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If The Sets A And B Are Defined As A X Y Y 1 X 0 X Belongs To R B X Y Y X X Belongs To R Then

Solution: (3) A = (x, y), x ∈ R, y = 1 / x A = {(1, 1), (2, 1 / 2), ……. (-1, -1), (-2, -1 / 2) …..} B = {(x, y), x ∈ R, y = - x B = {(1,... View Article

Let F X X Sin Pi X X 0 Then For All Natural Numbers N F Dash X Vanishes At

1) a unique point in the interval (n, n + (1 / 2)) 2) a unique point in the interval (n + (1 / 2), n + 1) 3) a unique point in the interval (n,... View Article

If A And B Are Any Two Sets Then A Union Of A Intersection Of B Is Equal To

Solution: (1) (A ∩ B) ⊆ A... View Article

Given The Sets A 1 2 3 B 3 4 C 4 5 6 Then A Union Of B Intersection C Is

Solution: (2) A = {1, 2, 3} B = {3, 4} C = {4, 5, 6} (B ∩ C) = {3, 4} ∩ {4, 5, 6} = {4} A ∪ (B ∩ C) = {1, 2, 3} ∪ {4} = {1, 2, 3, 4}... View Article

The Number Of Proper Subsets Of The Set 1 2 3 Is

Solution: (2) A = {1, 2, 3} n (A) = 3 The number of subsets of A = 2n = 23 = 8 Number of proper subsets = 8 - 1 = 7... View Article

If The Set Of A Has N Elements Then The Total Number Of Subsets Of A Is

Solution: (3) If set A consists of n elements, the total number of subsets of A is 2n.... View Article

The Set A X X Belongs To R X Power 2 16 And 2x Equals 6 Equals

Solution: (1) Given: A = { x : x ∈ R, x2 = 16 and 2x = 6 } x2 = 16 x = ± 4 2x = 6 x = 3 No value of x is satisfied. Therefore, A = null... View Article

Which Of The Following Is The Empty Set

1) {x : x is a real number and x2 – 1 = 0} 2) {x : x is a real number and x2 + 1 = 0} 3) {x : x is a real number and x2 – 9 = 0} 4) {x : x is... View Article

Let F 1 2 1 R The Set Of All Real Numbers Be A Positive Non Constant And Differentiable Function Such That F X 2 F X And F 1 2 1 Then The Value Of Integral 0 5 1 F X Dx Lies In The Interval

Solution: (4) f’ (x) - 2 f (x) < 0 f’ (x) e-2x - 2e-2x f (x) < 0 ex > 0 (1 / ex) > 0 e-x > 0 (d / dx) (e-2x . f (x)) <... View Article

For Two Events A And B Which Of The Following Is A Simple Expression Of A Intersection B A Intersection B A Dash B

Solution: (2)... View Article

If A And B Are Two Sets Then B B A

Solution: (2)... View Article

If A X Y X 2 Y 2 25 And B X Y X 2 9y 2 144 Then A B Contains

If A = {(x,y) / x2 + y2 = 25} and B {(x,y) / x2 + 9y2 = 144 } then A ∩ B contains 1) two points 2) one points 3) three points 4) four points... View Article

Let U Be The Universal Set And A Union B Union C U Then A B B C C A Equals

1) A ⋃ B ⋃ C 2) A ∩ B ∩ C 3) A ⋃ (B ∩ C) 4) A ∩ (B ⋃ C) Solution: (2) (A - B) ∪ (B - C) ∪ (C - A) will majority of the parts except for A... View Article

There Are Three Functions Given In Column A And Its Inverse In Column B Which One Of The Following Matches Is Correct

Column - A Column - B (1) f (x) = 1 - 2-x (a) f-1 (x) = x / √1 - x2 (2) f (x) = sin (tan-1 x) (b)... View Article

F X Sin 1 4 X 7 3 1 3 Then F 1 X

f (x) = sin-1 {4 - (x - 7)3}⅓ then f-1 (x) = ... 1) (7 - sin5 x)⅓ 2) 7 + (4 - sin5 x)⅓ 3) 7 + (4 + sin5 x)⅓ 4) (7 + sin5 x)⅓... View Article

If F R R F X X 2 1 Then F 1 2 Union F 1 17

Solution: (1) Here f-1 (-2) = {x ∈ R | f (x) = -2} = {x ∈ R | x2 + 1= -2} = ɸ = f-1 (17) = {x ∈ R | f (x) = 17} = {x ∈ R | x2 = 16} = {± 4}... View Article

Which Of The Following Relation Is One One

1) R1 = {(x,y) / x1 + y2 = 1, x, y ϵ R} 2) R2 = {(x, y) / y = ex^2 / x, y ϵ R} 3) R3 = {(x,y) / y = x2 - 3x + 3, x, y ϵ R} 4) None of these... View Article

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 - 26x + 5 4) x3 + x2 - x + 5 Solution: (2) g (x) = 3 + ∛x f (g (x)) = 2 - ∛x + x f... View Article

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 [(x + r) - [x] - r] = [x] + x - [x] [because (1 / 100) ∑i=1100 1... 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 = 7, 3 f (7) + 2f [11] = 100 --- (1) When x = 11, 3 f (11) + 2f [7] = 140... View Article

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