A fuzzy set A on R is ................. iff A(λx1 + (1 – λ)x2) ≥ min [A(x1), A(x2)] for all x1, x2 ∈ R and all λ ∈ [0, 1], where min denotes the minimum operator. (A) Support (B) α-cut (C) Convex (D) Concave

A fuzzy set A on R is ................. iff A(λx1 + (1 – λ)x2) ≥ min [A(x1), A(x2)] for all x1, x2 ∈ R and all λ ∈ [0, 1], where min denotes the minimum operator. (A) Support (B) α-cut (C) Convex (D) Concave 
by

1 Answer

Answer :

(C) Convex 
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A pushdown automation M = (Q, Σ, Γ, δ, q0, z, F) is set to be deterministic subject to which of the following condition(s), for every q ∈ Q, a ∈ Σ ∪ {λ} and b ∈ Γ (s1) δ(q, a, b) contains at most one element (s2) if δ(q, λ, b) is not empty then δ(q, c, b) must be empty for every c ∈ Σ (A) only s1 (B) only s2 (C) both s1 and s2 (D) neither s1 nor s2

Description : A pushdown automation M = (Q, Σ, Γ, δ, q0, z, F) is set to be deterministic subject to which of the following condition(s), for every q ∈ Q, a ∈ Σ ∪ {λ} and b ∈ Γ (s1) δ(q, a, b) contains at most one ... ) must be empty for every c ∈ Σ (A) only s1 (B) only s2 (C) both s1 and s2 (D) neither s1 nor s2

Last Answer : (C) both s1 and s2

Consider the following LPP: Min. Z = x1+x2+x3

Description : Consider the following LPP: Min. Z = x1+x2+x3 Subject to 3x1 + 4x3 ≤ 5 5x1 + x2 + 6x3 =7 8x1 + 9x3 ≥ 2 x1, x2, x3 ≥ 0 The standard form of this LPP shall be: (1) Min. Z = x1 + x2 + x3 + 0x4 + 0x5 Subject ... + 4x3 + x4 = 5; 5x1 + x2 + 6x3 + x6 = 7; 8x1 + 9x3 - x5 + x7 = 2; x1 to x7 ≥ 0

Last Answer : Answer: 1

The grammar with production rules S → aSb |SS|λ generates language L given by: (A) L = {w∈{a, b}* | na(w) = nb(w) and na(v) ≥ nb(v) where v is any prefix of w} (B) L = {w∈{a, b}* | na(w) = nb(w) and na(v) ≤ nb(v) where v is any prefix of w} (C) L = {w∈{a, b}* | na(w) ≠ nb(w) and na(v) ≥ nb(v) where v is any prefix of w} (D) L = {w∈{a, b}* | na(w) ≠ nb(w) and na(v) ≤ nb(v) where v is any prefix of w}

Description : The grammar with production rules S → aSb |SS|λ generates language L given by: (A) L = {w∈{a, b}* | na(w) = nb(w) and na(v) ≥ nb(v) where v is any prefix of w} (B) L = {w∈{a, b}* | na(w) = nb(w) and na(v ... (D) L = {w∈{a, b}* | na(w) ≠ nb(w) and na(v) ≤ nb(v) where v is any prefix of w}

Last Answer : (A) L = {w∈{a, b}* | na(w) = nb(w) and na(v) ≥ nb(v) where v is any prefix of w} 

Consider the two class classification task that consists of the following points: Class C1: [1 1.5] [1 -1.5] Class C2: [-2 2.5] [-2 -2.5] The decision boundary between the two classes using single perceptron is given by: (A) x1+x2+1.5=0 (B) x1+x2-1.5=0 (C) x1+1.5=0 (D) x1-1.5=0

Description : Consider the two class classification task that consists of the following points: Class C1: [1 1.5] [1 -1.5] Class C2: [-2 2.5] [-2 -2.5] The decision boundary between the two classes using single perceptron is given by: (A) x1+x2+1.5=0 (B) x1+x2-1.5=0 (C) x1+1.5=0 (D) x1-1.5=0

Last Answer : (C) x1+1.5=0 

A perceptron has input weights W1 = -3.9 and W2 = 1.1 with threshold value T = 0.3. What output does it give for the input x1 = 1.3 and x2 = 2.2? (A) -2.65 (B) -2.30 (B) 0 (D) 1

Description : A perceptron has input weights W1 = -3.9 and W2 = 1.1 with threshold value T = 0.3. What output does it give for the input x1 = 1.3 and x2 = 2.2? (A) -2.65 (B) -2.30 (B) 0 (D) 1

Last Answer : Answer: C

An artificial neurons receives n inputs x1, x2,...,xn with weights w1,w2,...,wn attached to the input links. The weighted sum ............... is computed to be passed on to a non-linear filter ϕ called activation function to release the output. (A) Σ wi (B) Σ xi (C) Σ wi + Σ xi (D) Σ wi . Σ xi

Description : An artificial neurons receives n inputs x1, x2,...,xn with weights w1,w2,...,wn attached to the input links. The weighted sum ............... is computed to be passed on to a non-linear filter ϕ called activation function to release the output. (A) Σ wi (B) Σ xi (C) Σ wi + Σ xi (D) Σ wi . Σ xi

Last Answer : (D) Σ wi . Σ xi

Let R and S be two fuzzy relations defined as: Image Then, the resulting relation, T, which relates elements of universe x to elements of universe z using max-min composition is given by

Description : Let R and S be two fuzzy relations defined as: Then, the resulting relation, T, which relates elements of universe x to elements of universe z using max-min composition is given by

Last Answer : Answer: C

A fuzzy set has a membership function whose membership values are strictly monotonically increasing or strictly monotonically decreasing or strictly monotonically increasing than strictly monotonically decreasing with increasing values for elements in the universe A. convex fuzzy set B. concave fuzzy set C. Non concave Fuzzy set D. Non Convex Fuzzy set

Description : A fuzzy set has a membership function whose membership values are strictly monotonically increasing or strictly monotonically decreasing or strictly monotonically increasing than strictly monotonically decreasing with increasing ... fuzzy set C. Non concave Fuzzy set D. Non Convex Fuzzy set

Last Answer : A. convex fuzzy set

A fuzzy set wherein no membership function has its value equal to 1 is called A. normal fuzzy set B. subnormal fuzzy set. C. convex fuzzy set D. concave fuzzy set

Description : A fuzzy set wherein no membership function has its value equal to 1 is called A. normal fuzzy set B. subnormal fuzzy set. C. convex fuzzy set D. concave fuzzy set

Last Answer : B. subnormal fuzzy set.

Compute the value of adding the following two fuzzy integers: A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)} B = {(0.5,11), (1,12), (0.5,13)} Where fuzzy addition is defined as μA+B(z) = maxx+y=z (min(μA(x), μB(x))) Then, f(A+B) is equal to (A) {(0.5,12), (0.6,13), (1,14), (0.7,15), (0.7,16), (1,17), (1,18)} (B) {(0.5,12), (0.6,13), (1,14), (1,15), (1,16), (1,17), (1,18)} (C) {(0.3,12), (0.5,13), (0.5,14), (1,15), (0.7,16), (0.5,17), (0.2,18)} (D) {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)}

Description : Compute the value of adding the following two fuzzy integers: A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)} B = {(0.5,11), (1,12), (0.5,13)} Where fuzzy addition is defined as μA+B(z) = maxx+y=z (min(μA(x), μB( ... ,18)} (D) {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)}

Last Answer : (D) {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)} 

Consider a fuzzy set old as defined below Old = {(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)} Then the alpha-cut for alpha = 0.4 for the set old will be (A) {(40, 0.4)} (B) {50, 60, 70, 80} (C) {(20, 0.1), (30, 0.2)} (D) {(20, 0), (30, 0), (40, 1), (50, 1), (60, 1), (70, 1), (80, 1)}

Description : Consider a fuzzy set old as defined below Old = {(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)} Then the alpha-cut for alpha = 0.4 for the set old will be (A) {(40, 0.4)} (B) {50, 60, ... , (30, 0.2)} (D) {(20, 0), (30, 0), (40, 1), (50, 1), (60, 1), (70, 1), (80, 1)}

Last Answer : (D) {(20, 0), (30, 0), (40, 1), (50, 1), (60, 1), (70, 1), (80, 1)}

A set of values X1,X2……..Xn which satisfies the constraints of the LPP is called_______ a. Solution b. Variable c. Linearity d. None of the above

Description : A set of values X1,X2……..Xn which satisfies the constraints of the LPP is called_______ a. Solution b. Variable c. Linearity d. None of the above

Last Answer : a. Solution

The number of strings of length 4 that are generated by the regular expression (0|∈) 1+2* (3|∈), where | is an alternation character, {+, *} are quantification characters, and ∈ is the null string, is: (A) 08 (B) 10 (C) 11 (D) 12

Description : The number of strings of length 4 that are generated by the regular expression (0|∈) 1+2* (3|∈), where | is an alternation character, {+, *} are quantification characters, and ∈ is the null string, is: (A) 08 (B) 10 (C) 11 (D) 12

Last Answer : (D) 12

A set of processors P1, P2, ......, Pk can execute in parallel if Bernstein's conditions are satisfied on a pair wise basis; that is P1 || P2 || P3 || ..... || Pk if and only if: (A) Pi || Pj for all i ≠ j (B) Pi || Pj for all i = j+1 (C) Pi || Pj for all i ≤ j (D) Pi || Pj for all i ≥ j

Description : A set of processors P1, P2, ......, Pk can execute in parallel if Bernstein's conditions are satisfied on a pair wise basis; that is  P1 || P2 || P3 || ..... || Pk if and only if: (A) Pi || Pj for all i ≠ j (B) Pi || Pj for all i = j+1 (C) Pi || Pj for all i ≤ j (D) Pi || Pj for all i ≥ j

Last Answer : (A) Pi || Pj for all i ≠ j Explanation: Bernstein's Condition: 1. If process Pi writes to a memory cell Mi, then no process Pj can read the cell Mi. 2. If process Pi read from a memory ... Mi. 3. If process Pi writes to a memory cell Mi, then no process Pj can write to the cell Mi.

For every context free grammar (G) there exists an algorithm that passes any w ∈ L(G) in number of steps proportional to (A) ln|w| (B) |w| (C) |w|2 (D) |w|3

Description : For every context free grammar (G) there exists an algorithm that passes any w ∈ L(G) in number of steps proportional to (A) ln|w| (B) |w| (C) |w|2 (D) |w|3

Last Answer : (D) |w|3

A vertex cover of an undirected graph G(V, E) is a subset V1 ⊆ V vertices such that (A) Each pair of vertices in V1 is connected by an edge (B) If (u, v) ∈ E then u ∈ V1 and v ∈ V1 (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1 (D) All pairs of vertices in V1 are not connected by an edge

Description : A vertex cover of an undirected graph G(V, E) is a subset V1 ⊆ V vertices such that (A) Each pair of vertices in V1 is connected by an edge (B) If (u, v) ∈ E then u ∈ V1 and v ∈ V1 (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1 (D) All pairs of vertices in V1 are not connected by an edge

Last Answer : (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1

Which of the following is FALSE ? (A) The grammar S ⟶ aSb|bSa|SS|∈, where S is the only non-terminal symbol and ∈ is the null string, is ambiguous. (B) SLR is powerful than LALR. (C) An LL(1) parser is a top-down parser. (D) YACC tool is an LALR(1) parser generator.

Description : Which of the following is FALSE ? (A) The grammar S ⟶ aSb|bSa|SS|∈, where S is the only non-terminal symbol and ∈ is the null string, is ambiguous. (B) SLR is powerful than LALR. (C) An LL(1) parser is a top-down parser. (D) YACC tool is an LALR(1) parser generator.

Last Answer : (B) SLR is powerful than LALR.

On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

Description : On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

Last Answer : (c) Symmetric only Let a ∈N. Then (a, a) ∉R as the GCD of a' and a' is a' not 2. R is not reflexive Let a, b ∈N. Then, (a, b) ∉R ⇒ GCD of a' and b' is 2 ⇒ GCD of b' and a' is 2 ⇒ (b, a) ∈R ∴ R ... , let a = 4, b = 10, c = 12 GCD of (4, 10) = 2 GCD of (10, 12) = 2 But GCD of (4, 12) = 4.

The height of h(A) of a fuzzy set A is defined as h(A) = sup A(x) xϵA Then the fuzzy set A is called normal when (A) h(A) = 0 (B) h(A) < 0 (C) h(A) = 1 (D) h(A) < 1

Description : The height of h(A) of a fuzzy set A is defined as h(A) = sup A(x)  xϵA Then the fuzzy set A is called normal when (A) h(A) = 0 (B) h(A) < 0 (C) h(A) = 1 (D) h(A) < 1

Last Answer : (C) h(A) = 1 

Center point of circle a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2 b.[x1-x2]/2; [y1-y2]/2; [z1-z2]/2 c.[x1-x2]; [y1-y2]; [z1-z2] d.[x2-x1]; [y2-y1]; [z2-z1]

Description : Center point of circle a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2 b.[x1-x2]/2; [y1-y2]/2; [z1-z2]/2 c.[x1-x2]; [y1-y2]; [z1-z2] d.[x2-x1]; [y2-y1]; [z2-z1]

Last Answer : a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2

Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th

Description : Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th

Last Answer : NEED ANSWER

Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th

Description : Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th

Last Answer : According to question find the value of z

The position vectors of three particles are given by  X1 = (5i + 5j)m, X2 = (5ti + 5tj)m, and X3 = (5ti + 10t^2tj)

Description : The position vectors of three particles are given by  X1 = (5i + 5j)m, X2 = (5ti + 5tj)m, and X3 = (5ti + 10t^2tj)

Last Answer : The position vectors of three particles are given by \(\overset\rightarrow{X}_1\) = (\(5\hat ... the velocity and acceleration for each, in SI units.

The turns ratio of transformer 'A' shown in the illustration is four to one and all taps are evenly spaced. If 120 volts were applied to terminals 'H1' and 'H3', what would appear at 'X1' and 'X2'? EL-0082 A. 15 volts B. 30 volts C. 480 volts D. 960 volts

Description : The turns ratio of transformer 'A' shown in the illustration is four to one and all taps are evenly spaced. If 120 volts were applied to terminals 'H1' and 'H3', what would appear at 'X1' and 'X2'? EL-0082 A. 15 volts B. 30 volts C. 480 volts D. 960 volts

Last Answer : Answer: A

The turns ratio of device 'B' shown in the illustration is two to one (total). If 220 volts were applied to terminals 'H1' & 'H2', what would be indicated across 'X1' & 'X4' with 'X2' & 'X3' connected and isolated? EL-0082 A. 55 volts B. 110 volts C. 220 volts D. 440 volts

Description : The turns ratio of device 'B' shown in the illustration is two to one (total). If 220 volts were applied to terminals 'H1' & 'H2', what would be indicated across 'X1' & 'X4' with 'X2' & 'X3' connected and isolated? EL-0082 A. 55 volts B. 110 volts C. 220 volts D. 440 volts

Last Answer : Answer: B

The turns ratio of device 'B' shown in the illustration is two to one (total). If 110 volts were applied to terminals 'X1,3' and 'X2,4', what would be indicated across 'H1' and 'H2'? EL-0082 A. 27.5 volts B. 55 volts C. 220 volts D. 440 volts

Description : The turns ratio of device 'B' shown in the illustration is two to one (total). If 110 volts were applied to terminals 'X1,3' and 'X2,4', what would be indicated across 'H1' and 'H2'? EL-0082 A. 27.5 volts B. 55 volts C. 220 volts D. 440 volts

Last Answer : Answer: D

The turns ratio of device 'B' shown in the illustration is two to one (total). If 440 volts were applied to terminals 'H1' & 'H2', what would be indicated across 'X1' & 'X4' with 'X2' & 'X3' connected and isolated? EL-0082 A. 110 volts B. 220 volts C. 880 volts D. 1760 volts

Description : The turns ratio of device 'B' shown in the illustration is two to one (total). If 440 volts were applied to terminals 'H1' & 'H2', what would be indicated across 'X1' & 'X4' with 'X2' & 'X3' connected and isolated? EL-0082 A. 110 volts B. 220 volts C. 880 volts D. 1760 volts

Last Answer : Answer: B

The turns ratio of device 'B' shown in the illustration is two to one (total). If 440 volts were applied to terminals 'H1' and 'H2', what would be indicated across 'X1,3' and 'X2,4'? EL-0082 A. 55 volts B. 110 volts C. 220 volts D. 880 volts

Description : The turns ratio of device 'B' shown in the illustration is two to one (total). If 440 volts were applied to terminals 'H1' and 'H2', what would be indicated across 'X1,3' and 'X2,4'? EL-0082 A. 55 volts B. 110 volts C. 220 volts D. 880 volts

Last Answer : Answer: B

The turns ratio of device 'A' shown in the illustration is four to one and all taps are evenly spaced. If 120 volts were applied to terminals 'H1' and 'H3', what would appear at 'X1' and 'X2'? EL-0082 A. 15 volts B. 30 volts C. 480 volts D. 960 volts

Description : The turns ratio of device 'A' shown in the illustration is four to one and all taps are evenly spaced. If 120 volts were applied to terminals 'H1' and 'H3', what would appear at 'X1' and 'X2'? EL-0082 A. 15 volts B. 30 volts C. 480 volts D. 960 volts

Last Answer : Answer: A

The turns ratio of device 'A' shown in the illustration is four to one and all the taps are equally spaced. If 120 volts were applied between 'X1' and 'X2', what would be indicated across 'H1' and 'H4'? EL-0082 A. 30 volts B. 120 volts C. 480 volts D. 1440 volts

Description : The turns ratio of device 'A' shown in the illustration is four to one and all the taps are equally spaced. If 120 volts were applied between 'X1' and 'X2', what would be indicated across 'H1' and 'H4'? EL-0082 A. 30 volts B. 120 volts C. 480 volts D. 1440 volts

Last Answer : Answer: D

In under damped vibrating system, if x1 and x2 are the successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to a) x1/x2 b) log (x1/x2) c) ln (x1/x2) d) log (x1.x2)

Description : In under damped vibrating system, if x1 and x2 are the successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to a) x1/x2 b) log (x1/x2) c) ln (x1/x2) d) log (x1.x2)

Last Answer : c) ln (x1/x2)

The molar excess Gibbs free energy, gE, for a binary liquid mixture at T and P is given by, (gE/RT) = A . x1. x2, where A is a constant. The corresponding equation for ln y1, where y1is the activity co-efficient of component 1, is (A) A . x22 (B) Ax1 (C) Ax2 (D) Ax12

Description : The molar excess Gibbs free energy, gE, for a binary liquid mixture at T and P is given by, (gE/RT) = A . x1. x2, where A is a constant. The corresponding equation for ln y1, where y1is the activity co-efficient of component 1, is (A) A . x22 (B) Ax1 (C) Ax2 (D) Ax12

Last Answer : (A) A . x22

Let x1(t) and x2(t) be periodic with fundamental periods T1 and T2 respectively. Under what

Description : Let x1(t) and x2(t) be periodic with fundamental periods T1 and T2 respectively. Under what condition be the sum x(t) = x1(t) + x2(t) be periodic ? (A) Only for T1 = T2 (B) Always periodic (C) For T1/T2 equal to a rational number (D) Not periodic

Last Answer : Let x1(t) and x2(t) be periodic with fundamental periods T1 and T2 respectively. Under what condition be the sum x(t) = x1(t) + x2(t) be periodic ? (A) Only for T1 = T2 (B) Always periodic (C) For T1/T2 equal to a rational number (D) Not periodic

Let pk(R) denotes primary key of relation R. A many-to-one relationship that exists between two relations R1 and R2 can be expressed as follows: (1) pk(R2)→pk(R1) (2) pk(R1)→pk(R2) (3) pk(R2)→R1∩R2 (4) pk(R1)→R1∩R2

Description : Let pk(R) denotes primary key of relation R. A many-to-one relationship that exists between two relations R1 and R2 can be expressed as follows: (1) pk(R2)→pk(R1) (2) pk(R1)→pk(R2) (3) pk(R2)→R1∩R2 (4) pk(R1)→R1∩R2

Last Answer : Answer: 2

Consider the formula in image processing RD = 1 - (1/CR) Where CR = n1/n2 CR is called as compression ratio n1 and n2 denotes the number of information carrying units in two datasets that represent the same information. In this situation RD is called as relative ................ of the first data set. (A) Data Compression (B) Data Redundancy (C) Data Relation (D) Data Representation

Description : Consider the formula in image processing RD = 1 - (1/CR) Where CR = n1/n2 CR is called as compression ratio n1 and n2 denotes the number of information carrying units in two datasets that represent ... . (A) Data Compression (B) Data Redundancy (C) Data Relation (D) Data Representation

Last Answer : (B) Data Redundancy

The membership values of the membership function are nor strictly monotonically increasing or decreasing or strictly monoronically increasing than decreasing. A. Convex Fuzzy Set B. Non convex fuzzy set C. Normal Fuzzy set D. Sub normal fuzzy set

Description : The membership values of the membership function are nor strictly monotonically increasing or decreasing or strictly monoronically increasing than decreasing. A. Convex Fuzzy Set B. Non convex fuzzy set C. Normal Fuzzy set D. Sub normal fuzzy set

Last Answer : B. Non convex fuzzy set

Consider the table Student(stuid, name, course, marks). Which one of the following two queries is correct to find the highest marks student in course 5? Q.1. Select S.stuid From student S Where not exists (select * from student e where e course='5' and e marks ≥ s marks) Q.2. Select S.stuid From student S Where s.marks > any (select distinct marks from student S where s.couse = 5) (A) Q.1 (B) Q.2 (C) Both Q.1 and Q.2 (D) Neither Q.1 nor Q.2

Description : Consider the table Student(stuid, name, course, marks). Which one of the following two queries is correct to find the highest marks student in course 5? Q.1. Select S.stuid From student S Where not exists (select * from student ... ) Q.1 (B) Q.2 (C) Both Q.1 and Q.2 (D) Neither Q.1 nor Q.2

Last Answer : (B) Q.2 Explanation: First query gives stuid of students whose marks are greater than all students taking course 5. Second query gives stuid of students whose marks are greater than any student taking ... comparison is between maximum of marks by any student in course 5. So the answer is option D.

Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ? (a) deg(v) ≥ n/2 for each vertex of G (b) |E(G)| ≥ 1/2 (n-1)(n-2)+2 edges (c) deg(v) + deg(w) ≥ n for every v and w not connected by an edge (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) (a), (b) and (c)

Description : Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ? (a) deg(v) ≥ n/2 for each vertex of G (b) |E(G)| ≥ 1/2 (n-1)(n-2)+2 edges (c) deg(v) + deg( ... edge (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) (a), (b) and (c)

Last Answer : (D) (a), (b) and (c)

. Which of the following relationships between co-efficient of friction (μ) between rock & roll and a (half of the angle of nip) of the particle to be crushed is correct? (A) μ > tan α (B) μ ≥ tan α (C) μ > tan 2α (D) μ ≤ tan α

Description : . Which of the following relationships between co-efficient of friction (μ) between rock & roll and a (half of the angle of nip) of the particle to be crushed is correct? (A) μ > tan α (B) μ ≥ tan α (C) μ > tan 2α (D) μ ≤ tan α

Last Answer : (B) μ ≥ tan α

The equivalent production rules corresponding to the production rules S→Sα1|Sα2|β1|β2 is (A) S→β1 | β2, A→α1A | α2A | λ (B) S→β1 | β2 | β1A | β2A, A→α1A | α2A (C) S→β1 | β2, A→α1A | α2A (D) S→β1 | β2 | β1A | β2A, A→α1A | α2A | λ

Description : The equivalent production rules corresponding to the production rules S→Sα1|Sα2|β1|β2 is (A) S→β1 | β2, A→α1A | α2A | λ (B) S→β1 | β2 | β1A | β2A,  A→α1A | α2A (C) S→β1 | β2, A→α1A | α2A (D) S→β1 | β2 | β1A | β2A,  A→α1A | α2A | λ

Last Answer : (D) S→β1 | β2 | β1A | β2A,  A→α1A | α2A | λ

Given the production rules of a grammar G1 as S1→AB | aaB A→a | Aa B→b and the production rules of a grammar G2 as S2→aS2bS2 | bS2aS2 | λ Which of the following is correct statement? (A) G1 is ambiguous and G2 is not ambiguous. (B) G1 is ambiguous and G2 is ambiguous. (C) G1 is not ambiguous and G2 is ambiguous. (D) G1 is not ambiguous and G2 is not ambiguous.

Description : Given the production rules of a grammar G1 as S1→AB | aaB A→a | Aa B→b and the production rules of a grammar G2 as S2→aS2bS2 | bS2aS2 | λ Which of the following is correct statement? ( ... G1 is not ambiguous and G2 is ambiguous. (D) G1 is not ambiguous and G2 is not ambiguous.

Last Answer : (B) G1 is ambiguous and G2 is ambiguous.

The Greibach normal form grammar for the language L={an bn+1|n≥0} is (A) S→a SB, B→bB|λ (B) S→a SB, B→bB|b (C) S→a SB|b, B→b (D) S→a Sb|b

Description : The Greibach normal form grammar for the language L={an bn+1|n≥0} is (A) S→a SB, B→bB|λ (B) S→a SB, B→bB|b (C) S→a SB|b, B→b (D) S→a Sb|b

Last Answer : (C) S→a SB|b, B→b 

Given the following statements: S1 : The grammars S→asb | bsa | ss | a and S→asb | bsa | a are not equivalent. S2: The grammars S→ss | sss | asb | bsa | λ and S→ss | asb | bsa | λ are equivalent. Which of the following is true? (A) S1 is correct and S2 is not correct. (B) Both S1 and S2 are correct (C) S1 is not correct and S2 is correct (D) Both S1 and S2 are not correct.

Description : Given the following statements: S1 : The grammars S→asb | bsa | ss | a and S→asb | bsa | a are not equivalent. S2: The grammars S→ss | sss | asb | bsa | λ and S→ss | asb | bsa | λ are equivalent. ... and S2 are correct (C) S1 is not correct and S2 is correct (D) Both S1 and S2 are not correct.

Last Answer : (A) S1 is correct and S2 is not correct.

The context free grammar for the language L = {an bm | n≤m+3, n≥0, m≥0} is (A) S→aaaA; A→aAb|B, B→Bb|λ (B) S→aaaA|λ, A→aAb|B, B→Bb|λ (C) S→aaaA|aaA|λ, A→aAb|B, B→Bb|λ (D) S→aaaA|aaA|aA|λ, A→aAb|B, B→Bb|λ

Description : The context free grammar for the language L = {an bm | n≤m+3, n≥0, m≥0} is (A) S→aaaA; A→aAb|B, B→Bb|λ (B) S→aaaA|λ, A→aAb|B, B→Bb|λ (C) S→aaaA|aaA|λ, A→aAb|B, B→Bb|λ (D) S→aaaA|aaA|aA|λ, A→aAb|B, B→Bb|λ

Last Answer : (D) S→aaaA|aaA|aA|λ, A→aAb|B, B→Bb|λ

The regular expression for the complement of the language L = {anbm|n≥4, m≤3} is: (A) (λ + a + aa + aaa)b* + a*bbbb* + (a + b)*ba(a + b)* (B) (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ab(a + b)* (C) (λ + a + aa + aaa) + a*bbbbb* + (a + b)*ab(a + b)* (D) (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ba(a + b)*

Description : The regular expression for the complement of the language L = {anbm|n≥4, m≤3} is: (A) (λ + a + aa + aaa)b* + a*bbbb* + (a + b)*ba(a + b)* (B) (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ab(a + b)* (C) (λ + a ... *bbbbb* + (a + b)*ab(a + b)* (D) (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ba(a + b)*

Last Answer : (D) (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ba(a + b)*

If A and B are two fuzzy sets with membership functions μA(x) = {0.6, 0.5, 0.1, 0.7, 0.8} μB(x) = {0.9, 0.2, 0.6, 0.8, 0.5} Then the value of μ(A∪B)’(x) will be (A) {0.9, 0.5, 0.6, 0.8, 0.8} (B) {0.6, 0.2, 0.1, 0.7, 0.5} (C) {0.1, 0.5, 0.4, 0.2, 0.2} (D) {0.1, 0.5, 0.4, 0.2, 0.3}

Description : If A and B are two fuzzy sets with membership functions μA(x) = {0.6, 0.5, 0.1, 0.7, 0.8} μB(x) = {0.9, 0.2, 0.6, 0.8, 0.5} Then the value of μ(A∪B)’(x) will be (A) {0.9, 0.5, 0.6, 0.8, 0.8} (B) {0.6, 0.2, 0.1, 0.7, 0.5} (C) {0.1, 0.5, 0.4, 0.2, 0.2} (D) {0.1, 0.5, 0.4, 0.2, 0.3}

Last Answer : (C) {0.1, 0.5, 0.4, 0.2, 0.2}

If A and B are two fuzzy sets with membership functions µA(X) = {0.2, 0.5, 0.6, 0.1, 0.9} µB(X) = {0.1, 0.5, 0.2, 0.7, 0.8} Then the value of µA∩B will be (A) {0.2, 0.5, 0.6, 0.7, 0.9} (B) {0.2, 0.5, 0.2, 0.1, 0.8} (C) {0.1, 0.5, 0.6, 0.1, 0.8} (D) {0.1, 0.5, 0.2, 0.1, 0.8}

Description : If A and B are two fuzzy sets with membership functions µA(X) = {0.2, 0.5, 0.6, 0.1, 0.9} µB(X) = {0.1, 0.5, 0.2, 0.7, 0.8} Then the value of µA∩B will be (A) {0.2, 0.5, 0.6, 0.7, 0.9} (B) {0.2, 0.5, 0.2, 0.1, 0.8} (C) {0.1, 0.5, 0.6, 0.1, 0.8} (D) {0.1, 0.5, 0.2, 0.1, 0.8}

Last Answer : (D) {0.1, 0.5, 0.2, 0.1, 0.8}

Suppose the function y and a fuzzy integer number around -4 for x are given as y=(x-3)2+2 Around -4={(2,0.3), (3,0.6), (4,1), (5,0.6), (6,0.3)} respectively. Then f(Around - 4) is given by: (A) {(2,0.6), (3,0.3), (6,1), (11,0.3)} (B) {(2,0.6), (3,1), (6,1), (11,0.3)} (C) {(2,0.6), (3,1), (6,0.6), (11,0.3)} (D) {(2,0.6), (3,0.3), (6,0.6), (11,0.3)}

Description : Suppose the function y and a fuzzy integer number around -4 for x are given as y=(x-3)2+2 Around -4={(2,0.3), (3,0.6), (4,1), (5,0.6), (6,0.3)} respectively. Then f(Around - 4) is given by: (A) {(2,0.6), (3,0.3), ... 6), (3,1), (6,0.6), (11,0.3)} (D) {(2,0.6), (3,0.3), (6,0.6), (11,0.3)}

Last Answer : (C) {(2,0.6), (3,1), (6,0.6), (11,0.3)}

Let A and B be two fuzzy integers defined as: A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)} B={(10,0.5), (11,1), (12,0.5)} Using fuzzy arithmetic operation given by Image (A) {(11,0.8), (13,1), (15,1)} (B) {(11,0.3), (12,0.5), (13,1), (14,1), (15,1), (16,0.5), (17,0.2)} (C) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,1), (16,0.5), (17,0.2)} (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}

Description : Let A and B be two fuzzy integers defined as: A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)} B={(10,0.5), (11,1), (12,0.5)} Using fuzzy arithmetic operation given by (A) {(11,0.8), (13,1), (15,1)} ( ... ,0.2)} (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}

Last Answer : (D) {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}