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If Set A Is Empty Set Then N P P P A

Solution: (4) The number of elements in A = 0 n (P (A)) = 20 = 1 P (A) consists of 1 element. n [P[P(A)]] = 21 = 2 [P[P(A)]] has 2... View Article

Suppose Sets Ai I 1 2 60 Each Set Having 12 Elements And Set Bj J 1 2 3 N Each Set Having 4 Elements Let

Suppose sets Ai (i = 1, 2, …. 60) each set having 12 elements and set Bj (j = 1, 2, 3 …. n) each set having 4 elements letand each element of C... View Article

Let A Theta Tan Theta Sec Theta Root 2 Sec Theta And B Theta Sec Theta Tan Theta Root 2 Tan Theta Be 2 Sets Then

Solution: (1) tan θ + sec θ = √2 sec θ sin θ = √2 - 1 sec θ - tan θ = √2 tan θ sin θ = 1 / (√2 + 1) sin θ = √2 - 1 A = B... View Article

In A Certain Town 30 Families Own A Scooter And 40 On A Car 50 Own Neither A Scooter Nor A Car 2000 Families Own Both A Scooter And Car Consider The Following Statements In This Regard

Solution: (4) Say x families are living in the town A = {families who own scooter} B = {families who own car} n (A) = 30x / 100 n (B) =... View Article

Let X X Y Z X Y Z Belongs To N X Y Z 10 X Y Z And Y X Y Z X Y Z Belongs To N Y X Z Then X Intersection Y Is Equal To

Solution: (4) X = {(1, 2, 7), (1, 3, 6), (1, 4, 5), (2, 3, 5)} element of X which belong to Y are (1, 4, 5) and (2, 3, 5) both so they belong... View Article

If Two Sets A And B Are Having 43 Elements Incommon Then The Number Of Elements Common To Each Of The Sets A Times B And B Times A Is

Solution: (1) n((A x B) ∩ (B x A)) = n ((A ∩ B) x (B ∩ A)) = n (A ∩ B) . n (B ∩ A) = 43 x 43 = 432... View Article

If X Union 3 4 1 2 3 4 5 6 The Which Of The Following Is True

Solution: (1) X ∪ {3,4} - {3, 4}= {1, 2, 5, 6} is the smallest set... View Article

A Survey Shows That 70 Of The Indian Like Mango Wheres 82 Like An Apple If X Of Indian Like Both Mango And Apples Then

Solution: (2) The percentage of people who like mangoes = n (A) = 70 The percentage of people who like apples = n (B) = 82 To find n (A ∩ B)... View Article

Two Finite Sets Have M And N Element Respectively The Total Number Of Subsets Of The First Set Is 112 More Than The Total Number Of Subsets Of The Second Set

Solution: The number of subsets of A consisting of m elements is 112 > the subsets of B having n elements. 2m − nn = 112 2n . (2m−n − 1)... View Article

If An Ax X Belongs To N And Bn Intersection Cn Dn Where B C Belongs To N Are Relatively Prime Then

Solution: (1) bN = {bx/x ∈ N} = the set that consists of +ve integer multiples of b cN = {cx/x ∈ N} = the set that consists of +ve integer... View Article

Let G X 1 X X And F X 1 X 0 0 X 0 1 X 0 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]... View Article

The Domain Of Definition Of F X Log 2 X 3 X 2 3x 2 Is

Solution: (4) f (x) = [log2 (x + 3)] / [x2 + 3x + 2] [x2 + 3x + 2] ≠ 0 (x + 1) (x + 2) ≠ 0 x ≠ -1, -2 x + 3 > 0 x > -3 Domain is... View Article

If F 1 Infinity 2 Infinity Is Given By F X X 1 X Then F 1 X Equals

1) [x + (√x2 - 4)] / 2 2) [x] / [1 + x2] 3) [x - (√x2 - 4)] / 2 4) 1 + √x2 - 4 Solution: (1) f is bijective. The inverse exists. y = f... View Article

The Inverse Of The Function F X Log 10 X Is

1) 10x 2) x10 3) e10 4) ex Solution: (1) Let y = f (x) = log10 x x = 10y f-1 (y) = 10y f-1 (x) = 10x... View Article

Let F X Ax X 1 X 1 Then For What Values Of A Is F F X X

Solution: (4) f (f (x)) = [a2x] / [ax + x + 1] Since, f (f (x)) = x, [a2x] / [ax + x + 1] = x Simplifying the equation, a2x = (a + 1)x2 +... View Article

Let F X F Y F X Root 1 Y 2 Y Root 1 X 2 For X Y Belongs To 1 1 And F 4x 3 3x K F X Then K

Solution: (3) Putting y = x, 2f (x) = f (2x √1 - y2) Take x = sin θ, 2 f (sin θ) = f (2 sin θ) Putting x = sin θ and y = sin 2θ in the given... View Article

Let F X X X 1 X X X Belongs To R Then Fr Is Equal To

Solution: (2) Let y = f (x) = [x - [x]] / [1 + x - [x]], x ∈ R If x ∈ I, then f (x) = 0 Again for any x ∈ R - I, x - [x] < 1 Hence 2 (x... View Article

Let F X E X E X 2 And If F G X X Then G X

Solution: (3) Since f (g (x)) = x (fog) (x) = x fog = 1 g (x) = f-1 (x) Now y = f (x) = [ex - e-x] / 2 2y = ex - [1 / ex] = [e2x - 1] /... View Article

Let F Theta Sin Theta Sin Theta Sin 3 Theta Then F Theta

Solution: (3) f (θ) = sin θ (sin θ + sin 3θ) = sin θ [sin θ + 3 sin θ - 4 sin3 θ] = sin θ [4 sin θ - 4 sin3 θ] = 4 sin2 θ [1 - sin2 θ] = 4... View Article

The Domain Of Definition Of The Function Y X Given By The Equation 2 X 2 Y 2 Is

1) 0 < x ≤ 1 2) 0 ≤ x ≤ 1 3) − ∞ < x ≤ 0 4) − ∞ < x < 1 Solution: (4) 2x + 2y = 2 2y = 2 . 2x log2 2y = log2 [2 - 2x] y =... View Article

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