Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2013MathematicsBinomial Theorem

The value of x in the expression (x+x^ ₁₀ x )^0 , if the third term in the expansion is 1,000,000 , is

Options

  1. A10,10^ -3 / 2
  2. B100 or 10^ -3 / 2
  3. C10 or 10^ -5 / 2
  4. DNone of these

Correct answer

C. 10 or 10^ -5 / 2

Step-by-step solution

x is defined only when x 0 Now, the 3^ rd term in the expansion T_ 2+1 = ^5 C₂ x⁵⁻² (x^ 00₁₀ x )^2=1,000,000 (given) x^ 3+2 ₁₀ x =10^5 . Taking logarithm of both sides, we get aligned & (3+2 ₁₀ x ) ₁₀ x aligned =5 2 y^2+3 y-5=0 where ₁₀ x=y array lc & (y-1)(2 y+5)=0 & y=1 or -5 / 2 & ₁₀ x=1 or -5 / 2 & x=10^1=10 or 10^ -5 / 2 array

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 Manipal MET PYQs