Download SGBAU BSc 2019 Summer 6th Sem Staticstics Question Paper

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1. Examination

B.Sc. Part-II (Semester-II)

STATISTICS (Maximum Marks : 80)

Time : Three Hours

1. (A) Fill in the blanks :
   1. Optimum solution of LPP occurs at ______ of feasible region.

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   2. Assignment problem is solved by ______ algorithm.
   3. In ANOVA ______ test is used.
   4. In m x m LSD the total number of experimental units needed are ______.
   (B) Choose the correct alternatives :
   1. In LPP the objective function and constraints are always ______
      1. Non-linear
      2. Exponential

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      3. Linear
      4. None of the above
   2. A necessary and sufficient condition for existence of a feasible solution to the transportation problem is ______
      1. ∑ai > ∑bi
      2. ∑ai ≥ ∑bi

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      3. ∑ai < ∑bi
      4. ∑ai ≤ ∑bi
   3. The principle of ______ is not used in CRD.
      1. Randomization
      2. Replication

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      3. Local control
      4. None of the above
   4. In 2³ factorial experiment the total treatment combinations will be ______ in number.
      1. 8
      2. 6

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      3. 4
      4. 12
   (C) Answer in ONE sentence :
   1. What is saddle point ?
   2. Define contrast.

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   3. What do you mean by feasible solution ?
   4. What is mean sum of squares ?
2. (A) State the standard form of LPP. 4 (B) Give the Simplex algorithm to solve LPP. 4

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OR

1. (P) Explain LPP in general. (Q) Define :
   1. Feasible solution
   2. Net evaluations

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   (R) Solve the given LPP graphically

   Max. Z = x + 2y

   subject to :

2. (A) What do you mean by transportation problem ? Give its mathematical formation. 4 (B) Explain matrix minima method and obtain an initial basic feasible solution to the given transportation problem using matrix minima method. 8

OR

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1. (P) Define :
   1. Basic feasible solution to T.P.
   2. Optimal solution to T.P.

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1. (Q) Explain North-West Corner rule of finding solution to T.P. and solve the given T.P. by this method : 8

1. (A) Explain Assignment problem. 4 (B) Define two person zero sum game. 4 (C) Solve the given sequencing problem : 4

Obtain optimum sequence of jobs.

OR

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1. (P) Explain Maximin and Minimax principle of the theory of games. 4 (Q) State the assumptions made in sequencing problem. 4 (R) Solve the following assignment problem : 4

1. (A) What is ANOVA ? State the assumption in ANOVA. 4 (B) Give the mathematical analysis of one-way classification. 4 (C) State the null hypothesis and ANOVA table for two-way classification with one observation per cell. 4

OR

1. (P) Give the null hypothesis and ANOVA table of one-way classification. 4 (Q) Write the ANOVA table along with null hypothesis for two-way classification with m observations per cell. 4 (R) Carry out the mathematical analysis of two-way classification with one observation per cell. 4

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1. (A) Define : 4
   1. Treatment
   2. Uniformity trials
   (B) State the principles of design of experiments and explain any one of them. 4 (C) What is randomized block design ? Give the particular layout of RBD with four treatments A, B, C and D replicated in three blocks 4

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OR

1. (P) Define CRD and give its mathematical model. 4 (Q) Give the null hypothesis and ANOVA table for RBD with t treatments and r replicates. 4 (R) State advantages and disadvantages of CRD. 4
2. (A) Define Latin square design. 4 (B) Give particular layout of 4 x 4 LSD with treatments A, B, C and D. 4 (C) Explain Yate’s method of obtaining factorial effect totals in 2⁴ factorial experiment. 4

OR

1. (P) Define factorial experiments and state its advantages. 4 (Q) Write the ANOVA table of m * m LSD. 4 (R) Give the ANOVA table for 2² factorial experiment. 4

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