Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2015MathematicsBinomial Theorem

If x= 1 5 + 1.3 5.10 + 1.3 .5 5.10 .5 + , then 3 x^2+6 x is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

Given that, aligned & x= 1 5 + 1 3 5 10 + 1 3 5 5 10 5 + & = 1 5 + 1 3 2 1 ( 1 5 )^2+ 1 3 5 3 2 1 ( 1 5 )^3+ & = 1 5 + 1 3 2 ! ( 1 5 )^2+ 1 3 5 3 ! ( 1 5 )^3+ aligned On adding 1 both the sides, we get 1+x=1+ 1 5 + 1 3 2 ! ( 1 5 )^2+ 1 3 5 3 ! ( 1 5 )^3+ Now, According to the binomial theorem for any index, aligned & (1- 2 5 )^ -1 / 2 =1+ 1 5 + 1 3 2 ! ( 1 5 )^2+ 1 3 5 3 ! ( 1 5 )^3+ & 1+x= (1- 2 5 )^ -1 / 2 1+x= ( 3 5 )^ -1 / 2 & 1+x= ( 5 3 )^ 1 / 2 & (1+x)^2= 5 3 & 1+2 x+x^2= 5 3 & 3+6 x+3 x^2=5 & 3 x^2+6 x=2 ali

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

If n 13 , n 14 and n 15 are in arithmetic progression, then the positive integer value of ' n ' can be 2026If the coefficients of x^2 and x^3 in the expansion of (3 + kx)^9 are equal, then the value of ' k ' is 2026The remainder when 7¹⁰³ is divided by 25 is 2026_ r=1 ¹⁵ r^2 ( ¹⁵ C_r 15 r-1 )= 20251 81^ n - ^ 2 n C ₁ 10 81^ n + ^ 2 n C ₂ 10^2 81^ n - + 10^ 2 n 81^ n = 2025If x is positive real number and the first negative term in the expansion of (1+ x )^ 27 / 5 is t _ k then k = 2025In the binomial expansion of (p-q)¹⁴ , if the sum of 7^ th term and 8^ th term is zero, then p+q p-q = 2025The numerically greatest term in the expansion of (x+3 y)¹³ , when x= 1 2 and y= 1 3 is 2025 Full Binomial Theorem list All AP EAMCET PYQs