If F 2x 3y 2x 3y 24xy Then F X Y Is
1) 2xy 2) 2(x2 – y2) 3) x2 – y2 4) none of these Solution: (3) f (2x + 3y,... View Article
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Consider An Infinite Geometric Series With First Term A And Common Ratio R If Its Sum Is 4 And The Second Term Is 3 4 Then
Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the... View Article
The Difference Between Two Numbers Is 48 And The Difference Between Their Arithmetic Mean And Their Geometric Mean Is 18 Then The Greater Of Two Numbers Is
Solution: Let a and b be the two numbers. a-b = 48 (√a-√b)(√a+√b) = 48 …(i) AM = (a+b)/2 GM... View Article
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 =... 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 =... 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... 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,... 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)... 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... 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,... 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... 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 =... 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... 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) = (x2-2xz+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 =... 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... 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... 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... 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... 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... View Article
