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CSIR NET Maths previous year question papers

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CSIR NET June 2025 · Part B (3 Marks)Probability, Statistics & Linear Programming#the-optimum-is-where-the-first-two-constraints-meet-not-the-first-and

Solve the following linear programming problem: maximize z = x + y subject to 5x + 3y ≤ 30, 2x + 6y ≤ 25, 2x − y ≤ 8, x ≥ 0, y ≥ 0. Then the optimal value of the objective function is

Single choice · Linear Programming

CSIR NET December 2025 · Part B (3 Marks)Probability, Statistics & Linear Programming#check-every-vertex-the-optimum-need-not-sit-where-the-loosest-looking

Consider the following linear programming problem: Maximize 3x1+4x23x_{1} + 4x_{2} subject to 3x1+2x2≤12,3x1+5x2≤15,2x1−x2≥0,x2≤23x_{1} + 2x_{2} \le 12, 3x_{1} + 5x_{2} \le 15, 2x_{1} - x_{2} \ge 0, x_{2} \le 2, and x1,x2≥0x_{1}, x_{2} \ge 0. Which of the following values is the optimum value of the objective function in the feasible region?

Single choice · Linear Programming

CSIR NET December 2024 · Part C (4.75 Marks)Probability, Statistics & Linear Programming#chain-the-constraints-to-bound-the-objective

Consider maximizing the objective function P=x1+2x2+3x3P = x_{1} + 2x_{2} + 3x_{3} subject to x1+x2≤5,x2+x3≤2,x1+x2+x3≤6,x1≥0,x2≥0,x3≥0x_{1} + x_{2} \le 5, x_{2} + x_{3} \le 2, x_{1} + x_{2} + x_{3} \le 6, x_{1} \ge 0, x_{2} \ge 0, x_{3} \ge 0. Then, which of the following statements are true?

Multi-select · full marks only for the exact set · Linear Programming

CSIR NET December 2024 · Part C (4.75 Marks)Probability, Statistics & Linear Programming#a-non-negative-sum-bounded-above-by-zero

Consider maximizing the objective function P=x1+x2P = x_{1} + x_{2} subject to x1+x2+2x3≤5,2x1−3x3≥1,x2+x3≤0,x1≥0,x2≥0,x3≥0x_{1} + x_{2} + 2x_{3} \le 5, 2x_{1} - 3x_{3} \ge 1, x_{2} + x_{3} \le 0, x_{1} \ge 0, x_{2} \ge 0, x_{3} \ge 0. Then, which of the following statements are true?

Multi-select · full marks only for the exact set · Linear Programming

CSIR NET June 2024 · Part C (4.75 Marks)Probability, Statistics & Linear Programming#an-unbounded-variable-hidden-among-bounded-ones

Consider the linear programming problem: max{x1+x2+x3x_{1} + x_{2} + x_{3}} subject to constraints x1+x2−x3≤1,x1+x3≤2,0≤x1≤1/2,x2≥0x_{1} + x_{2} - x_{3} \le 1, x_{1} + x_{3} \le 2, 0 \le x_{1} \le 1/2, x_{2} \ge 0, and 0≤x3≤10 \le x_{3} \le 1. Which of the following statements are true?

Multi-select · full marks only for the exact set · Linear Programming

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