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The Domain Of The Function F X Cos 1 Log 3 X 4 Is

Solution: (4) f (x) = cos-1 [log3 (x / 4)] -1 ≤ log3 (3 / 4) ≤ 1 -log 3 ≤ log (x / 4) ≤ log 3 (1 / 3) ≤ (x / 4) ≤ 3 (4 / 3) ≤ x ≤ 12... View Article

Two Finite Sets Have M And N Elements Respectively The Total Number Of Subsets Of The First Set Is 48 More Than The Total Number Of Subsets Of The Second Set And F I N Then F M N Is

Solution: (2) 2m = 2n + 48 2n [2m-n - 1] = 24 - 3 2n-4 [2m-n - 1] = 3 3 is a prime number, n = 4 and m = 6... View Article

Part Of The Domain Of The Function F X Root Cosx 1 2 6 35x 6x 2 Lying In The Interval 1 6 Is

1) [-1 / 6, π / 3] 2) [5π / 3, 6] 3) [-1 / 5, π / 3] ⋃ [5π / 3, 6] 4) (-1 / 6, π / 3] ⋃ [5π / 3, 6] Solution: (4) f (x) = √{cosx - (1 /... View Article

A Function F R R Satisfies The Equation F X F Y F X Y X Y For All X Y Belongs To R And F 1 0 Then

Solution: (3) f (x) f (y) - f (xy) = x + y x, y ∈ R always true If y = 0, f (x) f (0) - f (x . 0) = x + 0 f (x) f (0) - f (0) = x f (0) [f... View Article

X X 1 10 5 Hold If

|(x / [x + 1])| < 10-5 hold if 1) -105 < x + 1 < 10-4 2) -(100001)-1 < x < (99999)-1 3) (1 / 10000) < x < 1 4)... View Article

Domain Of Definition Of The Function F X 3 4 X 2 Log 10 X 3 X Is

Domain of definition of the function f (x) = 3 / [4 - x2] + log10 (x3 - x) is 1) (-1, 0) ⋃ (1, 2) ⋃ (2, ∞) 2) (-1, 0) ⋃ (1, 0) 3) (-2, 2) 4)... View Article

If F R S Defined By F X Sinx Root 3 Cosx 1 Is Onto Then The Interval Of S Is

Solution: (4) f (x) = sinx - √3 cosx + 1 -√(1)2 + (√3)2 ≤ sinx - √3 cosx ≤ √(1)2 + (√3)2 -√4 ≤ sinx - √3 cosx ≤ √4 -2 ≤ sinx - √3 cosx... View Article

The Range Of The Function F X 5 X P X 1

Solution: (2) 5-xPx-1 = (5 - x)! / (6 - 2x)! Now (5 - x) > 0, (x - 1) ≥ 0 and (5 - x) ≥ (x - 1) x < 5, x ≥ 1, x ≤ 3 x = 1, 2, 3... View Article

Given The Function F X 3 X 3 X 2 Then F X Y F X Y

Solution: (4) f (x) = [3x + 3-x] / 2 f (x + y) + f (x - y) = {[3x+y + 3-x-y] / 2} + {[3x-y + 3-x+y] / 2} = (1 / 2) {[3x + 3-x] / 2} + {[3y +... View Article

If F X 1 X 1 X Then F F Cos 2 Theta

Solution: (3) f (x) = [1 - x] / [1 + x] (f (cos 2θ)) = [1 - (cos 2θ)] / [1 + (cos 2θ)] = [1 - (1 - 2 sin2 θ)] / [1 + 2 cos2 θ - 1] = [2 sin2... View Article

The Domain Of F X 1 Root Mod Cosx Cosx Is

1) [(4n - 1)π / 2, (4n + 1)π / 2] 2) [(4n - 1)π / 2, (4n + 1)π / 2] 3) (nπ, (n + 1) π) 4) [2nπ - (π / 2), (π / 2) + 2nπ] Solution: (4) f... View Article

Let F R R G R R Be Two Functions Such That F X 2x 3 G X X 3 5 The Function Fog 1 X Is Equal To

Solution: (4) fog = f (g (x)) = 2 (g (x) - 3) g(x) = x3 + 5 f (g (x)) = 2 (x3 + 5) - 3 = 2x3 + 10 - 3 = 2x3 + 7 y = fog = 2x3 + 7 x3 =... View Article

Let F X X Sin Alpha X 1 X 1 F I F X 0 Then What Values Of Sin Alpha Is F F X X

Solution: (4) f (x) = [x sin ɑ] / [x + 1] fof (x) = [x sin2 ɑ] / [x (sin ɑ + 1) + 1] = x But fof (x) = x is given [x sin2 ɑ] / [x (sin ɑ +... View Article

Let F X Secx Tanx G X Tanx 1 Secx Statement 1 G Is An Odd Function Statement 2 F Is Neither An Odd Function Nor An Even Function

Solution: (3) f (x) = secx + tanx f (-x) = sec (-x) + tan (-x) = secx - tanx ≠ -f (x) Hence, f is neither odd nor an even function. g... View Article

Let F X X X 1 X X Where X Denotes The Greatest Integer Less Than Or Equal To X Then The Range Of F Is

Solution: (2) f (x) = [x - [x]] / [1 + x - [x]] x = [x] + {x} x - [x] = {x} f (x) = {x} / [1 + {x}], 0 ≤ {x} < 1 f (x) = 0, when x ∈ I... View Article

If F X Then F 1 F 2 F 3 F 100 Is Equal To

If f (x) =then f (1) + f (2) + f (3) + …. f (100) is equal to 1) 5 2) 8 3) 0 4) 10 Solution: (3) Since two rows of the determinant... View Article

If F R R Satisfies F X Y F X F Y For All X Y Belongs To R F 1 3 2 Then Summation Of R 1 N F R Is

Solution: (3) ∑r=1n f (r) = f (1) + f (2) + …. f (n) = (f (1) + f (1) + f (1)) +(f (2) + f (1)) + (f (3) + f (1)) …….. + (f (n - 1) + f (1))... View Article

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, 2x - 3y) = 24xy = (2x + 3y)2 - (2x - 3y)2 f (x, y) = x2 - y2... View Article

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 second term is 3/4, then (1) a = 4/7, r = 3/7... 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 = √(ab) AM -GM = 18 (a+b)/2 - √(ab) = 18... View Article

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