Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2011MathematicsSequences and SeriesActual

If the arithmetic and geometric means of two numbers are 10,8 respectively, then one number exceeds the other number by

Options

  1. A8
  2. B10
  3. C12
  4. D16

Correct answer

C. 12

Step-by-step solution

Let numbers are a and b A M = a+b 2 10= a+b 2 a+b=20 ...(i) G . M = a b 8= a b a b=64 (a-b)^2=(a+b)^2-4 a b aligned & =(20)^2-4(64) & =400-256=144 aligned a-b=12 ...(ii) from (i) and (ii) . array rl a+b & =20 a-b & =12 array ] a=16, b=4 16-4=12 one number exceeds the other number by 12 .

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