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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 - 1] / 3 4) [x2 - 3x + 1] / 6 Solution: (3) 2 f (x) + f (1 - x) = x2 --- (1) 2 [f... 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)) + (3x + (1 / 3x)) + 2 ≥ 2 √6x (1 / 6x) + 2 √3x (1 / 3x) + 2 [Because AP >... 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).... View Article

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 + g) (x)... View Article

The Domain Of The Function F X 1 Root X X Is

1) (- ∞, ∞) 2) (0, ∞) 3) (- ∞, 0) 4) (- ∞, ∞) - {0} Solution: (3) f (x) = 1 / √|x| - x |x| - x > 0 x - x > 0 0 > 0 [not... 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 equal to 1) x 2) 1 3) f(x) 4) g(x) Solution: (2) g (x) = 1 + x - [x] f... 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) = log5 [log6 [log8 x]] [log6 [log8 x]] > 0 [log8 x] > 60 x > 8... 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 ≤ [π2 / 9] |x| ≤ π / 3 f (-π / 3) = 0 f (0) = 3 sin (π / 3) = (3... 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 = (15×16/2)2 = (15×8)2 = 1202... 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 sum of first n natural... 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 of the first n natural... 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 + ...+ n = sum of n natural numbers... 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)... 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 ) + …..n The nth term Tn = 1+2+22+23+...2n This is a GP with first term a... 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 (4) 4 Solution:... 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! =... View Article

Sigma I Eq 1 To N Sigma J Eq 1 To I Sigma K Eq 1 To J 1 Is Equal To

Solution: ∑i = 1n ∑j = 1i∑k= 1j 1 = ∑i = 1n ∑j = 1i j = ∑i = 1n (1+2+3+...i) = ∑i = 1n (i(i+1)/2 (since sum of n natural numbers = n(n+1)/2)... View Article

Sum Of N Terms Of The Following Series 1 3 3 3 5 3 7 3 Is

Solution: 13+33+53+73+....+n3 = ∑r=1n(2r-1)3 = ∑r=1n(8r3-12r2+6r-1) = 8∑r=1nr3 -12∑r=1n r2+6∑r=1n r-∑r=1n1 =... View Article

If Hn 1 1 2 1 N Then The Value Of Sn 1 3 2 5 3 Is

If Hn = 1 + 1/2 + ...+ 1/n, then the value of Sn = 1 + 3/2 + 5/3 + ...+ (2n-1)/n is (1) Hn + 2n (2) n-1+Hn (3) Hn-2n (4) 2n-Hn Solution:... View Article

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