Math Chapter Wise

EnglishBihar (TRE 1.0) -2023

Q7221.The dual of the linear programming problem: Minimize CT x subject to Ax ≥ b and x ≥ 0 is

AMaximize bT w subject to AT w ≥ c and BMaximize bT w subject to AT w ≤ c and CMaximize bT w subject to AT w ≤ c and w is unrestricted. DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q7222.A transportation problem is

Adual problem Bnon-linear programming problem Cspecial case of linear programming problem DMore than one of the above ENone of the above

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EnglishKVS PGT 2023

Q7223.If the corner points of the LPP, Z = 13x - 15y subject to the constraints x + y ≤7, 2x - 3y ≥ 0, x ≥ 0 and y ≥ 0 are (0, 0), (7, 0), (3, 4) and (0, 2), then the value of Maximum Z+3 Minimum Z is:

A91 B181 C1 D-1

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EnglishKVS PGT 2023

Q7224.Which among the following is NOT a corner point of the LPP, maximize Z = 4x + y subject to the constraints, x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0?

A(0, 50) B(20, 30) C(50, 0) D(30, 0)

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EnglishRPSC PGT 2022

Q7225.A necessary and sufficient condition for a basic feasible solution to a minimization linear programming problem to be an optimum is that (for all j)-

Azj – cj = 0 Bzj – cj ≤ 0 Czj – cj ≥ 0 Dzj –cj ≠ 0

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EnglishRPSC PGT 2022

Q7226.Solution of minimal assignment problem whose effectiveness matrix is following – I II III IV A 2 3 4 5 B 4 5 6 7 C 7 8 9 8 D 3 5 8 4

AA → II, B → III, C → IV, D → I BA → III, B → II, C → IV, D → I CA → III, B → II, C → I, D → IV DAll above

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EnglishRPSC PGT 2022

Q7227.The objective function of the dual problem of the following primal problem is – Max (z) = 3x1 – 3x2 s.t. x1≤4 x2≤6 x1+x2≤5 –x2≤–1 X1,x2≥0

AMax (Z’) = –4w1–6w2–5w3+w4 BMin (Z’) = –4w1–6w2+5w3–w4 CMin (Z’) = 4w1+6w2+5w3+w4 DMin (Z’) = 4w1–6w2–5w3+w4

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EnglishDSSSB PGT 2021

Q7228.In hyperplane 2x1 + 3x2 + 4x3 – x4 = 5, the point (1, 2, 3, 4) lies in -

AOpen half space of type cx > z BOpen half space of type cx < z CClosed half space of type cx ≤ z DClosed half space of type cx ≥ z

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EnglishDSSSB PGT 2021

Q7229.The number of basic solution to the system- 3x1 + 4x2 + 3x3 + 8x4 = 7 2x1 – 3x2 + 2x3 – 6x4 = 13

A12 B4 C9 D6

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EnglishDSSSB PGT 2021

Q7230.If a constraint is multiplied by a non-zero constant of a L.P.P, then the solution

ADoes not change with original solution Bis increased by addition of that non-zero constant Cis increased by multiplication of that non-zero constant Dis decreased by subtraction of that non-zero constant

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EnglishDSSSB PGT 2021

Q7231.For a L.P.P, Minimise z = x1 + 5x2 – 3x3, Subjected to 2x1 + x2 + x3 = 5, 3x1 – x2 + 4x3 = 5, x1, x2, x3 ≥ 0, the solution (1, 2, 1) is–

AA basic but not feasible solution BA basic feasible solution CA feasible but not basic solution DNeither basic nor feasible solution

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EnglishDSSSB PGT 2021

Q7232.The solution (1, 0, 1) to be system x1 + x2 + x3 = 2, x1 – 3x2 + x3 = 2, 2x1 + 3x2 + 4x3 = 6 is

AA basic feasible solution BNot a basic solution CA basic but not feasible solution DA non-degenerate basic feasible solution

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EnglishDSSSB PGT 2021

Q7233.The minimum cost of the assignment problem:

A52 B45 C60 D50

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EnglishDSSSB PGT 2021

Q7234.The optimal value of the objective function of the L.P.P, Min z = 5x1 – 2x2; subjected to 2x1 + 3x2 ≥ 1 x1, x2, ≥ 0 is–

A−4/3 B5/2 C0 D−2/3

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EnglishDSSSB PGT 2021

Q7235.The pay-off matrix for a strictly determinable game is– The value of b is–

A–1 ≤ b ≤ 2 B0 ≤ b ≤ 2 C–2 ≤ b ≤ 2 D–8 ≤ b ≤ 5

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EnglishDSSSB PGT 2021

Q7236.Which one of the following is not a non- degenerate basic solution in a system of 2 equations with 4 unknowns?

A(10, – 42, 0, 0) B(0, 22, – 43, 0) C(0, 0, – 8, 0) D(7, 0, – 9, 0)

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EnglishJSSC PGT 2018

Q7237.A solution to linear programming problem that satisfies all the constraints, except the non- negativity constraint, is referred to as:

AFeasible solution BBasic solution COptimal solution DBasic feasible solution

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EnglishJSSC PGT 2018

Q7238.Below matrix gives the transportation cost of sending material from 3 depots to 5 final destinations. The storage capacity of the depots and the receiving capacity of final destination shops (represented as S1, S2,...) is also given. Find the minimal transportation cost satisfying the constraints on storage depots and receiver shops. S1 S2 S3 S4 S5 Dep A 3 6 1 1 1 4 Dep B 2 4 3 2 7 5 Dep C 1 1 2 1 2 6 2 2 3 4 4

A23 B25 C20 D21

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EnglishJSSC PGT 2018

Q7239.If at least one of the basic variables is zero in a basic feasible solution of LPP, the solution is said to be:

AOptimal BSingular CUnbounded DDegenerate

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EnglishJSSC PGT 2018

Q7240.In the simplex method, which variables are introduced to convert constraint conditions to equations?

AFeasible variables BBasic variables CDegenerate variables DSlack-variables

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