G R R G X 3 X And F G X 2 X X Then F X
1) x3 – x2 + x – 5 2) x3 – 9x2 + 26x + 22 3) x3 + 9x2... View Article
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If X Is An Integer Function And X X X Then F X X Summation R 1 100 X R 100
Solution: (4) f (x) = [x] + ∑r=1100 {x + r} / 100 = [x] + [1 / 100] ∑r=1100... View Article
If Function F Satisfies The Equation 3 F X 2f X 59 X 1 10x 30 X 1 Then F 7
Solution: (2) 3 f (x) + 2f [(x + 59) / (x – 1)] = 10x + 30 Put x... View Article
If F Is Satisfied The Condition 2 F X F 1 X X 2 X Belongs To R Then F X
1) [x2 + 2x – 1] / 6 2) [x2 + 4x – 1] / 3 3) [x2 + 2x... View Article
The Range Of F X 6 X 3 X 6 X 3 X 2 Is Subset Of
Solution: (4) f (x) = 6x + 3x + 6-x + 3x + 2 = (6x + (1 / 6x))... View Article
If Function F X 1 2 Tan Pi X 2 1 X 1 And G X Root 3 4x 4x 2 Then The Domain Of Gof Is
Solution: (1) The domain of f and the composite function gof is the same that is (-1, 1).
If F X 2x And G Is Identity Function Then
Solution: (3) [fog] (x) = 2 [g (x)] g + g (x) = 2 [g (x)] fog (x) = (g... View Article
The Domain Of The Function F X 1 Root X X Is
1) (- ∞, ∞) 2) (0, ∞) 3) (- ∞, 0) 4) (- ∞, ∞) – {0} Solution: (3) f... View Article
Let G X 1 X X And F X Then For All X F G X Is Equal To
Let g (x) = 1 + x – [x] and f (x) =Then for all x, f (g (x)) is... View Article
The Domain Of F X Log 5 Log 6 Log 8 X Is
1) x > 4 2) x > 8 3) x < 8 4) x < 4 Solution: (2) f(x) =... View Article
The Largest Interval In Which The Function F X 3 Sin Root Pi 2 9 X 2 Assumes Values Is
Solution: (3) f (x) = 3 sin [√[π2 / 9] – x2] [√[π2 / 9] – x2] > 0 x2... View Article
The Sum Of Series 1 Cube Plus 2 Cube Plus 15 Cube Is
Solution: 13+23+33+…153 We know sum of cubes of n natural numbers S = [n(n+1)/2]2 Here n = 15 S =... View Article
If The Sum Of First N Natural Numbers Is 1 By 78 Times The Sum Of Their Cube Then The Value Of N Is
Solution: Sum of first n natural numbers = n(n+1)/2 Sum of cubes of n natural numbers = [n(n+1)/2]2 Given the... View Article
If The Sum Of First N Natural Numbers Is 1 By 5 Times The Sum Of Their Squares Then The Value Of N Is
Solution: Sum of first n natural numbers = n(n+1)/2 Sum of squares of n natural numbers = n(n+1)(2n+1)/6 Given sum... View Article
The Sum Of N Terms Of The Series 1 By Root 1 Root 3 1 Root 3 Root 5 Is
Solution: Given series is [1/(√1+√3)] + [1/(√3+√5)]+ …. Tr = [1/(√(2r-1)+√(2r+1)] Sn = ∑Tr = ∑r =1n [1/(√(2r-1)+√(2r+1)] Multiply and... View Article
If Sn 1 3 2 3 N 3 And Tn 1 2 N Then
Solution: Given Sn = 13+23+33+…n3 = sum of cubes of n natural numbers = [n(n+1)/2]2 Tn = 1 + 2... View Article
The Sum Of The First N Terms Of The Series 1 Square 2 2 Square Is Where N Is Even When N Is Odd The Sum Is
Solution: Given when n is even, Sn = 12+2.22+32+2.42+52+2.62+… = n(n+1)2/2 When n is odd Sn = 12+2.22+32+2.42+52+2.62+…2(n-1)+n2 …(i) Here... View Article
The Sum Of The Series 1 Plus 2 Plus 1 Plus 2 Sq Up To N Terms Is
Solution: Given series (1 + 2)+ (1 + 2 + 22 ) + (1 + 2 + 22 + 23... View Article
If Sn 1 1 3 1 2 Then Sn Is Not Greater Than
If Sn = (1/1^3)+(1+2)/(1^3+2^3) +…+(1+2+…+n)/(1^3+2^3+…+n^3), n = 1,2,3… Then Sn is not greater than (1) 1/2 (2) 1 (3) 2... View Article
The Value Of 1 By 2 Factorial Plus 2 By 3 Factorial 999 By 1000 Factorial Is
Solution: 1/2! + 2/3! +…+ 999/1000! = (2-1)/1! +(3-1)/3! + (4-1)/4! +…. (1000-1)/1000! = (2/2!)-(1/2)!+(1/2!)-(1/3!)+(1/3!)-(¼!)…..(1/999!)-(1/1000!) = (1/1!)-(1/1000!) = (1000!-1)/1000!
