Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2018MathematicsLinear Programming

Consider the following two statements I . Any pair of consistent liner equations in two variables must have a unique solution. II . There do not exist two consecutive integers, the sum of whose squares is 365 . Then

Options

  1. Aboth I and II are true
  2. Bboth I and II are false
  3. CI is true and II is false
  4. DI is false and II is true

Correct answer

B. both I and II are false

Step-by-step solution

( I ) Any pair of consistent linear equation in two variables must have a unique solution. This statement is false. Consistent equation may have unique or infinite solution. ( II ) There do not exists two consecutive integers the sum of whose square is 365 . This statement is also false 13 2 + 14 2 = 365

Practice Linear Programming on Quantrex Academy →

More from Linear Programming

The feasible region represented by the constraints: x + 2y 120 ; x + y 60 ; x - 2y 0 ; x 0 and y 0 2026Which of the following is NOT a corner point of the feasible region determined by the constraints: x + 2y 4 ; x + y 2 ; x 0 and y 0 2026The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20) . Let z = px + qy where p, q > 0 . The relation betwe 2026In Linear Programming Problem (LPP), the objective function Z = ax + by has the same maximum value at two corner points. The number of points at which Z_ max occurs is 2026The LPP maximize z = 2x + 5y subject to x + 3y 6 , 2x + 6y 18 , x 0 , y 0 has 2026The difference between the maximum value and the minimum value of the objective function z = 3x + y subject to the constraints 2x + 3y 6 , x + y 1 , x 0 , y 0 is.... 2026An airplane can carry a maximum of 250 passengers. A profit of Rs 1500 is made on each executive class ticket and a profit of Rs 900 is made on each economy class ticket. The airli 2026The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities? 2026 Full Linear Programming list All KVPY PYQs