Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2017MathematicsSequences and SeriesActual

If x₁ and x₂ are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

Options

  1. Ax ₁+ x ₂ 2 x ₁ x ₂
  2. Bx ₁ + x ₂ 2
  3. C| x ₁ - x ₂ | 2
  4. Dx ₁+ x ₂ 2 ( x ₁ x ₂ +1 )

Correct answer

C. | x ₁ - x ₂ | 2

Step-by-step solution

Arithmetic mean of x₁, x₂= x₁+x₂ 2 Geometric mean of x ₁, x ₂= x ₁ x ₂ Given, x ₁+ x ₂ 2 - x ₁ x ₂ 1 x ₁+ x ₂ 2 x ₁ x ₂ +1 aligned & x ₁+ x ₂ 2 x ₁ x ₂ +2 & x ₁+ x ₂-2 x ₁ x ₂ 2 & ( x ₁ )^2+ ( x ₂ )^2-2 x ₁ x ₂ 2 aligned aligned & ( x ₁ - x ₂ )^2 2 & | x ₁ - x ₂ | 2 aligned

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Let p , q and r be three unequal numbers such that p , q and r are in AP. If (q-p) , (r-q) and p are in GP, then (p+q):(q+r):(r+p) equals 2026If p^ th term of an AP is k , then what is the sum of p^ th term, (p+q)^ th term and (p-q)^ th term of the AP ? 2026If p , g₁ , g₂ and q are in GP and m is the arithmetic mean of p and q , then g₁^2 g₂ + g₂^2 g₁ is equal to 2026The sum of the first n terms of an AP is 3n^2+5n . If the m^ th term of the AP is 68 , then what is the value of m ? 2026Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a , b and c are in AP. Question: If p , q and r are not in AP and b=c , then the line joining the points X , Y and Z 2026If (10 + ₁₀ x) , (10 + ₁₀ y) and (10 + ₁₀ z) are in AP, then consider the following statements: I. The GM of x and z is y^2 . II. The AM of ₁₀ x and ₁₀ z is ₁₀ y . Which of the sta 2025How many terms of the series 1 + 3 + 5 + 7 + amount to a sum equal to 12345678987654321 ? 2025For the following two (02) items: Let (6 + 10 + 14 + up to m terms ) = (1 + 3 + 5 + 7 + up to n terms ) , where m How many values of m are possible? 2025 Full Sequences and Series list All NDA PYQs