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If The Arithmetic Geometric And Harmonic Means Between Two Positive Real Numbers Be A G And H Then

(1) A2 = GH (2) H2 = AG (3) G = AH (4) G2 = AH Solution: Let a, b be the 2 positive numbers. AM, A = (a+b)/2 GM, G = √(ab) HM,... View Article

If In An Infinite Gp First Term Is Equal To The Twice Of The Sum Of The Remaining Terms Then Common Ratio Is

(1) 1 (2) 2 (3) 1/3 (4) -1/3 Solution: Let a, ar, ar2….∞ be the series. Sum of remaining terms = ar + ar2 + ….. = ar/(1-r)... View Article

Sum Of Infinite Number Of Terms In Gp Is 29 And Sum Of Their Square Is 100 The Common Ratio Of Gp Is

(1) 5 (2) 3/5 (3) 8/5 (4) 1/5 Solution: Let a, ar, ar2….∞ be the series. Given the sum of GP = 20 So a/(1-r) = 20 Squaring... View Article

0 5737373 Equals

(1) 284/497 (2) 284/495 (3) 568/990 (4) 567/990 Solution: Let x = 0.5737373… = 0.5+ (73/103) + (73/105) + … = (1/2) + (73/103)(1... View Article

The Value Of 4 1 By 3 4 1 By 9 4 1 By 27 Infinity Is

(1) 2 (2) 3 (3) 4 (4) 9 Solution: 41/3 41/9 41/27 ..... ∞ = 4(1/3 + 1/9 + 1/27 +.....∞) Let S = (1/3 + 1/9 + 1/27 +.....∞)... View Article

The value of [latex]a^{\log _{b}x}[/latex] where a = 0.2, b = √5, x = 1/4 + 1/8 + 1/16 + ….∞ is

(1) 1 (2) 2 (3) 1/2 (4) 4 Solution: Given x = 1/4 + 1/8 + 1/16 + ….∞ Here a = 1/4 r = 1/2 Sum = a/(1-r) = ¼ / (1-½) = 1/2 Given a =... View Article

The Sum Of The Series 5 05 Plus 1 212 Plus 0 29088 Plus Infinity Is

(1) 6.93378 (2) 6.87342 (3) 6.74384 (4) 6.64474 Solution: Given series is 5.05 + 1.212 + 0.29088 + ... ∞ This is an infinite GP... View Article

The Geometric Mean Of 1 2 2 Power 2 2n Is

(1) 2n/2 (2) n(n+1)/2 (3) 2n(n+1)/2 (4) 2(n - 1)/2 Solution: 1, 2, 22,..... 2n Here the number of terms = n+1 GM = (1×2×... View Article

Bar 423 Equals

equals (1) 419/990 (2) 419/999 (3) 417/990 (4) 423/999 Solution: Let x = 0.423423423…. 1000x = 423+ 0.423423423…. 1000x =... View Article

The First Term Of A Gp Whose Second Term Is 2 And Sum To Infinity Is 8 Will Be

(1) 6 (2) 3 (3) 4 (4) 1 Solution: Given the second term of GP = 2 ar = 2 r = 2/a Sum to infinity = 8 a/(1-r) = 8 8(1-2/a) = a a2-8a+16... View Article

The Sum Can Be Found Of An Infinite Gp Whose Common Ratio Is R

(1) For all values of r (2) For only positive value of r (3) Only for 0 < r < 1 (4) Only for –1 < r < 1 (r ≠ 0) Solution:... View Article

The Two Geometric Means Between The Number 1 And 64 Are

(1) 1 and 64 (2) 4 and 16 (3) 2 and 16 (4) 8 and 16 Solution: Let 1, G1, G2, and 64 be the series. Here a = 1 ar3 = 64 r3 = 64... View Article

The Product Of Three Geometric Means Between 4 And 1 By 4 Will Be

(1) 4 (2) 2 (3) -1 (4) 1 Solution: Let 4, G1, G2, G3, 1/4 be the series. Here a = 4 ar4 = 1/4 4(r4) = 1/4 r 4 = 1/16 r = 1/2... View Article

The Gm Of Roots Of The Equation X2 18x 9 0 Is

(1) 3 (2) 4 (3) 2 (4) 1 Solution: Given equation x2-18x+9 = 0 Let α, β are the roots of the equation. Product of the roots = c/a... View Article

If Five Gms Are Inserted Between 486 And 2 By 3 Then The Fourth Gm Will Be

(1) 4 (2) 6 (3) 12 (4) -6 Solution: Let the five GM’s be G1, G2, G3, G4, and G5. Then the series will be 486, G1, G2, G3, G4, G5,... View Article

If A B C Are In Ap Then 1 By Bc 1 By Ac 1 By Ab Will Be In

(1) A.P (2) G.P (3) H.P (4) None of these Solution: Given a, b, c are in AP. If we divide the numbers in AP with the same number,... View Article

The Product 32 32 1 By 6 32 1 By 36 Infinity Is

(1) 16 (2) 32 (3) 64 (4) 0 Solution: 32(32)1/6 (32)1/36 ….∞ = 321 + 1/6 +...∞ Here the power is an infinite GP with the first term, a = 1,... View Article

The Sum Of A Gp With Common Ratio 3 Is 364 And Last Term Is 243 Then The Number Of Terms Is

(1) 6 (2) 5 (3) 4 (4) 10 Solution: Given r = 3 Last term, arn-1 = 243 a(3n-1) = 243 a×3n = 729…(i) Sum of terms Sn,... View Article

The First Term Of A Gp Is 7 The Last Term Is 448 And Sum Of All Terms Is 889 Then The Common Ratio Is

(1) 5 (2) 4 (3) 3 (4) 2 Solution: Given a = 7 Last term = 448 arn-1 = 448 7rn-1 = 448 rn-1 = 64 rn = 64r …(i) Sum, Sn= 889... View Article

Three Numbers Are In Gp Such That Their Sum Is 38 And Their Product Is 1728 The Greatest Number Among Them Is

(1) 18 (2) 16 (3) 14 (4) None of these Solution: Let a/r, a, and ar be the three numbers in GP. Sum, a/r + a + ar = 38 …(i)... View Article