The first 3 terms in the expansion of (1+ax)n (n ≠ 0) are 1, 6x and 16x2.

Question

The first 3 terms in the expansion of

(1 + a x)^{n}

(n ≠ 0) are 1, 6x and 16

x^{2}

. Then the value of a and n are respectively

Options:

A . 2 and 9

B . 3 and 2

C . 23 and 9

D . 32 and 6

Answer: Option C
:
C

n_{c_{1}} . a x = 6 x; n_{c_{2}} (a x)^{2} = 16 x^{2} \Rightarrow a n = 6; \frac{n (n - 1)}{2} a^{2} = 16 \Rightarrow a = \frac{2}{3} \Rightarrow n = 9

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. In (3√2+13√3)n if the ratio of 7th term from the beginning to the 7th term from the end is 16, then ....7th term from the end is 16, then n =

Question 2. Find the value of (183+73+3⋅18⋅7⋅25)36+6⋅243⋅2+15⋅81⋅4+20⋅....Find the value of (183+73+3⋅18⋅7⋅25)36+6⋅243⋅2+15⋅81⋅4+20⋅27⋅8+15⋅9⋅16+6⋅3⋅32+64

Question 3. The number of terms which are free from radical signs in the expansion of (y15+x110)55 is....

Question 4. The value of (√2+1)6 + (√2−1)6 will be....

Question 5. If the coefficient of (2r+4)th and (r−2)th terms in the expansion of (1+x)18 are equal, then r =....

Question 6. The number of integral terms in the expansion of (512+716)642 is....

Question 7. The value of the expression (2+√2)4 lies between....

Question 8. If (1−3x)12+(1−x)53√4−x is approximately equal to a + bx for small values of x, t....bx for small values of x, then (a, b) =

Question 9. The coefficient of x3 in the expansion of (1+3x)21−2x will be....

Question 10. The value of C12 + C34 + C56 + ...... is equal to ....

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

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0