_one 9

looks_two 10

looks_3 11

looks_4 12

Option looks_two 10

Solution :
T_r+1 = ²¹C_r(1)^21-r(x)^r
the coefficient of x^r = ²¹C_r(1)^21-r = ²¹C_r
coefficient of x^r+1 = ²¹C_r+1(1)^20-r = ²¹C_r+1
the coefficient of x^r = the coefficient of x^r+1
21C_r = ²¹C_r+1

Question no. 22

The term independent of x in the expansion of will be

looks_one 5

looks_two 6

looks_3 7

looks_4 8

Option looks_3 7

Solution :
T_r+1 = ⁿC_r(a)^n-r(b)^r

Question no. 23

In the expansion of , the term independent of x is

looks_one⁹C₃ .(1/6³)

looks_two⁹C₃ .(3/2)³

looks_3 ⁹C₃

looks_4 None of these

Option looks_one⁹C₃ .(1/6³)

Solution :
T_r+1 = ⁿC_r(a)^n-r(b)^r

Question no. 24

In the expansion of , the term independent of x is

looks_one ¹⁵C₆ 2⁶

looks_two¹⁵C₅ 2⁵

looks_3 ¹⁵C₄ 2⁴

looks_4 ¹⁵C₈ 2⁸

Option looks_two¹⁵C₅ 2⁵

Solution :
T_r+1 = ⁿC_r(a)^n-r(b)^r
T_r+1 = ¹⁵C_r(x)^15-r(2/x²)^r
T_r+1 = ¹⁵C_r(x)^15-r(2)^rx^-2r
x⁰ = x^15-3r
15-3r = 0
r = 5
coefficient = ¹⁵C₅(2)⁵

Question no. 25

The term independent of x in the expansion of is

looks_one 160/9

looks_two 80/9

looks_3 160/27

looks_4 80/3

Option looks_3 160/27

Solution :

Question no. 26

The term independent of x in the expansion of is

looks_one 4320

looks_two 216

looks_3 -216

looks_4 -4320

Option looks_4 -4320

Solution :

Question no. 27

If the middle term in the expansion of is 924x⁶ , then n =

looks_one 10

looks_two 12

looks_3 14

looks_4 None of these

Option looks_two 12

Solution :
For even :

Question no. 28

The term independent of x in the expansion of is

looks_one 153090

looks_two 150000

looks_3 150090

looks_4 153180

Option looks_one 153090

Solution :

Question no. 29

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

looks_one

looks_two

looks_3

looks_4

Option looks_3

Solution :
Middle term :
T_n+1 = ²ⁿC_n(1)ⁿ(x)ⁿ
T_n+1 = ²ⁿC_nxⁿ
T_n+1 =

Question no. 30

The greatest coefficient in the expansion of is

looks_one 25840 /9

looks_two 24840 /9

looks_3 26840 / 9

looks_4 None of these

Option looks_one 25840 /9

very soon15

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