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If A1 X B 1 Y C 1 Z And A B C Are In Geometric Progression Then X Y Z Are In

Solution: Let a1/x = b1/y = c1/z = p a = px b = py c = pz b2 = ac (since a,b,c in GP) (py)2 = pxpz p2y = px+z Equating powers... View Article

If A B C Are In Gp And 4a 5b 4c Are In Ap Such That A B C 70 Then Value Of B Is

Solution: Since a,b,c are in GP b2 = 4ac 4a, 5b, 4c are in AP. 2(5b) = 4a+4c 10b = 4(a+c) (a+c) = 10b/4 (a+c) = 5b/2…(i) a + b + c = 70... View Article

In A Sequence Of 21 Terms The First 11 Terms Are In Ap With Common Difference 2 And The Last 11 Terms Are In Gp With Common Ratio

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the... View Article

If A B C Are In Gp And X Y Are Arithmetic Mean Of A B And B C Respectively Then 1 X 1 Y Is Equal To

Solution: Since a,b,c are in GP b2 = ac Also x, y are arithmetic mean of a, b and b, c respectively. So x = (a+b)/2 y = (b+c)/2... View Article

Gm And Hm Of Two Numbers Are 10 And 8 Respectively The Numbers Are

Solution: Let a, b be the 2 numbers Given GM = 10 => √ab = 10 ab = 100 …(i) HM = 8 => 2ab/(a+b) = 8 Substitute value of ab... View Article

If X Y And Z Are In Geometric Progression Then Logx 10 Logx 10 And Logx 10 Are In

Solution: Given x,y,z are in GP. So y2 = xz Taking log 2 log y = log x+ log z 2/logy 10 = 1/logx10 + 1/logz10 So logx 10, logx 10 and... View Article

If Logx Ax Logx Bx And Logx Cx Are In Ap Where A B C And X Belong To 1 Infinity Then A B And C Are In

Solution: Given logx ax, logx bx and logx cx are in AP. logx a +logx x, logx b +logx x, logx c +logx x are in AP. 1+logx a, 1+logx b, 1+logx... View Article

The Minimum Value Of 2 Sinx 2 Cosx Is

The minimum value of 2sinx + 2cosx is (1) 2(1 - 1/√2) (2) 2(1 + 1/√2) (3) 2√2 (4) 2 Solution: We know AM ≥ GM (2sin x+2cos x)/2 ≥... View Article

If Two Positive Numbers Are In The Ratio Of 3 2root 2 3 2root 2 Then The Ratio Between Their Am And Gm Is

Solution: Let a and b be two numbers, then a:b = 3 + 2√2 : 3 - 2√2 AM = (a+b)/2 = ((3+ 2√2)x + (3 - 2√2)x)/2 = 6x/2 = 3x GM = √(ab) = √(3... View Article

If 4a2 9b2 16c2 2 3ab 6bc 4ca Where A B And C Are Non Zero Numbers Then A B C Are In

Solution: Given 4a2 + 9b2 + 16c2 = 2(3ab + 6bc + 4ca) 2(4a2 + 9b2 + 16c2 = 2×2(3ab + 6bc + 4ca) 4a2+4a2+9b2+9b2+16c2+16c2-12ab-24bc-16ca = 0... View Article

If X Y Z Are In Hp Then Log X Z Log X 2y Z Is Equal To

Solution: Since x,y,z are in HP y = 2xz/(x+z) x-2y+z = x-(4xz/(x+z) )+ z = [x(x+z)-4xz+z(x+z)]/(x+z) = [x2+xz-4xz+zx+z2]/(x+z) =... View Article

If H Is The Harmonic Mean Between P And Q Then The Value Of H P H Q Is

Solution: Given H is the harmonic mean of P and Q. So H = 2PQ/(P+Q) H/P = 2Q/(P+Q) H/Q = 2P/(P+Q) H/P + H/Q = 2Q/(P+Q) + 2P/(P+Q) =... View Article

If Fx X 1 2 Then The Number Of Real Values Of X For Which The Three Unequal Terms Are In Hp Is

Solution: f(x) = x+½ = (2x+1)/2 f(2x) = 2x+½ = (4x+1)/2 f(4x) = 4x+½ = (8x+1)/2 Given f(x), f(2x) and f(4x) are in HP. So 1/f(x), 1/f(2x),... View Article

If S Is The Sum Of An Infinite Gp And A Is The First Term Then The Common Ratio R Is Given By

Solution: Sum of infinite GP, S = a/(1-r) 1-r = a/S 1-a/S = r So r = (S-a)/S Hence option (2) is the answer.... View Article

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

Solution: (32) (32)1/6 (32)1/36... to ∞ = 32(1+1/6 +1/36+... Sum of infinite GP = a/1-r Here a = 1 r = 1/6 a/1-r = 1/(1-⅙) = 6/5 So... View Article

If 0 Less Than Theta Less Than Pi 2 X Sigma N 0 To Infinity Cos 2n Theta Then Xyz

If 0<theta < pi/2, x = sigma n = 0 to infinity cos2n theta, y = sigma n = 0 to infinity sin2n theta and z = sigma n = 0 to infinity cos2n... View Article

If An Is A Sequence With A0 P And An An 1 R An 1 For N Greater Than Or Equal To 1 Then The Terms Of The Sequence Are In

If {an} is a sequence with a0 = p and an - an-1 = ran-1 for n ≥ 1, then the terms of the sequence are in (1) AP (2) GP (3) HP (4) an arithmetico... View Article

The Sum Of Infinity Of The Progression 9 3 1 1 3 Is

Solution: Given series is 9 - 3 + 1 - 1/3 + ... Here a = 9 r = -1/3 Sum of Infinite GP = a/(1-r) = 9/(1-(-⅓) = 9/(4/3) = 27/4 Hence... View Article

Fifth Term Of A Gp Is 2 Then The Product Of Its 9 Terms Is

Solution: Let a be the first term and r be the common ratio of a GP. Given fifth term = 2 => ar4 = 2 Product of its 9 terms =... View Article

If A1 A2 A50 Are In Gp Then A1 A3 A5 A49 A2 A4 A6 A50 Is Equal To

If a1, a2,...a50 are in GP, then (a1-a3+a5-...+a49)/(a2-a4+a6-...+a50) is equal to (1) 0 (2) 1 (3) a1/a2 (4) 2 a25/a24 Solution: Let a be... View Article

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